frontiers and foundations in ecology

FFE

http://people.biology.ufl.edu/osenberg/courses/FFE/2012_Fall/2012Fall/[18/11/2013 14:24:38]

Frontiers and Foundations inEcology

PCB 6049, section 08C51 credit seminar

Fall 2012Organizers: Craig Osenberg and Mike Gil

What: This seminar is designed to facilitate critical discussion of concepts in population and communityecology. We hope to attract ~10-12 graduate students and post-docs with diverse backgrounds in ecologyto discuss foundations and new frontiers in ecology.

Who: Graduate students and post-docs (as well as advanced undergraduates) with backgrounds in ecology.

When and Where: Wednesday evenings (730-930pm), approximately every other week, at my home. [although the time and day be modified after the organizational meeting]

Enrollment: Enrollment is controlled, so you'll need to email Craig Osenberg to have your name added tothe roster.

Format: Each two hour meeting will have three parts: 1) a brief lecture on history/context to establish thecontext for the paper; 2) a lively discussion of the paper; and 3) a lecture clarifying complex issues related tothe next class' paper. For each paper we read and discuss, there will be 2-3 lead discussants.

Responsibilities: The leads will have three roles:

1) At the end of the meeting before the scheduled discussion, the lead(s) will give a short lecture (on theorder of 5-20 minutes, depending on the subject) providing guidance on challenging parts of the paper(PRIOR to the time when other participants will read the paper). This lecture should provide clarification ofexperimental design or lay out some complicated mathematical or statistical issues raised in the paper. Thepurpose is to provide everyone one with some initial understanding to facilitate the reading of the paper andthus make for a more informed and engaged discussion during the next meeting.

2) At the start of the class session when we discuss the paper, the leads will provide a concise (10-15minutes; no more than 20) overview of their historical context for the paper -- they will put the paper incontext and set up why this paper is potentially important, what had been known previously, and how thispaper fits into the discipline (and/or links to other issues in science).

3) The leads will then facilitate a lively discussion of the paper, its limitations, its implications, and futureresearch suggested by the paper (or the insights we derive from the paper). The goal is to guide discussion,not provide a lecture.

Other participants are responsible for reading the paper (in detail), thinking about the paper prior to class,and engaging in a lively and fun exchange of ideas.

Logistics: I will have a LCD projector and a white board at my house. You will need to bring a laptop andany PPT/visuals that you want to use (as well as any special mac connectors you might need for your

FFE


laptop).

Organizational meeting: Monday, August 20th, 4pm, 620 Bartram Hall

Schedule (everyone must read the "frontier" paper in detail. The "foundation" paper is optional.) :

Date Paper Lecturers &Discussion leaders

Preparatorypresentation

Aug 20 Organizational meeting (620Bartram), 4pm

NA NA

Aug 29 Topic: Non-linearities andfragmentation.

Frontier: Blackburn etal. (2011). Ecology92:98-107.Foundation: Debinski &Holt (2000); Ewers andDidham (2006)

Mike Gil & AnyaBrown

Adrian Stier &Lianne Jacobson

Sep 05 no class NA NA

Sep 12 Topic: Metabolic Theory ofEcology

Frontier: Englund et al.(2011) Ecology Letters14:914-921Foundation: West &Brown (2005);O'Connor et al. (2007);O'Connor et al. 2011;Vasseur & McCann(2005)

Adrian Stier & LianneJacobson

Christine Angelini &Julian Resasco

Sep 19 Topic: CommunityPhylogenetics

Frontier: Hultgren &Duffy (2012)Foundation: May &MacArthur (1972);Cavender-Bares et al.(2009)

Christine Angelini &Julian Resasco

Elizabeth Hamman &Ed Camp

FFE


Sep 26 no class (CWO at NCEAS) NA NA

Oct 03 no class (CWO in Moorea) NA NA

Oct 10 no class (CWO in Moorea) NA NA

Oct 17 Topic:

Frontier:Foundation:

Elizabeth Hamman &Ed Camp

Luke Trimmer-Smith& Jennie Lord

Oct 24 Topic:


Luke Trimmer-Smith& Jennie Lord

Megan Seifert & MattPalumbo

Oct 31 no class (Halloween) NA NA

Nov 07 no class (WSN) NA NA

Nov 14 Topic:


Megan Seifert & MattPalumbo

Mollie Brooks &Vinny Cannataro

Nov 21 no class (Thanksgiving) NA NA

Nov 28 Topic:


Mollie Brooks & VinnyCannataro

NA

Dec 05 No formal discussion orpaper. End-of-the-termpotluck; starting at 7pm

Everyone Everyone

last update: 14 September 2012 by CWO

Ecology, 92(1), 2011, pp. 98–107� 2011 by the Ecological Society of America

Nonlinear responses to food availability shape effectsof habitat fragmentation on consumers

HEATHER B. BLACKBURN,1,2,3 N. THOMPSON HOBBS,1,2,4 AND JAMES K. DETLING1,2,3

1Graduate Degree Program in Ecology, Colorado State University, Fort Collins, Colorado 80523-1005 USA2Natural Resource Ecology Laboratory, Colorado State University, Fort Collins, Colorado 80523-1499 USA

3Department of Biology, Colorado State University, Fort Collins, Colorado 80523-1878 USA

Abstract. Fragmentation of landscapes is a pervasive source of environmental change.Although understanding the effects of fragmentation has occupied ecologists for decades,there remain important gaps in our understanding of the way that fragmentation influencesmobile organisms. In particular, there is little tested theory explaining the way thatfragmentation shapes interactions between consumers and resources. We propose a simplemodel that explains why fragmentation may harm consumers even when the total amount ofresources on the landscape they use remains unchanged. In particular, we show thatnonlinearity in the relationship between resource availability and benefits acquired byconsumers from resources can cause a decrease in benefits to consumers when landscapes aresubdivided into isolated parts and when the distribution of consumers in fragments is notmatched to the distribution of resources. We tested predictions of the model using a laboratorysystem of cabbage looper (Trichoplusia ni ) larvae on artificial landscapes. Consistent with themodel’s predictions, survivorship of larvae decreased when landscapes with heterogeneousresources were fragmented into isolated parts. However, average mass of surviving larvae didnot change in response to fragmentation. With basic knowledge of consumer resource usepatterns and landscape structure, our model, supported by our experiment, contributes newunderstanding of the resource-mediated effects of fragmentation on consumers.

Key words: cabbage looper; connectivity; consumer–resource interactions; food distribution; Jensen’sinequality; landscape fragmentation; landscape heterogeneity; nonlinearity; patchiness; resource distribution;Trichoplusia ni.

INTRODUCTION

Fragmentation, the dissection of landscapes into

spatially isolated parts, is a major driver of environ-

mental change worldwide (Fischer and Lindenmayer

2007). Landscape fragmentation customarily refers to a

reduction in connectivity between parts of a landscape

(Zhu et al. 2006) or the conversion of the landscape into

a mosaic of cover types, some of which differ from the

original habitat (Southworth et al. 2004, Gonzalez-

Abraham et al. 2007). The ecological implications of

these changes remain largely unresolved (Bowman et al.

2002, McGarigal and Cushman 2002, Stephens et al.

2003, Ryall and Fahrig 2006).

This absence of consensus in studies of fragmentation

can be explained, at least in part, from ambiguity in

terminology. The term ‘‘fragmentation’’ has been used in

the literature to encompass a broad variety of changes in

landscapes, changes that include reduction in habitat

area, increased isolation of habitat patches, extension of

the length of edges between habitats, and amplified

contrast between habitat and the surrounding matrix

(Wiens 1995, Jaeger 2000, Fahrig 2003, Southworth et

al. 2004, Zhu et al. 2006, Gonzalez-Abraham et al.

2007). These manifold changes in landscapes are often

confounded, for example, when patches of forest remain

standing within land cleared for agriculture (Castellon

and Sieving 2006). In this case, ‘‘fragmented’’ forest

patches are simultaneously smaller and more widely

separated; there is more edge between forested and

agricultural land, and a new type of habitat (plowed

ground) has appeared. Thus, the term ‘‘fragmentation’’

serves as a catchall for four confounded changes in the

landscape. Referring to a collection of changes as if they

were a single one is virtually certain to create ambiguity

in interpreting fragmentation research.

To remedy this problem, several researchers have

recommended using the term fragmentation to imply

loss of connectivity within a landscape apart from

habitat loss or changes in landscape composition,

thereby making a clear distinction between these types

of landscape change (Fahrig 1997, Harrison and Bruna

1999, Ryall and Fahrig 2006). Here, we follow this

recommendation and limit the use of the term fragmen-

tation to mean the loss of connectivity that occurs from

Manuscript received 4 April 2010; accepted 14 April 2010;final version received 1 June 2010. Corresponding Editor: R. J.Marquis.

4 Corresponding Author. Natural Resource Ecology Lab-oratory, 228 Natural and Environmental Sciences Building,Colorado State University, Fort Collins, Colorado 80523-1499 USA. E-mail: [email protected]

98

the breaking apart of a constant amount of habitat (Fig.

1A, B) or to imply that the effects of loss of connectivity

are distinct from the effects of reductions in habitat area

or change in landscape composition (Fig. 1C). This

definition of fragmentation has a functional component

(sensu Kotliar and Wiens 1990); landscape changes may

limit the mobility of some species and not others. For

example, construction of a highway across an otherwise

intact landscape might compress the movements of small

mammals while exerting minor effect on birds (Forman

and Alexander 1998).

Empirical studies of fragmentation and habitat loss

offer a wide array of conclusions (see reviews in Fahrig

2002, Ewers and Didham 2006) and the absence of clear,

predictive theory on effects of fragmentation contributes

to the lack empirical consensus (Ryall and Fahrig 2006).

A large body of theory predicts the population-level

consequences of loss of connectivity among habitat

patches (Roff 1974, Wiens 1976, Cantrell and Cosner

1991, 2001, Tischendorf et al. 2005, Wiegand et al.

2005). However, at the level of the individual, theory of

effects of fragmentation is less well developed. In

particular, there is no theory that predicts how

fragmentation, narrowly defined (Fig. 1), influences the

condition of individuals. These individual-level influenc-

es have consequences for populations and can help to

explain population level responses.

Building on established theory of resource matching

(Morris 2003), there is growing evidence (Galvin et al.

2007, Hobbs et al. 2008, Hobbs and Gordon 2010) that

mobility of consumers across landscapes is critical to

their foraging success, allowing them to exploit hetero-

geneity through selectivity. It follows that limiting

mobility by fragmenting landscapes into isolated parts

may harm consumers, even when the amount and

quality of resources on a landscape remains unchanged.

Yet, theory on how fragmentation influences consumers

is poorly developed. In this paper, we present a simple,

general model that portrays how fragmentation interacts

with the spatial distribution of resources on the

landscape to alter benefits to consumers. We then

challenge the model experimentally by comparing its

predictions with observation of the effects of fragmen-

tation on growth and survival of the cabbage looper

(Trichoplusia ni ) in the laboratory.

A MODEL OF RESOURCE-MEDIATED EFFECTS

OF FRAGMENTATION ON CONSUMERS

Consider a population of mobile consumers occupy-

ing a landscape that is divided into fragments such that

consumers can move freely within fragments but cannot

move among them (Fig. 1A, B, right panels). The

landscape contains a quantity of resources that limits

the growth of the consumer population. For the example

here, we will consider these resources to be food, but

they could be any limiting resource. We assume that the

benefit that accrues to an individual consumer from

exploiting resources is a decelerating function of per

capita resource availability (Fig. 2). If the rate of

increase in benefits to consumers decelerates with

increasing resource availability, as is commonly the case

(Spalinger and Hobbs 1992, Stelzer 2001, Bayliss and

Choquenot 2002, Polishchuk and Vijverberg 2005), then

the benefit function will be monotonically increasing and

asymptotic (Fig. 2). The asymptote represents the

maximum benefits accrued by consumers when resourc-

es are unlimited.

Because we assume that the landscape is subdivided

into fragments without altering the total quantities of

resources or consumers on the landscape, the overall

average resource availability (measured as food per

consumer or food per area) remains unchanged with

fragmentation. However, the resulting average benefit to

consumers in the fragmented environment will be lower

than the average benefit in the intact one whenever the

per capita resource availability differs among fragments

(Fig. 2). The decrease in benefits to consumers on the

fragmented landscape occurs as a result of Jensen’s

inequality (Jensen 1906), which states that the mean of

the output of a convex-up, nonlinear function will

always be less than the function of the mean of the

inputs (Fig. 2). This occurs as the result of the

differences in the slope of the function above and below

the point representing the average resource availability

on the landscape. When resource availability–benefit

functions are convex-up, the set of fragments with lower

FIG. 1. We define fragmentation as the loss of connectivityamong areas of the landscape that occurs from the breakingapart of a constant amount of habitat. This can occur (A) whenan intact landscape is subdivided by barriers to movement, or(B) when connectivity among patches is eliminated without anaccompanying reduction in their area. Our model also hasimplications for the case in which (C) isolated habitat patchesare created by land conversion because the predictions of themodel imply that the effect of fragmentation can add to theeffect of habitat loss.

January 2011 99EFFECTS OF FRAGMENTATION ON CONSUMERS

than average resource availability has a greater effect on

the mean benefit than the set of fragments above the

average resource availability. This causes a reduction in

the mean benefit among fragments in the fragmented

landscape relative to the unfragmented landscape when

resource availability differs among fragments.

A mechanism for effects of fragmentation on consumers

The theory developed in the preceding section predicts

that fragmentation will harm the population of con-

sumers on the landscape whenever the per capita

availability of resources is heterogeneous over space,

that is, when the resources differ among fragments. This

suggests that some of the harmful effects of fragmenta-

tion on consumers are a result of preventing them from

matching their spatial distribution to the distribution of

resources. If the spatial distribution of consumers is

proportional to the spatial distribution of resources, all

consumers experience the same average supply of

resources; we will refer to this situation as a matched

distribution. Graphically, this means that the per capita

resource availabilities for all consumers occupy a single

point on the benefit function (Fig. 2). Therefore, we

predict that when animals and resources are distributed

in a matched manner among newly created fragments,

fragmentation will not affect consumer performance

because there is no heterogeneity in availability of

resources per individual. However, if resources and

consumers are distributed in a way in which demand is

unmatched with availability, Jensens’s inequality com-

pels a reduction in the average benefit acquired by

consumers relative to the unfragmented case. We

emphasize that this reduction must occur despite the

fact that the total amount of resource on the landscape

remains unchanged.

Model predictions

The theory we developed above motivates the

following predictions. The spatial distribution of re-

sources relative to consumers will have no effect on theperformance of mobile consumers in intact landscapes

because consumers are able to match their foraging to

the distribution of resources. However, consumers with

convex-up resource use functions in fragmented, spa-

tially heterogeneous landscapes will show reducedbenefits, on average, relative to consumers in intact

landscapes if consumer distributions are not matched to

resources within fragments. Fragmentation operates by

preventing consumers from matching their distributionto resources. Thus, the effect of fragmentation depends

on resource distributions that are unmatched to

consumer density in habitat fragments.

METHODS

Experimental design

To test these predictions, we conducted two experi-

ments (Fig. 3). In Experiment 1, we created ahomogeneous distribution of consumers across the

landscape and allowed them to exploit foods in two

spatial distributions (homogeneous vs. heterogeneous)

at three levels of fragmentation (none, low, high). Thus,in Experiment 1 we compared matched and unmatched

consumer distributions that occurred as a result of

differences in the spatial distribution of food within

fragments used by the same distribution of consumers.

In Experiment 2, we used a heterogeneous distribution

FIG. 2. Illustration of a decrease in average benefit after fragmentation, without overall change in food availability. An intactlandscape has food availability V and resultant consumer benefit B. After division into two fragments, the food availabilities of thetwo fragments are v 0

1 and v 02, and the average food availability on the landscape is (v 0

1þ v 02)/2¼V0. The benefit after fragmentation is

(b 01 þ b 0

2)/2¼B0. Average food availability is unchanged (V¼V0 ). Gains in the average benefit due to b 02 are smaller than losses to

the average benefit due to b 01; therefore, the average benefit is decreased as a result of nonlinearity in the function and B0 , B.

Division of the landscape into two fragments with food availabilities (v 001 and v 00

2) that have greater variance than v 01 and v 0

2 results inaverage benefit (B00) that is lower than B0.

HEATHER B. BLACKBURN ET AL.100 Ecology, Vol. 92, No. 1

of consumers across the landscape and allowed them to

exploit foods that were either homogeneously or

heterogeneously distributed at three levels of fragmen-

tation (none, low, and high). Thus, in Experiment 2, we

could compare matched and unmatched consumer

distributions that occurred as a result of differences in

the spatial distribution of food within fragments using a

heterogeneous distribution of larvae. We predicted that

a fragmentation effect would occur only when food

distributions were unmatched with consumer distribu-

tions. The two experiments combined allowed us to test

for effects of fragmentation and to test the causal

mechanism by which it affects consumers: nonlinear

averaging of benefits when the distribution of food fails

to match the distribution of consumers.

Experimental procedure

The cabbage looper, Trichoplusia ni (Lepidoptera:

Noctuidae), has been widely used as a model organism

because it is easy to raise in large numbers in the

laboratory and because of its importance as an

agricultural pest (McEwen and Hervey 1960). Larvae

feed on the leaves of a wide range of cultivated plants,

particularly crucifers and cotton (Soo Hoo et al. 1984).

Cabbage looper larvae can be reared at high densities on

artificial diet and reach pupation at two weeks to more

than six weeks from hatch (McEwen and Hervey 1960).

The rate of development is largely dependent on

temperature (Shorey et al. 1962, Toba et al. 1973).

We obtained T. ni eggs before each replication of the

two experiments (Benzon Research, Carlisle, Pennsylva-

nia, USA) and portioned them onto artificial diet

substrate (Southland Products, Lake Village, Arkansas,

USA) in covered 236.6-mL squat Styrofoam cups (30

eggs/cup). Eggs for each experimental replicate were laid

on the day before receipt and hatched 48–96 hours after

receipt. Individuals hatched in the cups and fed on the

substrate until seven days from hatch, when they were

distributed on artificial landscapes. At the time of

distribution, 80% of larvae measured ;1.2 cm.

We constructed artificial landscapes to implement the

experimental design. These landscapes were square,

uncovered acrylic boxes (40.64 3 40.64 cm, 10.16 cm

in height). The construction of the landscapes imposed

the three levels of fragmentation using internal barriers.

Barriers were absent in the no-fragmentation treatment

level. We divided the landscape into four fragments of

equal size for the low-fragmentation level, and into 16

FIG. 3. Experimental design. We examined matched and unmatched consumer distributions in experimental landscapes thatwere fragmented and intact, using a laboratory system of cabbage looper (Trichoplusia ni ) larvae on artificial landscapes. Food perconsumer ratios are similar among all fragments in matched treatments. In unmatched treatments, food per consumer ratios aremore dissimilar than in matched treatments. Each experimental block contains six landscapes, consisting of one class of consumerdistribution (homogeneous in Experiment 1 or heterogeneous in Experiment 2), two classes of food distribution (homogeneous andheterogeneous), and three levels of fragmentation. Levels of fragmentation are labeled as follows: NO FRAG, no fragmentation;LOW FRAG, low fragmentation; HIGH FRAG, high fragmentation. Numbers in boxes are the numbers of larvae or units of foodin each quarter of the landscape.


fragments of equal size for the high-fragmentation level.

Heated barriers topping all internal subdivisions and the

inside of the external wall were used to contain larvae

within fragments (McEwen and Hervey 1960). Heated

barriers consisted of nickel chromium wire covered in

thermally conductive, electrically insulating epoxy.

When electrical current was applied to the wire through

a rheostat at 65 V, the epoxy was warm enough to

prevent the larvae from crossing but caused no apparent

injury to the larvae testing the barrier. Pilot studies

indicated that temperature inside the landscapes was

fairly consistent across treatments (within 28C). Humid-

ity in the room was kept above 60%.

We filled polyethylene tubing with artificial diet; when

the diet cooled, the tubing was cut into uniform lengths

of 1.27 cm and was distributed in the landscapes over

damp paper towels. In all landscapes, there were a total

of 400 introduced T. ni larvae and 88 units of food (one

unit contained 0.465 g food, r2 ¼ 0.003).

To achieve a heterogeneous distribution of food, we

distributed 8, 16, 24, and 40 units of food (sum ¼ 88)

among four quarters of the landscape (Fig. 3).

Homogeneous distributions were achieved by allocating

22 units of food for each quarter. To achieve a

heterogeneous distribution of consumers, we distributed

36, 72, 108, and 184 consumers in each quarter of a

landscape; homogeneous consumer distributions had

100 individuals in each quarter. Food and consumers

were distributed evenly within each quarter of a

landscape at all fragmentation levels. Therefore, the

high-fragmentation treatments (in which the landscapes

were divided into sixteenths) had four-sixteenths of each

level of food availability. For example, one-quarter of

the landscapes with heterogeneous food and heteroge-

neous consumers held eight units of food and 36

consumers; the corresponding quarter of the high-

fragmentation landscape consisted of four fragments,

each with two units of food and nine consumers.

Food was present in the landscapes when the larvae

were introduced, and was reapplied 48 h and 76 h after

larval introduction; 42 h after the last food addition, we

collected, weighed, and counted surviving larvae. The

average wet mass of survivors and the proportion of

survivors served as the two response variables. Both

experiments were repeated five times for a total of 10

runs.

Analysis

To estimate the shape of the relationship between

consumer benefits and resource availability, we used

data from the fragmented treatments of Experiments 1

and 2, each of which provided four different levels of per

capita resource availability (0.08, 0.16, 0.24, and 0.4

units of food per consumer in Experiment 1; 0.12, 0.20,

0.3, and 0.61 units of food per consumer in Experiment

2). We fit a quadratic model to the resource–benefit

curves to test for convexity; if the quadratic term was

significant, the form of the function was convex.

We predicted that there would be no influence of

resource matching when landscapes were intact because,

in this case, consumers were free to adjust their

distributions to the distribution of resources (Fig. 4A).

We predicted that there would be no effect of increasing

levels of fragmentation on the matched landscape (Fig.

4B). However, we predicted that both levels of

fragmentation on the unmatched landscape would show

reduced benefits relative to those observed on the intact

landscapes or on the fragmented levels of the matched

landscape (Fig. 4C). We also compared the low with the

high level of fragmentation on the unmatched land-

scape. Because these two levels contained the same ratio

of consumers to resources, we predicted no effect of

increasing fragmentation on consumer benefits between

these levels (Fig. 4D).

Comparisons were made in SAS using a mixed-model

ANOVA (proc MIXED) for linearity tests, a general-

ized linear mixed-model ANOVA (proc GLIMMIX) for

survivorship data, and proc MIXED for the average

mass of survivors. For average mass data, we used the

mixed-model ANOVA rather than a general linear

model (proc GLM) because there were missing data.

Differences among temporal replications of the exper-

iments necessitated comparisons within runs (using

replicate number as an indicator variable) rather than

pooling data across runs. All analyses were done using

SAS version 9.1 (SAS Institute 2004). We assumed

treatment differences to be statistically significant at P �0.05.

FIG. 4. Form of the hypothesized results of the experiment.We expect no effect of resource matching (A) when landscapesare intact because mobile consumers can adjust their densitiesto match resources. (B) In the case in which consumerdistributions are matched to resources, we expect no effect ofincreasing fragmentation. (C) We expect that the low- and high-fragmented treatments will show lower benefits than the intacttreatment in the unmatched landscape or any of the treatmentsin the matched landscape. (D) However, we expect nodifference between the low- and high-fragmentation levels inthe unmatched landscape because the ratio of resources toindividuals is the same in these treatments.


RESULTS

Resource benefit functions

We observed convex-up relationships between food

availability and survival in both experiments (Experi-

ment 1, F1,92¼ 7.80, P¼ 0.0063; Experiment 2, F1, 201¼73.75, P , 0.0001; Fig. 5A). We also observed a convex-

up relationship between food availability and average

mass of survivors in Experiment 1, when consumers

were homogenously distributed across heterogeneous

food (F1,92 ¼ 20.20, P , 0.0001; Fig. 5B), but not in

Experiment 2, when consumers were heterogeneously

distributed across homogeneous food (F1, 199¼ 1.31, P¼0.2542; Fig. 5B). Therefore, the only response variable

not expected to show fragmentation effects predicted by

our model was the average mass of larvae in Experiment

2, because in this case there was not a convex-up

relationship for resource benefits relative to availability.

Survival

Observations of survivorship were consistent with the

predictions of the model (Figs. 4, 6A, B). We observed

no effect of resource or consumer distribution in the

absence of fragmentation in either experiment, although

some of these effects approached significance (Experi-

ment 1, t20¼�1.87, P¼ 0.0763; Experiment 2, t20¼ 1.94,

P¼0.0660). In both experiments, fragmentation reduced

survival in the unmatched treatments (Experiment 1,

unfragmented vs. low fragmentation, t20 ¼ 3.19, P ¼0.0046; Experiment 2, unfragmented vs. low fragmenta-

tion, t20 ¼ 2.95, P ¼ 0.0079), but not in the matched

treatments (Experiment 1, unfragmented vs. low frag-

mentation, t20 ¼ �0.41, P ¼ 0.6849; Experiment 2,

unfragmented vs. low fragmentation, t20 ¼ 0.27, P ¼0.7895). Similarly, we observed effects of matching when

the landscape was fragmented (Experiment 1, high-

fragmentation treatment, t20 ¼ 2.98, P ¼ 0.0075;

Experiment 2, low fragmentation, t20 ¼ 4.61, P ,

0.0020; Experiment 2, high fragmentation, t20¼ 4.27, P

¼ 0.0004). However, the effect of matching was not

significant in the low-fragmentation treatment of Ex-

periment 1 (t20¼ 1.74, P¼ 0.0979). Thus, fragmentation

influenced survival only when resources and consumer

density were unmatched.

Body mass

Observations of average survivor mass were partially

consistent with model predictions (Figs. 4, 6C, D). In

Experiment 1, we observed no effect of consumer–

resource distribution in the absence of fragmentation

(t20¼1.44, P¼0.1643). As expected, when resources and

consumers were unmatched, average body mass of

survivors in the low-fragmentation treatment was less

than the average mass of those in the unfragmented

treatment; however, this difference was not statistically

significant (unfragmented vs. low fragmentation, t20 ¼1.41, P ¼ 0.1740). Fragmentation effects were not

observed in the high-fragmentation treatment relative

to the low treatment (low vs. high fragmentation, t20 ¼0.95, P¼ 0.3545). In the matched treatments, no effects

of fragmentation were evident (unfragmented vs. low

fragmentation, t20 ¼ 0.51, P ¼ 0.6161; low vs. high

fragmentation, t20 ¼ �1.17, P ¼ 0.2576). In summary,

Predictions A, B, and D (Fig. 4) were fully supported,

and Prediction C (Fig. 4) was not strongly supported in

Experiment 1.

Because the average mass of survivors was not found

to be significantly nonlinear in Experiment 2, we did not

expect to detect all predicted differences. In fact, the

only statistically significant effect was an unexpected

difference between the unfragmented and low-fragmen-

tation treatments in the matched landscapes (t20¼ 2.17,

P ¼ 0.0425; Fig. 6D). Other comparisons between

FIG. 5. Observed forms of the relationships between (A)survivorship and (B) average survivor mass and food availabil-ity for T. ni larvae in Experiments 1 and 2. Food is expressed asunits per T. ni larva, with one unit defined as 1.27 cm ofpolyethylene tubing filled with artificial diet. Error bars show6SE. The quadratic term was significant in both sets ofsurvivorship data (Experiment 1, F1,92 ¼ 7.80 P ¼ 0.0063;Experiment 2, F1, 201 ¼ 73.75, P , 0.0001; Fig. 5A) and inhomogeneous T. ni average mass data (F1,92 ¼ 20.20, P ,0.0001; Fig. 5B), indicating convexity. The quadratic term wasnot significant in Experiment 2 average mass data (F1, 199¼1.31,P ¼ 0.2542; Fig. 5B). These relationships were evaluated usingdata from fragmented landscapes with unmatched distributionsof larvae and food in both experiments.


treatments were nonsignificant, and ranged from P ¼0.2019 to P ¼ 0.5771.

DISCUSSION

We developed a new, general model to explain how

fragmentation affects interactions between individual

consumers and resources. Our model exploits a simple

observation: when resource–benefit functions are non-

linear and convex-up, dividing heterogeneous resources

among fragments will diminish the average benefit to

consumers relative to the case in which landscapes are

intact. The mechanism mediating harmful effects of

fragmentation on consumers is also simple: in fragment-

ed environments, individuals are unable to match their

distribution to the distribution of resources on the

landscape. Thus, our model predicts that the effects of

fragmentation on consumers depend in a truly funda-

mental way on the spatial distribution of consumers and

resources and the shape of the relationship that governs

the benefits that accrue from exploiting those resources.

Empirical observations were largely consistent with

the predictions of the model. Fragmentation diminished

consumer survival, but only when the distribution of

consumers was not matched to the distribution of

resources within fragments. Our experiment did not

provide support for predictions on the effect of

fragmentation on consumer body mass. There are two

potential reasons for this result. First, response of body

mass to food availability was not strongly nonlinear. We

observed only weak nonlinearity in Experiment 1 and

did not observe significant nonlinearity in Experiment 2.

Thus, the model did not predict strong effects of

fragmentation on body mass, and variance in the

average mass data was high. Any weak effects may

FIG. 6. Consumer benefit across three levels of fragmentation in matched and unmatched treatments. Three fragmentationlevels (none, low, and high) have 0, 4, or 16 fragments. Statistically significant differences (P , 0.05) between fragmentation levelswithin matched or unmatched treatments are marked with an asterisk (*), and statistically significant differences (P , 0.05)between matched and unmatched treatments within a fragmentation level are marked with a dagger (�). Observations of effects offragmentation and resource matching on survivorship (panels A and B) agreed closely with the predictions of theory. Observationsof average body mass (panels C and D) were moderately consistent with model predictions. Panels (A) and (C) are results fromExperiment 1 (homogeneous larval distribution); panels (B) and (D) are results from Experiment 2 (heterogeneous larvaldistribution). Error bars indicate 6SE, which overlap in the graphs even when data are significantly different (P , 0.05); this is dueto the inclusion of cross-replicate variance in the SEM. Replicate effects were large in our data; the statistical analysis comparedtreatments without incorporating among-replicate variability, but the error bars reflect the large variance among replicates andtherefore do not accurately reflect statistical significance.


have been masked by the high variance in mass

responses among individuals. Second, there may have

been a confounding effect of the survival response on the

body mass response. Reduced survival of individuals in

the low- and high-fragmentation treatments probably

increased the per capita availability of resources for

surviving individuals in those treatments, diminishing

the potential effect of fragmentation on mass.

Consistent with the predictions of the model, frag-

mentation did not affect consumers when resource–

benefit functions were not strongly nonlinear. The

observation of different forms of the benefit–food

function for different types of consumer responses is

not unusual. Arrivillaga and Barrera (2004) found a

convex-up effect of food availability on survival and

resistance to starvation in a mosquito, but a linear effect

on per capita mass of survivors. Similarly, Atlantic

Puffins showed a linear response of body mass to food

availability and a curvilinear response of several other

measures of growth (Oyan and Anker-Nilssen 1996).

As with all manipulative experiments, ours imposed

artificial conditions, and consequently, we need to be

clear about its relevance to natural systems. We designed

the experiment to challenge a theoretical prediction, and

it is the theory, buttressed by experiment, that has broad

application rather than the experiment itself. The

situations in which our theoretical results are relevant

are illustrated in Fig. 1. The theoretical prediction will

apply when landscapes are fragmented by barriers to

consumer movement that do not appreciably affect the

area of habitat (Fig. 1A), for example, when intact

landscapes are dissected by construction of roads or

fences, a human action that is truly ubiquitous

throughout the world (Forman and Alexander 1998,

Serrano et al. 2002, Galvin et al. 2007, Hobbs et al.

2008). The prediction will apply when connections

among habitat patches are severed without any change

in patch area (Fig. 1B). Our model has implications for

the case in which shrinking habitat patches simulta-

neously become disconnected (Fig. 1C), such as when

habitat is converted to new habitat types. In this case,

our model suggests that the effect of loss of connectivity

may add to the effect of habitat loss.

Our work offers a necessary first step in understanding

how fragmentation may affect consumers over the short

term. Our experiment did not allow for a multi-

generation, population response, which in temporally

stable environments would presumably allow consumer

populations to come into equilibrium with resources

(Fretwell and Lucas 1970, Schwinning and Rosenzweig

1990). Thus, under such conditions, we would expect that

per capita resource availability would become increas-

ingly similar among fragments over time and we would

expect the effect of fragmentation to fade as equilibrium

was reached. However, there is a growing view that such

equilibrial behavior may be the exception in nature

rather than the rule (reviewed by Wiens 1977, Ellis and

Swift 1988, Illius and O’Connor 1999, Galvin et al. 2007,

Owen Smith 2010). In systems where resources vary

dramatically over time and are not correlated over space,

density-independent forces will prevent the equilibration

of consumers and resources, thereby preserving frag-

mentation effect over time. However, the possibility of

long term-equilibrium does not contradict the funda-

mental prediction of our model and the empirical

support we obtained for it: when resource–benefit

functions are convex-up and consumer distributions are

not matched with resources, fragmentation will lead to a

reduction in the average benefit obtained by consumers

from resources. Our model makes clear, testable predic-

tions and our experiment suggests that testing these

predictions in other systems is promising.

Negative effects of fragmentation on consumers

within a heterogeneous landscape do not imply that

spatial heterogeneity in resources is bad for consumers.

Indeed, spatial heterogeneity has often been shown to be

beneficial for consumer populations on intact landscapes

(Senft et al. 1987, Mysterud et al. 2001, Choquenot and

Ruscoe 2003, Said and Servanty 2005, Wang et al.

2006). Rather, it is the loss of access to spatially

heterogeneous resources that negatively impacts popu-

lations. Although several workers have hypothesized

such impacts (Mysterud et al. 2001, Boone and Hobbs

2004, Fryxell et al. 2005) and recent observational

studies provide empirical evidence supporting them

(Wang et al. 2006, Hebblewhite et al. 2008), there has

been relatively little theoretically motivated experimen-

tal work showing evidence for loss of benefits to

consumers in response to fragmentation in heteroge-

neous environments. Searle et al. (2010) showed

experimentally that fragmentation can interfere with

the ability of mobile herbivores to track pulses of high-

quality resources that occur when phenology of plant

patches varies asynchronously over space and time. Our

results reinforce these findings by showing that frag-

mentation harms consumers by preventing them from

matching their spatial distribution to the spatial

distribution of resources.

It should not be surprising that isolation of individ-

uals in suboptimum patches harms their performance.

The unique contribution of this paper is to show that

isolation caused by fragmentation prevents patches that

are of high value from fully compensating for those that

are of low value. As a result, fragmented landscapes

offer diminished benefits to consumers, even when the

total amount and quality of resources on those

landscapes remains unchanged. This result occurs

because of nonlinearities in resource use functions.

Temporally and spatially nonlinear relationships

abound in natural systems. However, nonlinearity in

key relationships and the possible role of Jensen’s

inequality in ecological processes have not been widely

considered. Davis et al. (2002) recognized the signifi-

cance of Jensen’s inequality for numerical responses and

consumer population sizes. Consistent with Jensen’s

inequality, a convex-up numerical response decreased


long-term population growth rates when variance in the

independent variable was high. Other examples include

the effects of spatial variance of biodiversity on average

plant productivity (Benedetti-Cecchi 2005) and the

effects of environmental variation on optimal life history

strategy (Pasztor et al. 2000). Ruel and Ayres (1999)

cited several examples of the implications of Jensen’s

inequality for processes in physiological ecology, such as

the effects of variability in environmental conditions on

metabolic processes. Here, we show that nonlinearity in

the relationship between resource availability and

benefit to consumers has fundamental implications for

the effects of landscape fragmentation on consumers.

ACKNOWLEDGMENTS

Support for this work was provided by National ScienceFoundation Grants DEB-0444711 and DEB-0119618. Thework reported here was supported in part by the NationalScience Foundation while Hobbs was serving as a rotatingProgram Director in the Division of Environmental Biology.Any opinions, findings, conclusions, or recommendations arethose of the authors and do not necessarily reflect the views ofthe National Science Foundation.

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Review

A Survey and Overview of Habitat Fragmentation

Experiments

DIANE M. DEBINSKI* AND ROBERT D. HOLTt *Department of Animal Ecology, 124 Science II, Iowa State University, Ames, IA 5001 1, U.S.A., email [email protected] tNatural History Museum and Center for Biodiversity Research, Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045, U.S.A., email [email protected]

Abstract: Habitat destruction and fragmentation are the root causes of many conservation problems. We conducted a literature survey and canvassed the ecological community to identify experimental studies of terrestrial habitat fragmentation and to determine whether consistent themes were emerging from these studies. Our survey revealed 20 fragmentation experiments worldwide. Most studies focused on effects of fragmentation on species richness or on the abundance(s) ofparticular species. Other important themes were the effect offragmentation in interspecific interactions, the role of corridors and landscape connectivity in individual movements and species richness, and the influences of edge effects on ecosystem services. Our comparisons showed a remarkable lack of consistency in results across studies, especially with regard to species richness and abundance relative to fragment size. Experiments with arthropods showed the best fit with theoretical expectations of greater species richness on larger fragments. Highly mobile taxa such as birds and mammals, early-successional plant species, long-lived species, and generalist predators did not respond in the "expected" manner. Reasons for these discrepancies included edge effects, competitive release in the habitat

fragments, and the spati.al scale of the experiments. One of the more consistently supported hypotheses was that movement and species richness are positively affected by corridors and connectivity, respectively. Tran- sient effects dominated many systems;,for example, crowding of individuals on fragments commonly was observed afterfragmentation, followed by a relaxation toward lower abundance in subsequentyears. The three long-term studies (?14 years) revealed strong patterns that would have been missed in short-term investigations. Our results emphasize the wide range of species-specific responses to fragmentation, the need for eluci- dation of behavioral mechanisms affecting these responses, and the potentialfor changing responses to fragmentation over time.

Sondeo y Revisi6n de Experimentos de Fragmentaci6n de Habitat

Resumen: La destrucci6n y la fragmentaci6n del habitat son las causas fundamentales de muchos proble- mas de conservaci6n. Realizamos un sondeo de la literatura y examinamnos de cerca la comunidad ecol6gica para identificar estudios experimentales sobre la fragmentaci6n de habitats terrestres y para determinar si emergen temas homogeneos de estos estudios. Nitestro sondeo revela que existen 20 estudios experimentales de fragmentaci6n en el ambito mundial. La mayorfa de los estudios enfocan en los efectos de la fragment- aci6n sobre la riqueza de especies, o en la(s) abundancia(s) de ciertas especies en particular. Otros temas im- portantes fueron el efecto de la fragmentaci6n sobre las interacciones interespecfficas, el papel de los corre- doresy la conectividad delpaisaje en los movimientos individualesy la riqueza de especiesy la influencia de los efectos de bordes sobre los servicios proporcionados por el ecosistema. Nuestras comparaciones muestran una carenci.a notable de homogeneidad en los resultados de los estudios, especialmente en lo referente a la riqueza y a la abundancia de especies, y su relaci6n con el tanmafno de losfragmentos. Experimentos con ar- tr6podos demostraron que existia un mejor ajuste entre los valores te6ricos esperados y los valores reales de aumentos en la riqueza de especies en fragmentos grandes. Los taxones altamente m6viles (por ejemplo, aves y maminferos), las especies de plantas en sucesi6n temprana, las especies de gran longevidad y los depre- dadores generalistas no respondieron de la manera "esperada". Entre las razones que explican estas diver-

Paper submnitted February 23, 1998; revised manuiscript accepted September 22, 1999.

342

Conservation Biology, Pages 342-355

Volume 14, No. 2, April 2000

Debiniski & Holt Survey of Habitat Fragmentation Experiments 343

gencias se incluyen los efectos de bordes, la liberaci6n competitiva en losfragmentos de bhibitaty la escala es- pacial del experimento. Una de las hip6tesis mds aceptadas establece que el movimiento y la riqueza de especies son afectadas positivamente por los corredores y la conectividad, respectivamente. Algiunos efectos pasajeros dominaron nuchos sistemas; por ejemplo, el bacinamniento de individuos en fraggmentos se ob- serv6 a men udo despu6s de la fragmentacio6n, seguido de un dismrinuci6n de la abuindancia en los anos pos- teriores. Los tres estudios a largo plazo (= 14 afos) revelaron fuertes patrones que hubieran sido ignorados en investigaciones a corto plazo. Nuestros resultados senalan el amplio rango de respuestas especie-especffi- cas, la necesidad de elucidar mecanismos de comportamiento que afectan las respuestas a lafragmentaci6n y elpotencial de respuestas cambiantes a lafragmentaci6n a to largo del tiempo.

Introduction

Given the importance of habitat fragmentation in conservation, it is not surprising that there exists a burgeoning literature based on observational studies of fragmented landscapes (e.g., Wilcove et al. 1986; Quinn & Harrison 1987; Gibbs & Faaborg 1990; Blake 1991; Mc- Coy & Mushinsky 1994) and a substantial theoretical literature on the population and community effects of fragmentation (e.g., Fahrig & Paloheimo 1988; Doak et al. 1992; Nee & May 1992; Adler & Nuernberger 1994; Til- man et al. 1994; With & Crist 1995). In contrast, fewer researchers have deliberately created an experimentally fragmented landscape and then assessed the ecological consequences of the fragmentation (Margules 1996). It is easy to see why. Manipulation of entire landscapes tends to be large in scale, laborious, and costly. Yet the difficulty and expense of large-scale spatial experiments makes it particularly important that whatever data they generate be used to address general issues in ecology. In principle, fragmentation experiments could provide a rich testing ground for theories and methodologies dealing with spatiotemporal dynamics (Tilman & Kareiva 1997). Moreover, because of the logistical difficulty of such experiments, synthesis across studies may help provide guidelines and cautionary lessons for the design of future landscape experiments.

We present the results from a survey of studies conducted worldwide in experimentally fragmented habitats. By our definition, an experiment involves a delib- erate manipulation of the landscape, usually with an eye toward assessing a particular hypothesis. In many descriptive fragmentation studies, researchers cannot control attributes such as patch size, degree of replication, site initiation, and position on the landscape because they are investigating the effects of landscape manipulation (e.g., clearcutting in logging or plowing in agriculture) conducted by others. Thus, we excluded such studies from our review. We concentrated on terrestrial systems because of the major differences in the dynamics of colonization between terrestrial and aquatic systems.

Methods

We conducted a literature survey of the major ecological journals (Amnerican Naturalist, Biological Conservation, BioScience, Canadian Journal of Zoology, Conservation Biology, Ecography, Ecological Applications, Ecological Modeling, Ecological Monographs, Ecology, Evolution- ary Ecology, Forest Science, Heredity, Journal of Animal Ecology, Journal of Biogeography, Journal of Mammal- ogy, Landscape Ecology, Nature, Oecologia, Oikos, Theo- retical Population Biology, and Trends in Ecology and Evolution) since 1984 using the keywordfragmnentation. We also canvassed the ecological communiity using the In- ternet (CONSBIO listserver) and made informal contact with many colleagues. After compiling a list of candidate studies, we sent out a survey to the authors of the studies which asked questions about experimental design, focal organisms of study, hypotheses being tested, study length, and practical issues such as how the itntegrity of the experiment was maintained. We summnarized the results in the form of a vote count tally of the number of times the hypothesis was supported. We believe that a more formal meta-analysis (e.g., Gurevitch & Hedges 1993) of these experiments is not yet warranted because of the relatively small number of studies and because of the heterogeneity among study designs, spatial and temporal scales, and methodological protocols.

Results

Replication and Temporal Span

Based on our criteria for fragmentation experiments, we identified 20 experimental studies; 6 were conducted in forests and 14 were conducted in grasslands or old fields. The experimental studies clustered into evaluations of five broad focal issues: species ricmness, the interplay of connectivity versus isolation, individual species behavior, demography, and genetics. They tested six major hypotheses: (1) species richness increases with area, (2) species abundance or density increases with area, (3) interspe-

Conservation Biology Voltume 14, No. 2, April 2000

344 Survey of Habitat Fragmentation Experiments Debiaski & Holt

cific interactions are modified by fragmentation, (4) edge effects influence ecosystem services, (5) corridors enhance movement between fragments, and (6) connectivity between fragments increases species richness. For ease in following the discussion of the experiments included in our review (compiled in Table 1), we include within the text a number in brackets corresponding to the experiment number in Table 1.

The number of fragmentation experiments and the length of time for which they have been conducted have increased substantially in recent years (Table 1). A decade ago there were just 3 studies extant; at present 14 studies are ongoing. The geographic distribution of the 20 studies was primarily North America and Europe. The spatial scale (Fig. 1) ranged from grassland patches of <1 M2 (Quinn & Robinson 1987 [2]) to Amazonian rainforest fragments of 1000 ha (Bierregaard et al. 1992 [1]). Repli- cation (Fig. 1) varied from 1 to 160 per category of patch size. Patch sizes were chosen relative to the questions being addressed and the organism(s) of study. Generally, as the landscape scale increased, there were fewer replicates at larger fragment sizes. There was a threshold of decrease in degree of replication at roughly 0.2 ha; above this size, the number of replicates was usually <10. This weakens the statistical power of conclusions about the effects of large fragment size. The temporal spans for these studies ranged from 1 to 19 years, with a mean of just over 6 years (Table 1). Little experimental data exist on the long-term consequences of habitat fragmentation. Three experiments have been in progress for over a decade, and eight have been in progress for 5-10 years. The remaining projects were nin for 3 years or less.

These experiments contain taxonomic and habitat biases. Only a few studies explicitly focused on plant population and community dynamics (Table 2). Among animals, there was a heavy emphasis on songbirds and small mammnals. A number of studies focused closely on particular species, but few analyzed in detail the effects of fragmentation on pairwise or multispecies interactions (Kareiva 1987 [17] is a notable exception). Several of these projects examined responses across a variety of taxonomic groups simultaneously (BierTegaard et al. 1992 [1]; Margules 1992 [4]; Robinson et al. 1992 [3]; Baur & Erhardt 1995 [19]; D. Huggard, personal comnmunication [6]). There also were habitat biases in that most studies were conducted in either forest, grassland, or old fields. This may reflect the economics and mechanics of creating and maintaining experimental patches, such as using mowing in old fields or grassland and relying upon for- estry practices or clearcutting in forested biomes.

Predictions that Work

Numerous studies reported results that supported theoretical expectations; but many revealed effects con-

trary to initial theoretical expectations. Here we summa- rize results relative to the hypotheses tested (Table 2).

SPECIES RICHNESS

Following from the theory of island biogeography (Mac- Arthur & Wilson 1967), species richness in habitat fragments is expected to be a function of island size and degree of isolation. Smaller, more isolated fragments are expected to retain fewer species than larger, less isolated habitat tracts (Diamond 1975; Wilson & Willis 1975; Terborg 1976). A major focus of these studies has been the relationship among habitat size, species richness, and individual species' abundances.

Initial theoretical expectations regarding increased species richness with increasing area were supported in only 6 out of 14 examples (not including 3 taxa that exhibited changing patterns over time). In cases in which the hypotheses were upheld, the effects were often striking. For example, even in a 100-ha tropical forest fragment, a beetle community was recognizably different in composition and lower in species richness than those on control sites in continuous forest (Laurance & Bierregaard 1996 [1]). Collinge (1995 [8]) found that insect species diversity was lowest in the smallest fragments and highest in the largest fragments. In a comparison of several types of fragmented landscapes, Collinge and Forman (1998 [8]) found that large-bodied, initially rare species were concentrated in the remaining larger core habitats, as opposed to areas where a central portion of habitat was removed. T. Crist (personal communication [11]) found a similar decrease in arthropod species richness with increasing fragmentation of an old field and determined that the pattern was driven primarily by the loss of rare species. In an old-field study [31 in Kansas, larger patches had higher species richness of butterflies, but small mammals and plants tended to show less consistent differences in species richness among patch sizes (Robinson et al. 1992; Holt et al. 1995a, 1995b). Baur and Erhardt (1995 [19]) found that, after 2 years, isolated grassland fragments were less frequently occupied by various gastropod species than were control patches, leading to lower species richness in the fragments. This set of studies provides a reasonable match with theoretical expectations.

Comparable to the effect of area on species richness, one might expect to observe area effects on genetic diversity within species; smaller fragments should have lower effective population sizes, higher rates of genetic drift, and fewer immigrants (Jaenike 1973). In the experimental studies in our survey, the effect of fragmentation on genetic variation was studied infrequently. Baur and Erhardt (1995 [19]), however, found reduced fecundity and genetic diversity among herbaceous plant species in isolated patches. Interactions between plants and pollinators also exhibited modifications, with potential

Conservation Biology


Debiiiski & Hoft SitGrveY of Habitazt Frameonetationl Experimenlts 345

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ramifications for genetic diversity. For example, butterflies visited flowers less frequently in isolated patches, thus leading to reduced fecundity and possibly lower plant genetic diversity.

DENSITY AND ABUNDANCE OF SPECIES

The negative effects of fragmentation on species richness arise in part because of lower-level effects on population abundance and so should be evident even in those species that do not become extinct. The simplest a priori expectation is that, for habitat specialists restricted to the fragments and unable to use the matrix habitat, fragmentation reduces density. The mechanism for this reduced density could be increased demographic stochasticity or the disruption of metapopulation dynamics. The alternative hypothesis, however, is that species move from the matrix habitat to the remaining habitat patches after a disturbance, such that "crowding" ensues in the patches (Whitcomb et al. 1981; Fahrig & Palo- heimo 1988; Fahrig 1991). Our summary refers to density and abundance because some authors presented their results as density, whereas others presented results as abundance or trapping success per unit time.

Species abundance decreased with fragmentation in 6 out of 13 examples. For instance, Margules and Milkovits (1994 [4]) found that the abundance of amphipods (fam- ily Talltridae) decreased markedly in remnant forest patches relative to controls and that this effect was more dramatic on smaller remnants than on larger ones. In the Kansas project [3], the cotton rat (Sigmodon hispidus) and the white-footed mouse (Peromyscus leucopus) were differentially more abundant in larger patches (Foster & Gaines 1991; Robinson et al. 1992; Schweiger et al. 1999). H. Norowi (personal communication [16]) similarly found that weevil and parasitoid densities were consistently greater in contiguous habitat patches than in fragmented patches of equivalent area.

The density of tree seedlings declined significantly from continuous forest to forest fragments in the Amazonian Biological Dynamics Project [1] (Benitez-Malvido 1998). These results demonstrate the effect of fragmentation on key life-history stages in trees. In the Kansas study [3], which involves old-field succession, colonization by woody plant species is proceeding more rapidly in larger patches (Holt et al. 1995b; Yao et al. 1999). Thus, changes at the level of individual species can often be dis- cerned, even when coarser, whole-community effects of fragmentation are not apparent (Robinson et al. 1992).

INTERSPECIFIC INTERACTIONS AND ECOLOGICAL PROCESSES

Spatial dynamics can have profound effects on individual behavior (e.g., Hanski et al. 1995; Redpath 1995) and interspecific interactions such as predation (Aizen & Feinsinger 1994; Tilman & Kareiva 1997), so it is sensi-


Volume 14, No. 2, April 200(0

Debiniski & Holt Sutrvey of Habitat Fragmentation Experiments 347

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ble to expect that the effects of habitat fragmentation may be mediated or exacerbated through shifts in such interactions. Kareiva (1987 [17]) demonstrated this effect by performing experiments on a predator-prey interaction between an aphid and a coccinellid predator in monocultures of Solidago. The fragmented treatment had more frequent aphid outbreaks, apparently because fragmentation disrupted the ability of the predator to aggregate rapidly at localized clusters of the aphid in early phases of an outbreak. H. Norowi (personal communication [16]) found that the rate of weevil parasitism varied with parasitoid species and the spatial scale of analysis. W. Powell (personal communication [16]) similarly found that carabid beetle assemblages in experimentally fragmented agroecosystems revealed significant spatial and temporal effects arising from altered predator-prey interactions within grassland patches.

EDGE EFFECTS

Another rule derived from the theory of island biogeography is that reserves should minimize the edge-to-area ratio to maximize the effective core area of the reserve. Increasing the amount of edge can make a reserve more vulnerable to invasion by exotic species and subject it to more extreme abiotic influences such as wind and tem-

perature (Saunders et al. 1991). Physical changes associated with creating an edge can have profound effects on ecological processes. For instance, R. Bierregaard (personal communication [1]) documented that edge effects penetrate 300 m or more into a tropical forest remnant, and Didham (1997 [1]) showed that isolated patches have leaf-litter insect fauna substantially different than that of continuous forest.

In principle, the altered abiotic conditions associated with fragmentation can also influence ecosystem services such as nutrient cycling (Saunders et al. 1991). Three projects have addressed ecosystem consequences of fragmentation with varying results. Two forest projects found effects on nutrient cycling (Bierregaard et al. 1992 [1]; Klenner & Huggard 1997 [6]), whereas the Kansas old- field study [3] did not (Robinson et al. 1992). In the Bio- logical Dynamics Project [1] and other forest studies, the contrast in abiotic conditions between fragments (e.g., tall forest) and the surrounding matrix (e.g., pasture) is dramatic. In other systems, there are less dramatic differences between the matrix and fragments, so one niight expect ecosystem effects to be less noticeable.

Because fragmentation inevitably leads to the juxtapo- sition of qualitatively different habitats, flows of materials and individuals between them can indirectly exert profound influences on within-fragment communities

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348 Survey of Habitat Fragmentationa Experiments Debiniski CJ Holt

(Polis et al. 1997). In the Kansas study [3], for instance, generalist arthropod predators such as web-builcling spiders are more abundant in the fragments, particularly along edges, where they can profit from the aerial "drift" of insects from the surrounding productive, mown inter- stitial turf (T. Jackson et al., unpublished data). Smaller forest fragments similarly had greater conmmunity invasibility for successional tree species in the Biological Dynamics P'roject [1] (Benitez-Malvido 1998). Laurence et al. (1998) found that recruitment rates were markedly higher near forest edges and highest witliin 1(00 m of forest edges.

CORRIDORS AND MOVEMENT/CONNECTIVITY

Fragmentation creates barriers to dispersal (e.g., Mader 1984), and behavioral responses to fragmentation may underlie many observed effects at higher organizational levels such as populations and communities. Even narrow breaks (50-l100 m) in continuous forest habitat produce substantial barriers to the movement of many species of birds and some insects. Of the five fragmentation experiments that directly tested the effects of corridors, all but one found tlhat corridors enhanced movement for some of the species examined (Collinge 1995 [8]; Haddad 1997 [10]; Schmiegelow et al. 1997 [9]; Wolff et al. 1997 114]). Collinge (1995 [8]) found that corridors slightly decreased the rate of species loss and that tlhis effect was greatest in medium-sized fragments. In another experiment (Haddad 1999; Haddad & Baum 1999 [10]), three open-habitat butterfly species (Jutononia coenia, Phoe- bis sennae, and Eupto/eta claudia) reached higher densities in patches connected by corridors than in isolated patches. But the abundance of a fourth, generalist species, Pap/lio troiluts, was insensitive to forest corridors.

Related to corridors is the effect of landscape pattern on movement, as expressed for instance in rates of colonization and dispersal. H. Norowi (personal comtmunica- tion [16]) found that the presence of a hedgerow on one side of an experimental patch affected the pattern of colonization of newly created habitat patches by one species of weevil (Gj'mnetron pascutorium). Kruess and Tscharntke (1994 [12]) found substantial distance effects on colonization by parasitoids in a clover field but only minor effects on colonization by herbivores. This led to release from parasitism on the isolated patches, analogous to the effects of fragmentation in the predator-prey interaction studied by Kareiva (1987 [17]). Parasitoid species that failed to establish tended to be those with low and variable populations. These patterns have persisted over several years (T. Tscharntke, personal communication).

There is a growing literature on small mammals focusing on the effects of experimental fragmentation on dispersal and home-range size. Diffendorfer et al. (1995a,b 13]) showed that fragmentation reduced the movement rates and altered spatial patterning of distances moved in several small-mammal species. Wolff et al. (1997 [14])

found that fragmentation reduced vole (Microtus canica a- duw) movements considerably. Ims et al. (1993 [15]) found decreased home-range size and more home range overlap in small mammals on smaller patches. Harper et al. (1993 [18]) found that the shape of habitat patches af fected the number of voles that dispersed when population densities were low but not when densities were h-igh. Furthermore, the shape of the habitat patches affected the space-use behavior of resident voles. Bowers et al. (1995 [13]) exanmined the space-use behavior of voles (Microtus pennsylvanicus) and found that adult females at edges tended to have larger home ranges, body sizes, residence times, and reproductive rates than individuals in the interior of a patch. Bowers et al. (1995 [13]) suggest that tlhis edge effect could account for the inverse patch-size effects on abundance for small mammals noted in several studies (e.g., Foster & Gaines 1991 [3]). Finally, Ims et al. (1993 [15]) stuLdied the effects of fragmentation on aggressive and docile strains of voles (Microtus oecono,nus) and found that different sex and age groups are likely to exhibit different spatial responses to fragmentation.

Predictions that Do Not Work

SPECIES RICHNESS

In a number of experiments, species richness either increased with or was unaffected by fragmentation. In most cases, these effects could be attributed to an increase in early-successional species, transient species, or edge effects (community "spillover" from surrounding habitats; Holt 1997). For instance, Schmiegelow et al. (1997 [9]) examined passerine data gathered before fragmentation and during the 2 years thereafter. Despite effects on turnover rates, they found no significant change in species richness as a result of harvesting, except in the 1-ha connected fragment treatment, where the number of species actually increased 2 years after isolation. This increase reflected transient species rather than species breeding in the patches, suggesting that buffer strips were being used as corridors.

In the Biological Dynamics Project [1], frog diversity increased after fragmentation because of unpredicted immigration by generalist species that flourished in the matrix of pasture surrounding the forest fragments (Lau- rance & Bierregaard 1996). The Wog Wog Study [4] in southeast Australia (Margules 1996; Davies & Margules 1998; Margules et al. 1998) revealed that different taxa had highly disparate responses to fragmentation, incluLd- ing a lack of response. Plant communities in several experiments have exhibited species-richness patterns contrary to the expectations of island biogeography models. Quinn and Robinson (1987 [2]) found increased flowering-plant and insect species richness with increasing habitat subdivision. They hypothesized that these patterns might reflect the effect of fragmentation on competition

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Volulmie 14, No. 2, April 2000

Debinski & Holt Survey of Habitat Fragmentation Experinments 349

Table 2. A vote-count summary of fragmentation-experiment results, separated by hypothesis tested.*

Hypothesis Project name Taxonomic group supported Reference or contact

Species richness increases with area 1. Biological dynamics birds yes Bierregaard et al. 1992;

Stouffer & Bierregaard 1995 beetles no Laurance & Bierregaard 1996 frogs no Laurance & Bierregaard 1996 primates yes Bierregaard et al. 1992

2. California grassland plants no Quinn & Robinson 1987; Robinson et al. 1995

insects no Quinn & Robinson 1987; Robinson et al. 1995

3. Kansas fragmentation study small mammals no Holt et al. 1995a, 1995b; Robinson et al. 1992

plants no Robinson et al. 1992; Holt et al. 1995a, 1995b

butterflies yes Holt et al. 1995a 4. Wog Wog study millipedes no, years 1-7; Margules 1992

yes, years 7- present

frogs yes, years 0-5; Margules 1996 no, years 5- present

beetles no Davies & Margules 1998 8. Colorado grassland insects yes Collinge 1995; Collinge &

Forman 1998 9. Boreal mixed-wood dynamics project birds no, treatments and Schmiegelow et al. 1997

controls yes, isolated

fragments 11. Miami University fragmentation project insects yes Crist & Golden, personal

communication 19. Swiss Jura mountains gastropods yes Baur & Erhardt 1995

Species abundance or density increases with area 1. Biological dynamics trees (woody) yes Benitez-Malvido 1998

trees (seedling no Benitez-Malvido 1998 recruitment)

beetles yes Bierregaard et al. 1992 birds no (short term); Bierregaard & Lovejoy 1989

yes later 3. Kansas fragmentation study trees yes Holt et al. 1995b; Yao et al.

1999 small mammals mixed Foster & Gaines 1991;

Schweiger et al. 1999 4. Wog Wog study amphipod density yes Margules & Milkovits 1994

scorpions no Margules & Millkovits 1994 8. Colorado grassland insects no Collinge & Forman 1998 9. Boreal mixed-wood dynamics project birds no, treatments and Schmiegelow et al. 1997

controls yes, isolated Schmiegelow et al. 1997

fragments 13. Blandy farm fragmentation study small mammals no Bowers & Matter 1997;

Dooley & Bowers 1998 14. Vole behavior and fragmentation small mammals no Wolff et al. 1997 15. Evensted research station small mammals no Ims et al. 1993 16. Long Ashton weevils and yes W. Powell, personal

parasitoids communication 17. Predator-prey interactions and fragmentation insects yes Kareiva 1987 18. Ohio old-field project small mammals no Barrett et al. 1995;

Collins & Barrett 1997 Interspecific interactions are modified by fragmentation

12. German fragmentationl study parasitoids yes (less parasitism Kruess & Tscharntke 1994 on far patches)

conti'nued

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350 Survey of Habitat Fragmentationl Experiments Debinski & Hoit

Table 2. (continued)

Taxonomnic Hypothiesis Project name group supported Reference or contact

16. Long Ashton beetles yes W. Powell, personal communication

17. Predator-prey interactions and fragmentation insects yes Kareiva 1987 Edge effects influence ecosystem services

1. Biological dynamics nutrient cycling yes Bierregaard et al. 1992 6. Kamloops project nutrient cycling yes Klenner & Huggard 1997 3. Kansas fragmentation study nutrient pools no Robinson et al. 1992

Corridors enhance movement between fragments 8. Colorado grassland insects yes Collinge 1995 9. Boreal mixed-wood dynamics project birds no for Neotropical Schmiegelow et al. 1997

migrants yes for transient

species 10. Savannah river site corridor project butterflies yes for some; Haddad 1997

no for others small mammals no Danielson & Hubbard 2000

14. Vole behavior and fragmentation small mammals yes Wolff et al. 1997 Connectivity between fragments increases species

richness 8. Colorado grassland insects yes Collinge 1995 9. Boreal mixed-wood dynamics project birds no for Neotropical Schmiegelow et al. 1997

migrants yes for transient Schmiegelow et al. 1997

species * Where multiple taxa. uwere examined in a single study, there are multiple entries for the same experimental site.

among plants. In small patches, for instance, short-stat- ured plant species could persist in edges and priority effects could permit local dominance not possible in a single large patch. Robinson et al. (1995 [2]) also examined invasibility by a native California poppy (Eschscholzia californica) in these same plots and found the species- rich plots more invasible. Contributing factors included a positive effect of small-mammal disturbance and a negative effect of Bromus diadrus coverage.

Invasion by species from the surrounding matrix could lead to a temporary increase in species richness within patches, at least if extinction rates are slow. If smaller fragments experience higher disturbance rates, this could shift competitive regimes such that in some situations species richness is enhanced. During the first 8 years of the Kansas [3] old-field experiment, patch size had little effect on successional replacement of major plant frinctional groups. Rather, the main influence of patch size was on the spatial autocorrelation of herbaceous community structure and on local persistence of some rare or clonal plant species (Robinson et al. 1992; Holt et al. 1995a, 1995b; Heisler 1998). In contrast, patch size had substantial effects on the colonization and growth rate of woody species (Yao et al. 1999).

DENSITY AND ABUNDANCE OF SPECIES

In several fragmentation experiments, population densities increased on the smaller fragments, perhaps be-

cause of the crowding effects of fragmentation. This was especially prevalent in small-mammal studies but was also observed in birds and insects. Barrett et al. (1995 [18]) found vole densities to be greater in a more fragmented landscape. In a review of patch-size effects on small-mammal communities, Bowers and Matter (1997 [13]) noted that inverse relations between density and patch size are frequently observed, particularly at the smaller patch sizes used in experimental landscape studies.

In some cases, the unexpected effect of fragmentation on density seems to reflect the ability of a focal species to utilize both the matrix habitat and the fragment. For instance, Foster and Gaines (1991 [3]) observed a high density of deer mice on small fragments and substantial numbers in the intervening matrix. They interpreted this pattern as simply a reflection of habitat generalization, but more recent work (Schweiger et al. 1999) suggests that a combination of habitat generalization and competitive release on small patches may explain this density relationship.

There appears to be a complex relationship between patch fragmentation and social structure that may underlie some of the inverse-density relationships. For instance, Collins and Barrett (1997 [18]) found that fragmented patches of grassland support greater densities of female voles than unfragmented sites. Aars et al. (1995 [20]) found differences in sex ratios among some litters of root voles and speculated that resource conditions (as affected by fragmentation) could lead to such biases.


Voltume 14, No. 2, April 2000

Debinski &Holt Slrvey ofHabitat Fragmentation Experiments 351

Dooley and Bowers (1998 [13]) found weak fragment- size effects on the density and recruitment of Microtus pennsylvanicus in a grassland fragmentation experiment. They postulate that higher recruitment rates on fragmented patches result from diminished social costs and enhanced food resources on fragments. Andreassen et al. (1998 [15]) also found complex behavioral responses of voles to habitat fragmentation. Wolff et al. (1997 [14]) found that habitat loss did not decrease adult survival, reproductive rate, juvenile recruitment, or population size in the gray-tailed vole (Microtus cani- caudus); surviving voles simply moved into remaining fragments. An influx of unrelated females into habitat fragments, however, resulted in decreased juvenile recruitment in those fragments.

Crowding effects have also been observed after fragmentation in bird and insect communities. Schmiegelow et al. (1997 [9]) noted that this crowding effect disap- peared for birds after the second year of their study. Margules and Milkovits (1994 [4]) found that two milli- pede species experienced population explosions after treatment in both the remnants and the intervening cleared area, but they returned to pretreatment levels after 7 years. Collinge and Forman (1998 [8]) found crowding effects on fragments in an insect community but did not collect data long enough to test for a temporal effect.

CORRIDORS AND MOVEMENT/CONNECTIVITY

A few studies showed movement patterns contrary to what are generally expected to be the effects of habitat fragmentation, patch shape, and corridors. Barrett et al. (1995 [18]) showed that patch shape does not markedly affect dispersal or demographic variables of the meadow vole (Microtuspennsylvanicus). Andreassen et al. (1998 [15]) found that the rate of interfragment movements of small mammals actually increases with habitat fragmentation. Even more surprisingly, Danielson and Hubbard (2000 [10]) found that the presence of corridors reduces the probability that old-field mice (Peromrnscus poliono- tus) will leave a patch in a forest fragment. In this same landscape Haddad (1997 [10]) found one butterfly species that does not respond to corridors. Schmiegelow et al. (1997 [9]) showed that Neotropical migrants declined in all fragmented areas, regardless of connectivity. As one might imagine, the use of corridors and the effect of fragmentation on movement patterns seems to be highly species-specific. These results suggest a need for ftrther study of the potentially complex interactions between fragmentation and individual behavior.

Logistical Problems and Considerations

We concentrated on the fruits of experimentation in the study of habitat fragmentation. But our survey did reveal

recurrent problems with such experiments, which future workers attempting to conduct fragmentation experiments need to be aware of and consider in designing their experiments. These considerations are important in that they define the likely scope of the applicability of results from fragmentation experiments.

Common problems in orchestrating fragmentation experiments mentioned to us by a number of investigators in our survey included the costs and difficulty of ade- quate replication of large patches, the struggle to maintain patches, and the problems of identification of speci- mens in many species-rich taxa. Patches carved out of preexisting vegetation are likely to be heterogeneous in many respects; careftil thought must be given to overlay- ing fragmentation treatments on preexisting heteroge- nous landscapes, especially with a low degree of replication. In cases in which patch sizes are large, costs and other problems with establishing the largest patches often result in low replication. In any system operating within a fixed area, there is a necessary trade-off among interpatch distance, patch size, and replication. Because of such constraints, out of the full domain of potential landscape configurations, experiments are likely to focus on only a modest swath of parameter space (Holt & Bowers 1999).

Maintenance of the experimental area also can be ex- pensive, time-consuming, and uncertain. Collaboration between government agencies and/or private landown- ers and researchers is often key to establishing and maintaining a landscape for experimental purposes. In highly productive habitat such as tropical rainforest, the rate of secondary succession can be so high that it is difficult to keep patches "isolated" (e.g., Bierregaard et al. 1992). If the surrounding sea of vegetation is not completely inhospitable, this could skew results in experiments testing for the effects of isolation.

In small experimental fragments, the effects of sampling can be problematic, especially if multiple investigators are collecting data on several taxonomnic groups. For example, to sample small patches without trampling the vegetation, G. Robinson (personal communication [2]) had to build portable scaffolds over the patches. Fi- nally, taxonomic problems were noted by many investigators working on plants and insects (Holt et al. 1995a [3]; S. Collinge, personal communication [8]; C. Mar- gules, personal communication [4]). This mundane problem is important if species-rich groups tend to have stronger responses to fragmentation.

Discussion

There was a considerable lack of consistency in results across taxa and across experiments. The two most frequently tested hypotheses, that species richness increases with fragment area and that species abundance

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352 Suivey of Habitat Fragmentation Experiments Debinski & Holt

or density increase with fragment area, showed entirely mixed results. Some of these discrepancies may be explained by differential relaxation times (Brown 1971) and rates of responses to fragmentation by different taxa. Most of the studies that fit initial theoretical expectations about the effects of fragmentation upon species richness involved arthropod assemblages. The species in these assemblages were typically small in body size (relative to the fragment sizes) and short in generation length (relative to the length of the fragmentation experiments). These assemblages might be expected to show responses over time scales commensurate with the time frame of typical field experiments. One of the more consistently supported hypotheses was that corridors supported connectivity between fragments. In four out of five cases, the presence of corridors enhanced movement for at least some of the species examined, and in two out of two examples the presence of corridors increased species richness in fragments.

Taxonomic groups that did not respond in the expected manner displayed a range of responses to fragmentation. Some examples include highly mobile taxa wlhose population-level responses may integrate over spatial domains much larger than that of a single fragment. At short time scales, behavioral responses by mobile organisms can generate idiosyncratic patterns. Crowding of individuals was commnonly observed after fragmentation, followed by a relaxation in subsequent years. Other groups that responded differently than expected include long-lived species unlikely to show dramatic population responses in short- term experiments and taxa with generalized habitat requirements. Predicting fragmentation effects depends on a basic knowledge of the range of habitats that different taxa can utilize and on the factors limiting and regulating population abundance in -unfragmented landscapes. The pleth- ora of contradictory results for small manunals in fragmentation experiments seems to be caused by several factors, including habitat generalization, disparate responses among species to edges and corridors, and social interactions that may be modified by landscape changes.

Many of the "contrary" results we report may reflect the relatively short time span of the experiments. A number of studies used patches that lasted only one season or an annual cycle to examine changes in the behavior or demography of particular species. The advantage of this approach is that it permits a clearer evaluation of potential mechanisms underlying landscape effects. A disadvantage is that such experiments cannot evaluate the multiplicity of indirect feedbacks that occur in anthropogenically disturbed landscapes. Long-term experiments are vital because they reveal processes that are obscured at shorter time scales. The three long-term studies [1, 3, 4] each revealed strong phenomena that would have been missed in short-term investigations.

Some key findings of experimental habitat fragmentation studies might be difficult to achieve in purely obser-

vational studies, reflecting in part the value of good experimental controls and properly randomized designs. We do not imply that experimental fragmentation projects are more rigorous than observational studies. Experimental fragmentation studies often suffer from the intellectual costs of focusing on small spatial and temporal scales and the use of species that may not serve as good models for the effects of fragmentation on species of conservation concern. Although observational studies pay a price by lacking "controls," they nonetheless provide more realism with respect to landscape scale and species of concern. The value of having real controls, however, should not be underestimated; controls proved vital in interpreting results in many of these experiments (e.g., Robinson et al. 1995 [2]; Collins & Barrett 1997 [18]; Davies & Margules 1998 [4]; Lau- rance et al. 1998 [1]; Danielson & Hubbard 2000 [10]).

Future fragmentation studies should focus on understanding the mechanisms behind observed community- and population-level patterns. For example, a critical issue is how fragmentation affects dispersal and movement. Similarly, a better understanding of species interactions, such as plant-pollinator interactions or competition in fragmented landscapes, is essential. Analysis of the matrix habitat may be crucial for understanding the dynamics of remnant fragments. The most important determinant of which species are retained in isolated patches appears to be the interaction of patches with the surrounding habitat matrix (Bierregaard & Stouffer 1997 [1]; Tocher et al. 1997 [1]). There is a growing recognition that connection among habitats that differ in productivity and structure is often a crucial determinant of community dynamics (Holt 1996; Polis et al. 1997), and fragmentation experiments provide a natural forum for analyzing such dynamics. Finally, more analysis of how fragmentation influences genetic variation for both neutral alleles and traits related to fitness would be particularly valuable.

Choosing an appropriate landscape scale for the taxonomic group(s) of interest can have major implications for the findings of fragmentation studies. Communities are composed of species that experience the world on a vast range of spatial scales (Kareiva 1990; Holt 1993). In all the studies we reviewed, there were some mobile and/or large-bodied organisms for which the patches were small pieces of a fine-grained environment much smaller than a home range. Usually, however, some species will be present that experience the patches in a coarse-grained manner. An important challenge is to map out an intellectual protocol for applying these fine- scale experimental studies to scales that are more directly pertinent to conservation problems.

The studies described in our review provide a first step in understanding the effects of fragmentation. Our results, however, emphasize the wide range of species- specific responses and the potential for changing results

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Debiuiski & Holt Survey of Habitat Fragmentation E.Aperiments 353

over time. Fragmentation effects cascade through the community, modifying interspecific interactions, providing predator or competitive release, altering social relationships and movements of individuals, exacerbating edge effects, modifying nutrient flows, and potentially even affecting the genetic composition of local populations. Perhaps it is not surprising then that fragmentation shows inconsistent effects across the experimental studies of fragmentation to date.

Acknowledgments

We thank all those investigators who provided insights into their experiences with fragmentation studies. This manuscript benefited from the comments of G. Belovsky and two anonymous reviewers. The research was supported by grant 93-08065 from the Long-Term Research in Environmental Biology program of the National Sci- ence Foundation. This is journal paper J-17802 of the Iowa Agriculture and Home Economics Experiment Sta- tion, Ames, Iowa (project 3377).

Note added in proof: Since this paper was written, we have become aware of an additional experimental study of fragmentation involving microinvertebrate species assemblages on moss patches on boulders. Gonzalez et al. showed strong effects of fragmentation on species diversity and population size (A. Gonzalez, J. H. Lawton, F. S. Gilbert, T. M. Blackburn, and I. Evans-Freke. 1998. Meta- population dynamics, abundance, and distribution in a mricroecosystem. Science 281:2045-2047.).

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Conservation Biology Voltime 14, No. 2, April 2000

Confounding factors in the detection of species

responses to habitat fragmentation

Robert M. Ewers1,2,3* and Raphael K. Didham1

1 School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

(E-mail : [email protected])2 Smithsonian Tropical Research Institute, Apartado 0843-03092, Balboa, Panama, Republic of Panama3 Current address : Institute of Zoology, Zoological Society of London, Regents Park, London NW1 4RY, UK, and Department of Zoology,

Cambridge University, Downing Street, Cambridge CB2 3EJ, UK

(Received 9 November 2004; revised and accepted 19 September 2005)

ABSTRACT

Habitat loss has pervasive and disruptive impacts on biodiversity in habitat remnants. The magnitude of theecological impacts of habitat loss can be exacerbated by the spatial arrangement – or fragmentation – ofremaining habitat. Fragmentation per se is a landscape-level phenomenon in which species that survive inhabitat remnants are confronted with a modified environment of reduced area, increased isolation and novelecological boundaries. The implications of this for individual organisms are many and varied, because specieswith differing life history strategies are differentially affected by habitat fragmentation. Here, we review theextensive literature on species responses to habitat fragmentation, and detail the numerous ways in whichconfounding factors have either masked the detection, or prevented the manifestation, of predicted fragmentationeffects.

Large numbers of empirical studies continue to document changes in species richness with decreasing habitatarea, with positive, negative and no relationships regularly reported. The debate surrounding such widelycontrasting results is beginning to be resolved by findings that the expected positive species-area relationshipcan be masked by matrix-derived spatial subsidies of resources to fragment-dwelling species and by the invasionof matrix-dwelling species into habitat edges. Significant advances have been made recently in our understandingof how species interactions are altered at habitat edges as a result of these changes. Interestingly, changes inbiotic and abiotic parameters at edges also make ecological processes more variable than in habitat interiors.Individuals are more likely to encounter habitat edges in fragments with convoluted shapes, leading toincreased turnover and variability in population size than in fragments that are compact in shape. Habitatisolation in both space and time disrupts species distribution patterns, with consequent effects on metapopulationdynamics and the genetic structure of fragment-dwelling populations. Again, the matrix habitat is a strongdeterminant of fragmentation effects within remnants because of its role in regulating dispersal and dispersal-related mortality, the provision of spatial subsidies and the potential mediation of edge-related microclimaticgradients.

We show that confounding factors can mask many fragmentation effects. For instance, there are multiple waysin which species traits like trophic level, dispersal ability and degree of habitat specialisation influence species-level responses. The temporal scale of investigation may have a strong influence on the results of a study, withshort-term crowding effects eventually giving way to long-term extinction debts. Moreover, many fragmentationeffects like changes in genetic, morphological or behavioural traits of species require time to appear. By contrast,synergistic interactions of fragmentation with climate change, human-altered disturbance regimes, speciesinteractions and other drivers of population decline may magnify the impacts of fragmentation. To conclude, weemphasise that anthropogenic fragmentation is a recent phenomenon in evolutionary time and suggest that thefinal, long-term impacts of habitat fragmentation may not yet have shown themselves.

* Address for correspondence : Department of Zoology, Cambridge University, Downing Street, Cambridge CB2 3EJ, UK(Tel : (+44) 1223 336675; Fax : (+44) 1223 336676; E-mail : [email protected]).

Biol. Rev. (2006), 81, pp. 117–142. f 2005 Cambridge Philosophical Society 117doi:10.1017/S1464793105006949 Printed in the United Kingdom

Key words : area effects, edge effects, habitat fragmentation, habitat loss, invertebrate, isolation, matrix, shapeindex, synergies, time lags.

CONTENTS

I. Introduction ................................................................................................................................................. 118(1) Causes of habitat fragmentation ......................................................................................................... 118(2) Approaches to the study of fragmentation ........................................................................................ 119(3) Structure of this review ........................................................................................................................ 119

II. Habitat area ................................................................................................................................................. 119(1) Species-area relationships : predicting extinction rates from habitat loss ...................................... 120(2) Landscape and extinction thresholds ................................................................................................. 122(3) The population consequences of small habitat area ........................................................................ 122

III. Edge effects ................................................................................................................................................... 123(1) Community composition at habitat boundaries ............................................................................... 123(2) Edges as ecological traps ...................................................................................................................... 123(3) Edges alter species interactions ........................................................................................................... 124(4) Variability and hyperdynamism at edges .......................................................................................... 124

IV. Shape complexity ........................................................................................................................................ 124V. Isolation ........................................................................................................................................................ 125VI. Matrix effects ................................................................................................................................................ 125

(1) Can matrix quality mitigate fragmentation effects? ......................................................................... 126(2) Matrix and dispersal ............................................................................................................................. 126(3) Matrix and edge effects ........................................................................................................................ 127

VII. Confounding factors in the detection of fragmentation impacts .......................................................... 127(1) Trait-mediated differences in species responses to fragmentation ................................................. 127(2) Time lags in the manifestation of fragmentation effects .................................................................. 129

(a) Time lags in population responses to fragmentation ................................................................. 129(b) Biogeographic factors controlling fragmentation responses ...................................................... 130(c) Altered selection pressures and developmental instability ......................................................... 131

(3) Synergies magnify the impacts of fragmentation .............................................................................. 131(a) Fragmentation and pollination ...................................................................................................... 131(b) Fragmentation and disease ............................................................................................................. 132(c) Fragmentation and climate change .............................................................................................. 132(d ) Fragmentation and human-modified disturbance regimes ........................................................ 133

VIII. Implications for fragmentation research .................................................................................................. 133IX. Conclusions .................................................................................................................................................. 134X. Acknowledgements ...................................................................................................................................... 134XI. References .................................................................................................................................................... 134

I. INTRODUCTION

The magnitude of habitat fragmentation reflects the per-vasive influence of humans on the environment at all scalesfrom local (Lord & Norton, 1990) through to regional(Ranta et al., 1998), national (Heilman et al., 2002) andglobal (Riitters et al., 2000). While the direct effects of habitatloss per se are typically considered to pose the greatest currentthreat to biodiversity (Tilman et al., 1994; Dobson,Bradshaw & Baker, 1997), the size and spatial arrangementof remnant fragments is recognised to have a major effecton population dynamics and species persistence (Barbosa &Marquet, 2002; Hanski & Gaggiotti, 2004), with impactsthat are ‘more insidious ’ than habitat loss alone (With,1997). As a consequence, habitat fragmentation has becomea central issue in conservation biology (Meffe & Carroll,1997).

(1) Causes of habitat fragmentation

Fragmentation, as an expression of the size and spatialarrangement of habitat patches, is not a purely anthro-pogenic process. Naturally fragmented habitats are widelydistributed around the world at a range of scales (Watson,2002). For example, alpine environments that occur assmall habitat islands separated by a matrix of sub-alpineand lowland environments (Burkey, 1995), river systemsthat are isolated from each other by terrestrial and coastalmarine habitats (Fagan, 2002), and rock outcrops in alpinegrasslands (Leisnham & Jamieson, 2002) are all naturallyfragmented systems. However, the most important andlargest-scale cause of changes in the degree of fragmenta-tion is anthropogenic habitat modification, with nearlyall fragmentation indices being strongly correlated withthe proportion of habitat loss in the landscape (Fahrig,2003).

118 Robert M. Ewers and Raphael K. Didham

Fragmentation is the process whereby habitat loss resultsin the division of large, continuous habitats into smaller,isolated habitat fragments (Ranta et al., 1998; Franklin,Noon & George, 2002). As a landscape becomes progress-ively fragmented, a greater number of fragments of varyingshapes and sizes are created (Baskent & Jordan, 1995) andthese are scattered through a matrix of modified habitat(Opdam & Wiens, 2002). The conditions in the matrixsurrounding a habitat fragment determine the extent towhich exterior environmental conditions penetrate a frag-ment (Baskent & Jordan, 1995). The portions of a fragmentthat are altered by external conditions are termed edgehabitat, while unaffected portions are called core habitat.The proportion of a fragment that is core habitat is acomplex function of fragment size and shape and the natureof the surrounding landscape matrix (Laurance & Yensen,1991; Baskent & Jordan, 1995).

Fragmentation is not just a patch-level phenomenon,although this is the scale at which many of its biologicalimpacts are observed. In fact, fragmentation only occurswhen habitat loss reaches a point at which habitat continuityis broken (Opdam & Wiens, 2002) and this is quite clearlya landscape-level attribute that describes the size and spatialarrangement of remaining habitat (Baskent & Jordan, 1995).The degree of habitat connectivity is partly determined bythe physical continuity of habitat, but it is also a function ofthe degree to which a landscape facilitates or impedes themovement of individuals between fragments (Langlois et al.,2001). As a consequence, connectivity is influenced bothby the physical location of habitat fragments as well as bycharacteristics of the surrounding habitat matrix (Baskent &Jordan, 1995).

(2 ) Approaches to the study of fragmentation

The study of fragmentation has its roots in classical islandbiogeography theory (IBT, MacArthur & Wilson, 1967),which emphasised area and isolation effects to the exclusionof landscape structure (Didham, 1997; Laurance &Cochrane, 2001). Theoretical developments in spatialtheory (Forman, 1997) and macroecology (Gaston &Blackburn, 2000) saw IBT superseded in the 1980s bylandscape ecology, with a new focus on the spatial arrange-ment of fragments and the structure of the matrix (Laurance& Cochrane, 2001; Haila, 2002). However, the basic tenetsof IBT remain relevant to fragmentation, and recent theoryhas overcome some of the shortcomings of the classicalmodel by incorporating landscape ecological principles(Hanski & Gyllenburg, 1997; Polis, Anderson & Holt, 1997).

In parallel with these changing paradigms underpinninghabitat fragmentation studies, the last decade has beenwitness to an explosion in the amount and types of researchbeing conducted. Complex, community-level studies andcross-species comparisons are now more frequently con-ducted, reflecting the ease with which multivariate statisticscan handle large data sets. Experimental approaches, ledby the Biological Dynamics of Forest Fragments Projectin the Brazilian Amazon (Bierregaard et al., 1992; Lauranceet al., 2002), have become more common (Debinski & Holt,2000; McGarigal & Cushman, 2002), and the scale of

investigation now ranges from microcosms (Burkey, 1997;Gonzalez & Chaneton, 2002) to the entire globe (Riitterset al., 2000). Advances in associated disciplines such asmolecular ecology now allow the investigation of historical(Fisher et al., 2001) and sub-lethal (O’Ryan et al., 1998)genetic impacts, while the application of newly developed‘tools of the trade, ’ such as stable isotope markers, meansthat the dispersal of even very small animals can be trackedthrough time and space (Caudill, 2003).

(3 ) Structure of this review

Several recent reviews of the fragmentation literature havesynthesised the ecological impacts of fragmentation at thelandscape scale (Fahrig, 2003; Tscharntke & Brandl, 2004),or have focused on a single aspect of habitat fragmentationsuch as the creation of habitat boundaries (Ries et al., 2004).Nevertheless, fragmentation effects in the empirical litera-ture are still commonly grouped under five categories thattogether describe the spatial attributes of individual patchesin fragmented landscapes : (1) fragment area, (2) edge effects,(3) fragment shape, (4) fragment isolation, and (5) matrixstructure. In this review, we examine species and com-munity responses to these five, patch-scale categories.However, one of the most significant advances in therecent fragmentation literature has been the recognitionthat the effects of processes within these five categoriescan be either masked or enhanced by confounding factorsthat operate over large temporal and spatial scales. Wediscuss how the susceptibility of species to habitat fragmen-tation varies depending on their particular life history strat-egies (summarised in Figs 1 & 2). It is also now apparent thatthe effects of fragmentation can take many decades to beexpressed and that synergies between fragmentation andother extrinsic drivers of population decline can magnify thedetrimental impacts of fragmentation on species. We stressthe importance of taking a mechanistic approach to thestudy of fragmentation and conclude by highlighting gapsin the current literature and providing some directions forfuture research.

II. HABITAT AREA

A direct reduction in habitat area is thought to be one ofthe major causes of species extinctions (Tilman et al., 1994)and typically has a strong, negative effect on biodiversity(Fig. 1A; Fahrig, 2003). Reduced habitat area in a land-scape leads to a decrease in the size of fragments and anincrease in fragment isolation (Andren, 1994), with conse-quent reductions in population size and colonisation ratesthat directly increase the risk of local extinctions (Bowers &Matter, 1997; Bender, Contreras & Fahrig, 1998; Hanski,1998; Crooks et al., 2001; Hames et al., 2001; Schoerederet al., 2004). Furthermore, in a recent review, Fahrig (2003)demonstrated the impact of habitat loss on several measuresof community structure including species richness, thestrength of species interactions and trophic chain length infood webs, as well as on several measures of population

Detection of species responses to habitat fragmentation 119

structure, including population distribution and abundance,dispersal, reproductive output, foraging success and geneticdiversity. However, fragmentation of the remaining habitathas important, additional impacts on biodiversity that areindependent of habitat loss (Tscharntke et al., 2002a ; Fahrig,2003). In the context of our review of habitat fragmentation,we explicitly consider habitat loss because habitat area hasbeen consistently used to predict changes in species diversityunder the IBT framework. Furthermore, species and popu-lation responses are commonly non-linear below thresholdvalues of habitat loss, and these responses are moderatedby the size and spatial arrangement of the remaining habitat(With & King, 2001).

(1 ) Species-area relationships: predictingextinction rates from habitat loss

By explicitly considering habitat fragments as islands, manyresearchers have followed the IBT approach and con-structed species-area (SA) curves to describe rates of speciesloss with decreasing fragment area (Fig. 1A; Pimm &Askins, 1995; Pimm et al., 1995; Brooks, Pimm & Collar,1997; Brooks et al., 2002; but see Anderson & Wait, 2001;Cook et al., 2002). The approach itself is relatively straight-forward, with the calculation of a simple species lossfunction St+1/St=(At+1/At)

z (Pimm et al., 1995) ; where Stis species richness before habitat loss, St+1 is species rich-ness following habitat loss, At is the original amount ofhabitat area, At+1 is habitat area following habitat lossand z is the slope of the SA curve, which is assumed toaverage a typical value such as 0.25 for the relationship be-tween habitat area and species richness (Pimm & Askins,1995; Brooks et al., 1997, 2002). As the species loss functionuses the proportion of habitat lost to estimate the proportionof species expected to become extinct, the analysis isassumed to be independent of absolute differences inhabitat extent, biogeographic scale, or the size of the totalspecies pool.

Despite the simplicity of the approach, there are anumber of important caveats on interpreting observed versuspredicted extinction rates following habitat loss, most ofwhich stem from the fact that raw SA predictions almostalways exceed observed extinction rates (Pimm & Askins,1995; Pimm et al., 1995; Brooks et al., 1997, 2002;

Cowlishaw, 1999). First and foremost is whether habitat‘ islands ’ are analogous to real islands in an IBT context(Anderson & Wait, 2001; Cook et al., 2002; Haila, 2002).For a comparable distance of isolation, populations withinfragments are much more likely to be ‘rescued’ by dispersalof individuals between adjacent fragments than are popu-lations within islands (Brown & Kodric-Brown, 1977;Forare & Solbreck, 1997; Menendez & Thomas, 2000). As aresult, some species that occur in small fragments maybe able to persist by combining resources from a numberof fragments (Tscharntke et al., 2002a), so that the area of anindividual habitat fragment does not necessarily representthe actual extent of resources available to the speciesoccupying it. The net outcome will be fewer observedextinctions than predicted by the SA model. Of course,fragment isolation is a species-specific variable, so thatstrong positive slopes for SA curves may be found for sometaxa, but not others within the same set of habitat fragments(Fig. 2A–E). For instance, highly dispersive ground beetleshave shallower SA curves than do less dispersive groups,because increased dispersal rates can reduce extinctionrates in small fragments (Fig. 2B; de Vries, den Boer & vanDijk, 1996).

Second, it is thought that inclusion of both endemic andnon-endemic species in SA predictions at a regional scalecan cause an overestimate of the number of predictedextinctions, because populations of non-endemic speciescan be ‘rescued’ by immigration from extra-regionalpopulations in areas not subject to habitat loss (Pimm &Askins, 1995; Pimm et al., 1995; Brooks et al., 1997, 2002).This problem has been countered by taking the moreconservative approach of considering only endemic species,globally restricted to the region in which habitat loss rateswere estimated, in SA models (Pimm et al., 1995; Brookset al., 2002).

Third, habitat loss is non-random (Seabloom, Dobson &Stoms, 2002), and in some situations the spatial arrange-ment of the remaining fragments can have at least as largean impact on total extinction rate as the absolute amountof habitat lost. Moreover, within-fragment extinctionsreflect changes in a-diversity (the total number of species ata given site), but ignore the fact that high levels of b-diversityamong fragments (a measure of species turnover amongsites) may augment total species richness in the landscape

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Fig. 1. Widely-held generalisations about community responses to habitat fragmentation. Predictions of how species richnesschanges as the five main components of the spatial context of habitat fragments are altered. Predictions are derived from currenttheoretical understanding of fragmentation effects, as discussed in the main text.


(Crist et al., 2003). This forms the basis of the ongoingSLOSS (Single Large or Several Small) debate that aimsto maximise species diversity within reserve networks(Quinn & Harrison, 1988). For instance, more butterflyspecies were present in a series of small habitat fragmentsthan in several large fragments of the same total area, inboth grasslands in Germany (Tscharntke et al., 2002b) and

forests in Spain (Baz & Garcia-Boyero, 1996). Similarly, theb-diversity of aquatic invertebrates was greater in frag-mented than continuous floodplain channels (Tockner et al.,1999). These results probably occur because a series of smallfragments spread over a wide geographic area encompassa wider range of environmental heterogeneity than does asingle large fragment (Tscharntke et al., 2002b). However,

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Fig. 2. Trait-mediated differences in species responses to fragmentation. Predictions of how species responses to the five mainspatial components of habitat fragmentation vary as a function of species traits. Predictions are derived from current theoreticalunderstanding of fragmentation effects (e.g. Laurance, 1991; Didham et al., 1998b ; Davies et al., 2000; Tscharntke et al., 2002a ;Henle et al., 2004), as discussed in the main text.


large reserves are still considered to be superior to smallreserves for the long-term persistence of area-sensitive andextinction-prone species (Burkey, 1995; Ferraz et al., 2003),because they retain larger populations and the habitat isless likely to degrade through time (Connor, Courtney &Yoder, 2000; Tscharntke et al., 2002b).

Lastly, but often critically, the time-frame across whichextinction rates are measured can have a major bearingon the apparent accuracy of SA models, because therecan be a long lag-time to extinction for threatenedspecies (Tilman et al., 1994; Brooks, Pimm & Oyugi, 1999;Cowlishaw, 1999) (see Section VII.2). Consequently, somestudies (e.g. Brooks et al., 2002) have included threatenedspecies as ‘ impending extinctions ’ within extinction ratecalculations, providing better fits between observed andpredicted extinctions.

(2 ) Landscape and extinction thresholds

The number, size and spatial arrangement of remaininghabitat fragments in the landscape does not change linearlywith increasing habitat loss. Instead, there are ‘rapidchanges in the size and isolation of patches at critical pro-portions of habitat in the landscape’ (Andren, 1994). Theselandscape thresholds have important consequences forspecies persistence in fragmented landscapes. Most of therecent advances in our understanding of landscape thresh-olds have stemmed from the use of metapopulation modelsthat describe the landscape as a mosaic of patches, and focuson the balance between colonisation and extinction rates(Hill & Caswell, 1999). A simple, but important observationis that populations will not occupy all available sites at anygiven point in time, and that site occupancy depends greatlyon the degree of connectivity in the landscape (Bascompte& Sole, 1996). Consequently, there is a critical amountof habitat cover below which colonisation becomes tooinfrequent to overcome local extinctions and so meta-population extinction is inevitable (Kareiva & Wennergren,1995; Ovaskainen et al., 2002). A large number of theoreti-cal models have been constructed along these lines and theyconsistently predict the existence of an extinction threshold(Andren, 1994, 1996, 1999; Bascompte & Sole, 1996;Fahrig, 1997; With, 1997; With, Gardner & Turner, 1997;Boswell, Britton & Franks, 1998). The extinction thresholdcompounds the risks posed by habitat destruction(Amarasekare, 1998), as even a small loss of habitat nearthe threshold may result in a precipitous decline in theprobability of metapopulation persistence (With & King,1999). This obviously has serious ramifications for conser-vation management, but it should not be forgotten thathabitat fragmentation effects are only one of many inter-acting causes of population declines and that many speciesmay well go extinct long before the threshold is reached(Andren, 1999; Monkkonen & Reunanen, 1999).

Estimates of the level of habitat destruction at whichthe extinction threshold occurs are varied. Fahrig (1997)suggested that metapopulation survival would be virtuallyassured if 20% or more of the landscape retained breedinghabitat, but the literature belies such a simple rule ofthumb, with Bascompte & Sole (1996) and Andren (1997a)

suggesting that the threshold will vary across species andlandscapes. For example, experimental estimates of theextinction threshold for rare butterfly species varied from20 to 60% (Summerville & Crist, 2001). The exact valuewill likely depend heavily on individual species traits andlocal landscape structure, as indicated by With & King’s(2001) models and small-scale experiments on populationpersistence for four species ‘ types ’ in fractal landscapes.They discovered that the location of the extinction thresholdvaried from 5 to 90% habitat loss in the landscape,depending on both the species’ responses to habitat frag-mentation (sensitivity to habitat area and/or edge effects)and the spatial arrangement of the remaining habitat (With& King, 2001). In the null case, where spatial arrangementof fragments is assumed to be random, the extinctionthreshold is more pronounced and occurs at a lower pro-portion of habitat loss in the landscape than for fractallandscapes (Hill & Caswell, 1999; With & King, 1999;Fahrig, 2002). Fractal landscapes contain fewer, largerfragments with a more clumped distribution, thus main-taining connectivity across a wider range of habitat loss(With, Caderet & Davis, 1999; With & King, 1999). Such anarrangement serves to enhance dispersal success, allowingpopulations to occupy nearly all patches at any given time(With & King, 1999) and thereby reducing the likelihoodof the extinction threshold occurring. Because the processof habitat loss is patently non-random (Seabloom et al.,2002) and fractal landscapes are probably more represen-tative of natural habitat dispersion (With & King, 1999), thehypothesised effects of spatial arrangement on the extinctionthreshold are of considerable relevance to conservationmanagement (Ovaskainen et al., 2002).

(3) The population consequences of smallhabitat area

Near the extinction threshold the majority of fragmentsare small and almost inevitably contain relatively smallpopulations of most species. For many organisms, thispattern is exacerbated by decreases in population densitywith decreasing fragment area (Bowers & Matter, 1997;Connor et al., 2000), although for invertebrates such asimple generalisation cannot be made because of inconsist-ent results in the literature (Didham et al., 1998a ; Matter,2000; Steffan-Dewenter & Tscharntke, 2000; J. A. Thomaset al., 2001; Krauss et al., 2003a). Irrespective of variabilityin the density-area relationship between species, small frag-ment area imposes a maximum limit on population sizethat leaves species vulnerable to local extinction (Lande,1993; Hanski et al., 1995; Amarasekare, 1998; Burkey,1999; Brook, Burgman & Frankham, 2000; Brook et al.,2002). The underlying mechanisms driving this relation-ship can be divided into four categories (Shaffer, 1981) : (1)environmental stochasticity, (2) demographic stochasticity,(3) natural catastrophes and (4) reduced genetic diversity(see also review by Gaggiotti & Hanski, 2004). While it isconvenient to categorise these processes for discussion, itis important to note that they seldom act independently.Rather, all four have potential to interact with, and magnifythe effects of, the other three, creating what have been


described as ‘extinction vortices ’ (Leigh, 1981; Gilpin &Soule, 1986). These processes lie at the heart of populationviability analyses (PVA), which comprise a set of analyticaland modelling techniques for predicting the probability ofspecies extinction (Soule, 1987; Beissinger & McCullough,2002). The wider field of PVA has been extensively andthoroughly reviewed elsewhere (Soule, 1987; Beissinger &McCullough, 2002), but of particular relevance here isthe application of metapopulation concepts and patchoccupancy models to PVA for species in highly fragmentedlandscapes (Hanski, 2002; Holmes & Semmens, 2004). Thisapproach has clearly shown that small populations thatare restricted to small habitat remnants (within a patchnetwork) are far more likely to go extinct than populationsthat remain large (Hanski, 2002). More importantly,though, a species with a small total population size dis-tributed as a metapopulation across a network of habitatpatches typically has a greater probability of extinctionthan a species with the same total population size in whichall individuals have a similar chance of encountering eachother.

One of the key conclusions from metapopulationmodelling is that the probability of population extinctiondepends not only on habitat area, or quality, but on spatiallocation within the metapopulation network (Ovaskainen& Hanski, 2004). Furthermore, deterministic drift towarda predicted equilibrium in habitat occupancy and colonis-ation-extinction dynamics in spatially-explicit models canbe strongly influenced by stochastic fluctuations in localconditions. Again, such stochastic extinctions are mostimportant for small populations in situations in whichspatially-correlated local dynamics (Gu, Heikkila & Hanski,2002), or temporally varying environmental conditions(Ovaskainen & Hanski, 2004), amplify stochastic populationfluctuations. The net result is that small populations thatmight otherwise be predicted to persist, instead have anincreased probability of extinction due to spatial correlationin demographic or environmental stochasticity (Casagrandi& Gatto, 1999, 2002).

III. EDGE EFFECTS

(1) Community composition at habitat boundaries

The structure and diversity of invertebrate communitiesis characteristically altered at habitat edges. Typically,species richness is negatively correlated with distance fromthe fragment edge into the fragment interior (Ingham &Samways, 1996; Didham et al., 1998a ; Bolger et al., 2000;Denys & Tscharntke, 2002; Magura, 2002; Kitahara &Watanabe, 2003; Klein, Steffan-Dewenter & Tscharntke,2003; Major et al., 2003). The most common explanationfor this trend is that there is a mixing of distinct fragmentand matrix faunas at habitat edges, giving rise to a zoneof overlap with greater overall species richness (Ingham &Samways, 1996; Magura, 2002). While this is the mostgeneral species richness pattern, it is by no means universal,as a number of studies have found either no edge effectfor species richness (Davies & Margules, 1998; Monkkonen

& Mutanin, 2003) or a positive correlation (Davies,Melbourne & Margules, 2001b ; Barbosa & Marquet, 2002;Bieringer & Zulka, 2003). Evidently, in some systems manyspecies avoid edges and the matrix-dwelling fauna is notalways speciose enough to compensate for the loss of speciesat edges (Fig. 1B). Not only is species richness altered athabitat edges, but there can be substantial turnover inspecies composition, with community similarity decreasingwith distance from edge to interior (Didham et al., 1998a ;Carvalho & Vasconcelos, 1999; Harris & Burns, 2000;Davies et al., 2001b ; Dangerfield et al., 2003).

Ultimately, changes in both species richness and com-position are a composite of individual species responses,which are extremely varied both within and betweenstudies. Studies that have investigated the densities ofmultiple species at the same sites typically show contrastingedge responses between species with differing life historystrategies and habitat requirements, although these contrastsare not necessarily consistent among studies (Fig. 2F–J ;Davies & Margules, 1998; Didham et al., 1998a ; Kotze &Samways, 1999, 2001; Bolger et al., 2000). In a study ofspider communities in forest fragments in Finland, it wasshown that large hunting spiders were most abundant nearforest edges where the environment was warmer, moreopen, and the leaf litter layer was thick enough to allowstratification of adults and juveniles, which reduced theprobability of cannibalism (Pajunen et al., 1995). By contrast,in the same forest fragments, small web-building spiderswere more likely to inhabit the forest interior, where theherb and moss cover provided suitable microhabitatstructures for web construction (Pajunen et al., 1995). Evendifferent species within a single genus can have completelycontrasting responses to edges, as exemplified by the leaf-litter-dwelling beetle genus Araptus in Central Amazonia(Didham et al., 1998a). Didham et al. (1998a) showed thatsome Araptus species were apparently insensitive to forestfragmentation, whereas others became locally extinct insmall fragments. Furthermore, another Araptus species wasmost abundant in small fragments and at forest edges,while yet another species was most likely to occur deepin undisturbed forest (Didham et al., 1998a). Such variedresponses to fragmentation within a genus were strikingand possibly reflected subtle differences among species lifehistories and the effects of species-level resource partitioning(Didham et al., 1998a).

(2 ) Edges as ecological traps

Curiously, some animals appear to select or prefer edges assuitable breeding habitat, despite the fact that mortalityrates at edges can be much higher than in fragmentinteriors. This phenomenon has been termed an ‘ecologicaltrap’ and was originally introduced in the avian literature(Gates & Gysel, 1978; Flaspohler, Temple & Rosenfield,2001; Ries & Fagan, 2003). However, two recent studiesof edge effects have expanded the concept to includeinvertebrates. In a thorough study, McGeoch & Gaston(2000) showed that the abundance of the English hollyleaf miner Phytomyza ilicis was greatest at woodland edges,indicating that adults prefer to oviposit at edges than in the


woodland interior. Despite this preference, survivorship waslowest at the edge, possibly because of host-plant-inducedmortality (McGeoch & Gaston, 2000). Similarly, Ries &Fagan (2003) found the density of mantid egg cases wasgreatest at the edges of cottonwood and desert shrubriparian zones, where bird predation rates were significantlyhigher.

(3 ) Edges alter species interactions

Habitat edges can alter the nature of species interactionsand thereby modify ecological processes and dynamics ata wide range of scales (Fagan, Cantrell & Cosner, 1999).Examples of altered herbivory (McKone et al., 2001), seedpredation (Burkey, 1993), competition (Remer & Heard,1998), predation (Ries & Fagan, 2003) and parasitism rates(Tscharntke et al., 2002b ; Cronin, 2003b) are relativelycommon, and explicit recognition of these responses hasapplied significance in the field of biological control inagroecosystems (Thies & Tscharntke, 1999; With et al.,2002). However, habitat edge effects can sometimes bedependent on landscape context, with diverse, structurallycomplex landscapes negating differences between fragmentedges and interiors (Thies & Tscharntke, 1999; Tscharntke& Brandl, 2004). For instance, Thies & Tscharntke (1999)showed that parasitism rates of the rape pollen beetleMeligethes aeneus in field interiors were much lower than atfield edges when fields were surrounded by homogenouslandscapes, but not when the surrounding landscape washeterogeneous.

(4 ) Variability and hyperdynamism at edges

Perhaps one of the most intriguing aspects of edge effectsis that interactions between species may become lessstable at edges. This possibility, though not widely tested,is hinted at by the results of several recent studies. In anextensive study of beetle communities in Amazonian forestfragments, Didham et al. (1998a) showed that the com-munity composition at edges was more variable than inundisturbed forest sites. This result was driven by the factthat most edge species were localised to just one or a fewedges, but were seldom located at all edges, indicating thatedges support higher b-diversity than fragment interiors(Didham et al., 1998a). Similarly, variability in invertebratepredator abundance within an apple orchard decreasedwith distance from orchard edge to interior (Brown &Lightner, 1997), and the parasitism risk to the planthopperProkelisia crocea was 60% more variable at the edge than inthe interior of prairie cordgrass patches (Cronin, 2003b).One important outcome of increased variability in trophicinteraction strengths may be hyperdynamism in a rangeof ecosystem process rates, where the frequency and/oramplitude of ecosystem dynamics is increased (Laurance,2002). Hyperdynamism in fragmented landscapes occursbecause habitat fragments are more prone than large areasof continuous habitat to environmental stochasticity andthe penetration of external dynamics from the matrix intofragments, and can result in the destabilisation of animalpopulations (Laurance, 2002). For example, population

outbreaks by the tent caterpillar Malacosoma disstria (Roland& Taylor, 1997) and aphids (Kareiva, 1987) were increasedin fragmented habitats following reductions in predationand parasitism.

IV. SHAPE COMPLEXITY

Shape complexity is a fragment attribute that has raisedsurprisingly little interest in fragmentation studies, butmay in fact be extremely important. At the most basic level,shape is determined by an interaction between fragmentarea and perimeter that determines the amount of corehabitat remaining in any given habitat fragment (Laurance& Yensen, 1991; Collinge, 1996). It is the relationshipbetween these two variables that forms the basis of mostquantitative shape indices (reviewed by Baskent & Jordan,1995 and Riitters et al., 1995). Unfortunately, the mostcommonly used shape index is the perimeter to area ratio(Kupfer, 1995), which is not independent of area and canyield large errors when used to estimate the amount of coreand edge habitat (Laurance & Yensen, 1991). Furthermore,analyses of large-scale geographic data sets have shown aconsistent positive correlation between fragment area andshape complexity (Cochrane & Laurance, 2002). Conse-quently, many studies that claim to show shape effectsmay in fact have confounded shape with area effects. Forinstance, Baz & Garcia-Boyero (1995) found butterflyspecies richness to be higher in compact shapes, but only ifarea was not included in the model. The importance ofchoosing an appropriate shape index was shown clearly byMoser et al. (2002), who found that the sign of the relation-ship between fragment shape and species richness could beeither positive or negative for the same data set, dependingon how shape complexity was calculated.

Fragments with complex shapes have a much higherproportion of total fragment area that is edge, rather thancore habitat (Laurance & Yensen, 1991), accentuating theextent to which edge effects permeate the habitat (Collinge,1996). Furthermore, the convoluted nature of complexshapes can result in the division of core habitat into mul-tiple, disjunct core areas that are separated by regions ofedge-affected habitat (Ewers, 2004). Population estimatesbased on a literature review of the density-area relationship(Bender et al., 1998; Bowers & Matter, 1997; Connor et al.,2000) showed that disjunct cores in large fragments canreduce invertebrate populations to one-fifth of the popu-lation size that could be supported if core habitat werecontinuous (Ewers, 2004). Moreover, communities in frag-ments with narrow, elongated shapes may exhibit changesin species richness and abundance that are analogous toarea effects (Fig. 1C). Individuals in narrow fragments arelikely to have reduced encounter rates relative to individualsin compact fragments, which may lead to shape-inducedAllee effects, and reductions in parasitism rates (Thies &Tscharntke, 1999).

Perhaps the most consistent pattern that emerges withregard to shape is that complex fragments are colonisedmore frequently than are compact patches (Game, 1980;


Collinge, 1996; Hamazaki, 1996; Bevers & Flather, 1999;Collinge & Palmer, 2002; Cumming, 2002). This patternis also found in two-dimensional marine substrates(Minchinton, 1997; Tanner, 2003) and has been applied tothree-dimensional patches in marine ( Jacobi & Langevin,1996) and aquatic (Lancaster, 2000) habitats. Increasedcolonisation of complex fragments occurs because fragmentswith high shape complexity have a proportionally greateramount of edge, increasing the likelihood that a patch willbe encountered by a moving individual (Collinge & Palmer,2002). However, colonisation probability can be moderatedby fragment orientation. When species movements occurin a predictable pattern, such as migration (Gutzwiller &Anderson, 1992) or tidal movements (Tanner, 2003), longthin patches are more likely to be colonised than compactfragments, but only if they are oriented perpendicular tothe direction of movement.

The corollary of increased colonisation of complex shapesis that emigration is also likely to be increased (Van Kirk& Lewis, 1999), although this may depend upon boundarypermeability (Stamps, Buechner & Krishnan, 1987;Collinge & Palmer, 2002). As a result, the probability ofpopulation persistence in fragments with complex shapesis reduced (Fig. 1C; Bevers & Flather, 1999; Van Kirk &Lewis, 1999), leading to higher patch occupancy in compactfragments (Helzer & Jelinski, 1999). Furthermore, the com-bination of increased emigration and colonisation leadsto greater variability in the population size of long, thinpatches (Hamazaki, 1996).

Theory suggests that the effects of shape are likely toscale with fragment area. It is likely that small fragmentsare most heavily impacted by having complex shapes,because any deviation from circularity will greatly reducethe amount of interior habitat (Laurance & Yensen, 1991;Kupfer, 1995). The problem associated with testing forthese effects is that shape and area are intimately correlated,as shown by studies including thousands of fragments(Cochrane & Laurance, 2002; Ewers, 2004) or as few as17 fragments (Watson, 2003). While some experimentalstudies have varied shape while holding area constant(Hamazaki, 1996), none have independently varied bothshape and area.

V. ISOLATION

One of the obvious spatial consequences of habitatfragmentation is that fragments become isolated in spaceand time from other patches of suitable habitat. Isolationdisrupts species distribution patterns (Fig. 1D) and forcesdispersing individuals to traverse a matrix habitat thatseparates suitable habitat fragments from each other. Whileisolation is most often defined by the Euclidean distancebetween habitat fragments, it is, in fact, matrix depend-ent. An extreme example of this was highlighted byBhattacharya, Primack & Gerwein (2003), who found thattwo species of Bombus bumblebees would rarely cross roadsor railways despite the presence of suitable habitat thatwas within easy flying range. Because some matrix habitats

inhibit dispersal more than others (see Section VI.2;Fig. 1E; Ricketts, 2001; Roland, Keyghobadi & Fownes,2000) and because species differ in their willingness todisperse through matrix environments (Laurance, 1991;Haddad & Baum, 1999; Collinge, 2000), the literature isfull of seemingly disparate results regarding the effects ofisolation on species and communities. For instance, geneticdifferentiation between invertebrate populations wasclearly related to fragment isolation in some studies (VanDongen et al., 1998; Schmitt & Seitz, 2002; Krauss et al.,2004), but not in others (Ramirez & Haakonsen, 1999;Wood & Pullin, 2002). Similarly, the relationship betweeninvertebrate species richness and isolation can be positive(Baz & Garcia-Boyero, 1996), negative (Baz & Garcia-Boyero, 1995) or absent (Brose, 2003; Krauss et al., 2003a ;Krauss, Steffan-Dewenter & Tscharntke, 2003b). One likelyreason for these conflicting results is that species with dif-ferent traits differ in their susceptibility to isolation (seeSection VII; Fig. 2P–T).

The intuitive conservation response to isolation is toconnect isolated fragments with corridors of suitable habitat(Hill, 1995). Corridors can increase the density and diversityof invertebrate species and communities (Hill, 1995;Gilbert, Gonzalez & Evans-Freke, 1998; Haddad & Baum,1999; Collinge, 2000), and are most effective for speciesthat never, or rarely, disperse through the matrix surround-ing habitat patches (Schultz, 1998). This was convincinglydemonstrated in an experimental grassland systemby Collinge (2000) and in a natural grassland system byHaddad & Baum (1999). In both studies, species that wererestricted to habitat patches benefited from the presence ofcorridors, whereas no strong benefits were observed forhabitat generalists. Corridors have also been shown to havea small positive effect for less vagile species (Collinge, 2000)and strongly increased the survival of predators in anexperimentally fragmented moss microecosystem (Gilbertet al., 1998). Interestingly, the current primary role of corri-dors is to facilitate metapopulation persistence within alandscape (Collinge, 1996; Jordan et al., 2003), but in thefuture corridors may be required to facilitate speciesmigrations between landscapes in response to climatechange (Collingham & Huntley, 2000; Opdam & Wascher,2004; Stefanescu, Herrando & Paramo, 2004).

VI. MATRIX EFFECTS

A growing body of evidence suggests that matrix qualityis crucially important in determining the abundance andcomposition of species within fragments (Figs 1E, 2U–Y;Laurance, 1991; As, 1999; Gascon et al., 1999; Kotze &Samways, 1999; Cook et al., 2002; Perfecto & Vandermeer,2002). The traditional IBT approach to the study of habitatfragmentation failed to recognise that the penetration ofedge effects from outside a fragment alters habitat charac-teristics within the fragment (Didham, 1997) and that thematrix may not be completely inhospitable to the fragment-dwelling fauna (Gustafson & Gardner, 1996). In fact, thereis often substantial overlap between species that inhabit


fragments and matrix habitat (Cook et al., 2002). Thisspecies ‘ spill-over ’ is most prevalent in small patchesand at the edges of large patches, and may obscure area andisolation effects (Cook et al., 2002; Brotons, Monkkonen &Martin, 2003). Cook et al. (2002) went on to show that IBTpredictions had a better fit when species that occurred inthe matrix were removed from the analysis. In addition,increasing species’ mortality rates in the matrix can havethe drastic effect of completely reversing the outcome ofcompetitive interactions within fragments, allowing inferiorspecies to supplant dominant ones within fragments(Cantrell, Cosner & Fagan, 1998).

(1 ) Can matrix quality mitigatefragmentation effects?

Habitat remnants are not necessarily the only parts of thelandscape that provide resources relevant to species persist-ence, and some fragment-dwelling species are able to com-pensate for habitat loss by making use of resources availablein the matrix (Bierregaard et al., 1992; Davies, Gascon &Margules, 2001a ; Denys & Tscharntke, 2002; Ries et al.,2004). In these cases, it is not strictly correct to applythe term ‘matrix ’ to the habitat surrounding fragments, asthe term carries connotations of inhospitable environments.In fact, for some species the ‘matrix’ may actually representa set of resources that are complementary to, and unavail-able in, habitat remnants (Ries & Sisk, 2004). Thus, therecan be great difficulty involved in arbitrarily splitting com-ponents of a landscape into the categories ‘patch ’ and‘matrix. ’ This is illustrated by the results of Perfecto &Vandermeer (2002), who demonstrated that ants inhabitingforest fragments in Mexican coffee plantations were activelyforaging in the surrounding matrix and that some specieswere even able to survive in matrix habitat in perpetuity.Furthermore, an increase in matrix quality was associatedwith an increase in the number of species and individualsthat occurred in the matrix (Perfecto & Vandermeer, 2002).In other cases, species with complex life histories mayrequire different resources from multiple habitat typesduring their life cycle (Ries et al., 2004). For instance, Thies& Tscharntke (1999) found that parasitoids required boththe availability of hosts within crop fields as well as the avail-ability of perennial hibernation sites within the surroundinglandscape matrix.

A species’ ability to utilise resources from the matrixcan alter the intensity of fragmentation effects (Fig. 2X).In model simulations, Andren (1997b) demonstrated thatgeneralist species maintained higher populations in frag-mented landscapes than specialist species that dependedon resources available only in fragments. Increasing thedegree of habitat specificity further amplified populationreductions when habitat was lost and fragmented (Andren,1997b). In a similar model, Estades (2001) showed thatincreasing matrix quality (i.e. providing resources in thematrix) increased population density within a fragment.Several empirical studies have now confirmed the import-ance of matrix quality for population persistence withinfragments (Thies & Tscharntke, 1999; Ricketts, 2001;Vandermeer et al., 2001), and that temporal changes in

matrix quality can reverse trends in species abundances.For instance, dramatic declines in the abundances of threeEuglossa bee species were recorded within months of thecreation of experimental forest fragments at the BiologicalDynamics of Forest Fragments Project in Brazil (Powell &Powell, 1987; Cane, 2001), yet after several years of matrixregeneration (which provided the bees with a new foodsource) their numbers had rebounded to become higherin fragments than in continuous forest (Becker, Moure &Peralta, 1991; Cane, 2001). Similarly, variation in thequality of spatial subsidies from matrix habitat can eitherincrease or decrease species richness within fragments byalternately increasing resource availability or competition,respectively (Anderson & Wait, 2001). Studies on oceanicislands have convincingly demonstrated that spatial sub-sidies from the surrounding environment can increaseisland productivity, and that subsidies have the greatestrelative effect on small islands with greater edge to arearatios (Polis & Hurd, 1995, 1996; Anderson & Wait, 2001).If this concept can reasonably be extrapolated to habitatfragments, it seems likely that spatial subsidies from thesurrounding landscape matrix may alter the species richnessof small fragments.

(2) Matrix and dispersal

Dispersal between habitat fragments is essential for long-term metapopulation persistence (Gustafson & Gardner,1996), but is at least partially dependent on matrixproperties (Franklin, 1993). Although one of the definingcharacteristics of a matrix is that movement of individualsis different to that observed in habitat patches (as demon-strated by Schultz, 1998; Kindvall, 1999; Hein et al., 2003),altering the structure of the matrix further influences ananimal’s movement potential (Szacki, 1999). Differencesin matrix quality affect dispersal and movement of indi-viduals in fragmented systems (Gustafson & Gardner, 1996;Bierregaard & Stouffer, 1997; Moilanen & Hanski, 1998;Davies et al., 2001b) and may function as a ‘qualitative filter ’(Szacki, 1999) for individuals at specific life history stages. Asa result, matrix structure can alter colonisation-extinctiondynamics (Brotons et al., 2003; Cronin & Haynes, 2004),which can lead to changes in population density (Gustafson& Gardner, 1996) and structure (Szacki, 1999). Further-more, changes to matrix structure can increase variabilityin species interactions, as demonstrated for host-parasitoiddynamics in cordgrass patches of the North American GreatPlains (Cronin & Haynes, 2004).

The degree of contrast between fragment and matrixhabitat largely determines the permeability of edges toanimal movement across fragment boundaries (Stampset al., 1987; Holmquist, 1998; Collinge & Palmer, 2002).Typically, low-contrast boundaries are predicted to bemore permeable (Collinge & Palmer, 2002), as found instudies on butterflies (Ries & Debinski, 2001), hymenop-teran parasitoids (Cronin, 2003a) and shrimp (Holmquist,1998). However, these results are highly species specific anddepend entirely on the species’ perception of the habitatboundary (Schultz & Crone, 2001). Ries & Debinski (2001)found a link between edge contrast and permeability for


a generalist butterfly, whereas a specialist was unlikely toemigrate from a fragment, regardless of edge structure.Similarly, motile species found edges more permeable thanother, more sedentary species (Holmquist, 1998). It shouldalso be noted that edge structure is not the sole determinantof permeability ; other factors such as conspecific density,wind direction and time of day or year all significantlyinfluenced edge permeability (Holmquist, 1998; Ries &Debinski, 2001). Changes to edge permeability may beeither positive or negative for populations, depending on theparticular landscape and species being studied. Long-termpersistence of metapopulations requires individuals tocross habitat edges and disperse between habitat remnants(Hanski, 1998), so some degree of permeability is clearlyessential. However, edges that are ‘ too’ permeable may actas population sinks. For instance, nocturnal foraging of thecarnivorous New Zealand Paryphanta spp. landsnails acrosspermeable forest edges leaves them prone to mortality fromdesiccation in the surrounding pasture matrix during theday, because they are unable to return quickly enough tothe shaded safety of the forest (Ogle, 1987).

Once an animal has left a fragment, the structuralcharacteristics of the matrix can resist, hinder or enhancemovement behaviour (Gustafson & Gardner, 1996; Rolandet al., 2000; Chardon, Adriaensen & Matthysen, 2003).For example, Cronin (2003a) found that hymenopteranparasitoids were most likely to colonise cordgrass fragmentsthat were surrounded by a matrix of native or exotic grass,rather than fragments in a mudflat matrix. Similarly,Ricketts (2001) showed that a meadow-dwelling butterflyspecies had higher dispersal through willow than conifermatrix, although this result was species specific, with severalother species showing no difference. Ricketts (2001) con-cluded that matrix quality alters ‘effective isolation’ in waysthat vary among even closely-related species. The conceptof effective isolation has been applied by other authorsunder a series of different names including cumulativeresistance (Knaapen, Scheffer & Harms, 1992), functionalconnectivity (Tischendorf & Fahrig, 2000), effective distance(Moilanen & Hanski, 1998; Roland et al., 2000; Ferreras,2001) and cost-distance (Chardon et al., 2003). Instead ofmeasuring fragment isolation in terms of Euclidean dis-tance, effective isolation weights Euclidean distance accord-ing to matrix viscosity (Ferreras, 2001). Ferreras (2001)assigned matrix habitats a ‘ friction value ’ based on Jacobs’Selection Index [ Jacobs (1974) cited in Ferreras (2001)],which reflects a particular habitat’s viscosity to the move-ment of a particular study animal. Both Ferreras (2001)and Chardon et al. (2003) found effective isolation was amore accurate predictor of connectivity than Euclideandistance.

(3 ) Matrix and edge effects

The strength of an edge effect can be greatly moderatedby changes in matrix structure. Edges with a high contrastbetween the fragment and matrix are more likely to gener-ate stronger edge effects than low-contrast edges (Franklin,1993; Demaynadier & Hunter, 1998; Zheng & Chen, 2000;Laurance et al., 2002). This has been demonstrated for

edge-related gradients in the density of hymenopteranparasitoids (Cronin, 2003a). Furthermore, Perfecto &Vandermeer (2002) found that ant species richness declinedfrom the fragment edge into the matrix, but the rate ofdecline was slower when edge contrast was lowest, andHolmquist (1998) showed that edge permeability in themarine environment was a function of edge contrast.

VII. CONFOUNDING FACTORS IN THE

DETECTION OF FRAGMENTATION IMPACTS

The literature on habitat fragmentation is replete withexamples of apparently contradictory results that cannotbe explained solely by reference to differences betweenthe environments or methods used in separate studies.These differences highlight the emerging realisation thata wide range of confounding factors can either obscure orenhance the detection of fragmentation effects.

(1 ) Trait-mediated differences in speciesresponses to fragmentation

Many seemingly contradictory responses to fragmentationcan be adequately explained by investigating the mechan-isms driving species-level patterns, and the individual traitsthat determine species’ susceptibilities to those underlyingprocesses. In general, there is a suite of traits that is com-monly hypothesised to increase a species’ vulnerability tofragmentation, including large body size, low mobility,high trophic level, and matrix tolerance (Fig. 2 ; Laurance,1991; Didham et al., 1998b ; Davies, Margules & Lawrence,2000; Tscharntke et al., 2002a ; Henle et al., 2004). Byexplicitly considering the effect of species traits, it becomespossible to explain many of the apparently conflicting resultsin the fragmentation literature.

For instance, a number of studies have shown that thenature of the SA relationship describing species loss fromhabitat fragments is confounded by differences in speciestraits. Species at higher trophic levels, habitat specialists,species with large body size and those with poor dispersalabilities or a reliance on mutualist species are expected togo extinct first when habitat area decreases (Fig. 2A–D;Rathcke & Jules, 1993; Didham et al., 1998a, b ; Holt et al.,1999; Davies et al., 2000; Steffan-Dewenter & Tscharntke,2000; Tscharntke et al., 2002a ; Steffan-Dewenter, 2003;Davies, Margules & Lawrence, 2004). Consequently, taxawith these traits frequently exhibit steeper SA curves.For example, Krauss et al. (2003a) showed that generalistbutterflies had a shallower SA curve than did specialistbutterflies. Similarly, Tscharntke and Kruess (1999) foundthat SA curves for parasitoid species were steeper than forherbivores, although Steffan-Dewenter (2003) failed tofind any difference between bees, wasps and their naturalpredators and parasitoids. Interestingly, recent analyses ofnested communities, in which the composition of species-poor communities are hierarchically arranged, non-randomsubsets of species-rich communities (Patterson, 1987) showthat species extinction occurs in a consistent, sequential


pattern as fragment area decreases (Wright et al., 1998;Lovei & Cartellieri, 2000; Loo, Mac Nally & Quinn, 2002),indicating a gradient in extinction vulnerability amongspecies. To date, attempts to integrate the study of nestedcommunities with theoretical predictions of extinctionsusceptibility for species with particular trait complexeshave been largely ad hoc, although this emerging field ofresearch promises to shed further light on area-relatedextinction patterns.

Similarly, many of the contrasting results found in studiesof habitat isolation can be explained by more explicit con-sideration of species traits. Species at higher trophic levels,such as predators and parasitoids, appear to be more heavilyaffected by isolation than those at lower trophic levels(Fig. 2P; Tscharntke, Gathmann & Steffan-Dewenter,1998; Zabel & Tscharntke, 1998), and species with highmobility are more likely to survive in fragmented landscapesthan species with low mobility (Nieminen, 1996; Thomas,2000). Interestingly, Thomas (2000) showed that butterflyspecies with intermediate mobility were more likely todecline in abundance following habitat fragmentationthan were butterflies with either high or low mobility (Fig. 3).He explained this unexpected result by reference to theprobable underlying mechanism. Highly vagile specieswere able to disperse freely between fragments and so wererelatively unaffected by fragmentation, and at the oppositeextreme, species with low vagility tended to stay within afragment, thereby avoiding dispersal-related mortality.By contrast, intermediate mobility resulted in individualsdispersing away from one fragment but failing to reachthe next, leading to an overall increase in the mortalityrate for these species. This mechanistic explanation leadsdirectly to the prediction that habitat fragmentation willcreate local selection pressures to favour simultaneouslyeither of the two extremes of dispersal ability. This pre-diction is at least partially supported by population-levelincreases in the dispersal power of butterflies in fragmentedlandscapes (C. D. Thomas, Hill & Lewis, 1998; Hill,Thomas & Lewis, 1999) and the reduction in mobility ofcarabid beetles in populations that inhabit fragments forlong periods of time (Desender et al., 1998).

Simple tests for the impacts of species traits on species’vulnerability to fragmentation are likely to be confoundedby interactions between traits. In a recent review by Henleet al. (2004), it was shown that six traits have sufficientempirical support to justify being considered strong pre-dictors of species’ sensitivity : population size, populationvariability, competitive ability and sensitivity to disturbance,degree of habitat specialisation, rarity, and biogeographiclocation. However, any given species comprises a suite oftraits that are strongly intercorrelated (Laurance, 1991;Henle et al., 2004), and can interact with each other to in-crease susceptibility to fragmentation. For example, Davieset al. (2004) showed that a synergistic interaction betweenthe traits of rarity and habitat specialisation made beetlespecies that were both rare and specialised more vulnerableto fragmentation than predicted by the simple additiveeffects of the two traits in isolation (Fig. 4). Furthermore,some traits interact with environmental heterogeneitysuch that the determinants of species vulnerability in one

environment will not necessarily be the same in a differentenvironment (Henle et al., 2004). One potential solution tothis problem is to work explicitly in terms of trait complexes,rather than dealing with traits individually. Extinction fre-quency is seldom randomly distributed across familiesor genera (Bennett & Owens, 1997; Purvis et al., 2000a),because traits that bias species to extinction are oftenphylogenetically conservative (McKinney, 1997). By usingcomparative analyses that control for phylogeneticallycorrelated suites of traits, it should be possible to elucidatemore clearly the roles of individual traits (e.g. Owens &Bennett, 2000; Purvis et al., 2000b). This approach hasyet to be applied to predictors of species’ vulnerability to

0.00–0.39 0.40–0.79 0.80–1.00

Proportion of regions where surviving

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Fig. 3. Some apparently idiosyncratic responses to frag-mentation can be explained by reference to the underlyingmechanism of species response. On average, UK butterflyspecies with intermediate mobility (17 species) have smallergeographic ranges and are more likely to go locally extinct thanspecies with either high (10 species) or low (29 species) mobility,which both suffer lower levels of dispersal-related mortality(see text). Proportions of butterfly species surviving in 21 UKregions are plotted for butterflies within each of three classesof differing dispersal ability. A relatively high proportion ofspecies with intermediate mobility survive only in very few(0–39%) of the regions from which they were originally present,implying that many have gone locally extinct from most oftheir former range. By contrast, species with either high orlow mobility are less likely to have suffered local extinctions,and are more likely to have survived in the majority of theiroriginal range than species with intermediate mobility. Figurereproduced from Thomas (2000, p. 141).


habitat fragmentation, but could be of considerable usein rigorously determining a reliable set of predictor traits.

(2 ) Time lags in the manifestation offragmentation effects

The long-term effects of fragmentation are relatively poorlyknown (McGarigal & Cushman, 2002; Watson, 2003), asmost studies of anthropogenically-fragmented landscapeshave been conducted less than 100 years after fragmentation(Watson, 2002, 2003). While some authors (e.g. Renjifo,1999) consider time-scales of 50 to 90 years as ‘ long-term’and sufficient to ensure that diversity patterns have reacheda dynamic equilibrium, this time frame may not be longenough to allow the full spectrum of fragmentation effectsto be exhibited (particularly for long-lived organisms). Ingeneral, many of the fragmentation effects that are mostcommonly studied are not exhibited immediately followinghabitat loss, because not all individuals or species exhibitshort-term responses to habitat changes (Wiens, 1994).What we know so far from the spatial and temporalscales applied in the majority of studies, is that short- to

medium-term time lags in species responses to fragmen-tation are almost ubiquitous.

(a ) Time lags in population responses to fragmentation

There is a strong temporal component to the manifestationof species responses following fragmentation. In the shortterm, crowding effects (Bierregaard et al., 1992; Debinski& Holt, 2000) occur when organisms that survive theimmediate process of habitat loss are concentrated intothe much smaller amount of remaining habitat, therebyincreasing population densities and species richness withinhabitat fragments (Collinge & Forman, 1998). For example,this displacement phenomenon (Hagan, Haegen &McKinley, 1996) occurred almost immediately followinghabitat loss in Amazonian bird communities (Lovejoyet al., 1986) and in grassland invertebrates of the westernUSA (Collinge & Forman, 1998), but was not observed atall for Lumholtz’s tree kangaroo, Dendrolagus lumholtzi,following deforestation in tropical northern Australian(Newell, 1999). In the latter species, individuals exhibitedstrong site fidelity and chose to remain in the deforested,degraded habitat rather than move to nearby continuousforest (Newell, 1999). While crowding was only discoveredby taking an experimental approach to forest fragmentation(Lovejoy et al., 1983; Schmiegelow, Machtans & Hannon,1997), it paradoxically presents the greatest problem toexperimental studies, because many responses to experi-mental treatments are measured soon after fragmentation.

Typically, fragments are unable to support all survivingindividuals and species in the long term, as shown by sub-sequent reductions in species abundance and richnessthrough time (Debinski & Holt, 2000). For example, theelevated post-fragmentation population densities of speciesin Amazonian bird communities declined steadily over thefollowing 16 months (Bierregaard et al., 1992, Stouffer &Bierregaard, 1995). A similar pattern was found for birdsin the boreal forests of Canada (Schmiegelow et al., 1997).By contrast, reductions in arthropod abundance usuallyoccur over much shorter time frames. For instance, inan experimentally-fragmented moss system in the UK,Gonzalez & Chaneton (2002) found that reductions inmicroarthropod biomass and abundance occurred over aneight month period. An even shorter time lag was observedin an experimentally-fragmented grassland in Australia,where invertebrate abundance declined over a four monthperiod post-fragmentation (Parker & Mac Nally, 2002).Collinge & Forman (1998) also documented reductionsin invertebrate abundance and species richness, and theseeffects were noticeable after just five weeks.

Reductions in species richness following fragmentationare commonly termed ‘extinction debts, ’ and occur overthe medium- to long-term. The term was described byTilman et al. (1994) as a ‘ time-delayed but deterministicextinction of the dominant competitor in remnant patches, ’and describes a time lag between the process of habitatloss and the eventual collapse of populations (Cowlishaw,1999). The extinction debt is illustrated by negativecorrelations between species richness and fragment age,measured as time since isolation (Wilcox, 1978; de Vries

0 20 30 40

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Fig. 4. Single-factor explanations for the influence of indi-vidual traits on species responses to fragmentation ignore thefact that synergistic interactions between traits can make somespecies more susceptible to fragmentation. For 53 beetle speciesin Australian forest fragments, species that were both rare andspecialised were more affected by fragmentation than predictedfrom either trait operating alone. The y-axis represents thechange in the post-fragmentation growth rate of species infragments compared to continuous forest. Negative valuesrepresent reductions in average growth rates. Natural abun-dance was measured for two years pre-fragmentation. Filledcircles (and solid fitted line) are habitat specialists and opencircles (and dashed fitted line) are habitat generalists. Figurereproduced from Davies et al. (2004, p. 269).


et al., 1996; Brooks et al., 1999; Bolger et al., 2000; Parker &Mac Nally, 2002). Furthermore, Komonen et al. (2000)showed that the number of insect trophic levels supportedby bracket fungus decreased with fragment age, as did theprobability of native ants occupying a fragment (Suarez,Bolger & Case, 1998). However, several studies have alsofound species richness to be greatest in fragments of inter-mediate (Fahrig & Jonsen, 1998) or old age (Assmann, 1999;Denys & Tscharntke, 2002), because of longer-term tem-poral changes in habitat diversity that can also result inaltered species interactions (Tscharntke & Kruess, 1999;Denys & Tscharntke, 2002).

Extinction debts are paid through time as fragment-inhabiting communities gradually relax to a new equilib-rium number of species (Brooks et al., 1999), with the rateof relaxation being a function of fragment area, fragmentisolation and generation time of the study organism.Community relaxation approximates an exponential decaywith a half-life from 25 to 100 years for birds (Brookset al., 1999; Ferraz et al., 2003) and 50 to 100 years forprairie-dwelling plants (Leach & Givnish, 1996). Althoughno direct estimates have yet been made for the half-lifeof invertebrate extinction debts, Gonzalez (2000) andGonzalez & Chaneton (2002) found that the extinctiondebt of microarthropods in an experimentally fragmentedmoss microsystem was apparently paid in six to twelvemonths. This probably reflects both the very small size of thefragments in these studies and the rapid generation timesof invertebrates relative to vertebrates. The exact value ofthe half-life may also depend heavily on spatial attributesof the remaining habitat, with small, isolated fragmentshaving much shorter half-lives than large and less-isolatedfragments (Fig. 5; Brooks et al., 1999; Ferraz et al., 2003).Similarly, recent modelling studies suggest that the half-life to community relaxation may be a function of theproportion of habitat cover remaining in the landscape,with time lags to extinction being greater at, or below, theextinction threshold (Ovaskainen & Hanski, 2002, 2004).Hanski & Ovaskainen (2002) present an empirical examplein which the number of regionally extinct old-growth forestbeetles in Finland was proportional to the length of timethat forests had been managed for timber production

within different regions, and the amount of available intacthabitat. They showed that the extinction debt was especiallygreat for communities in which many species were near thethreshold for metapopulation extinction (i.e. the ‘capacity ’of the landscape to ensure metapopulation persistence ;Hanski & Ovaskainen, 2000), and that some species onlysurvived in the more recently disturbed regions becausethere had not been enough time for all local populationsto become extinct (Hanski & Ovaskainen, 2002). Suchtransient metapopulation dynamics for individual specieshas been well described by Ovaskainen & Hanski (2004).They suggest that the length of time taken for a newmetapopulation equilibrium to stabilise following habitatloss (whether this is equilibrium persistence or equilibriumextinction) increases with the degree of change in habitatcover, the life span of the organism, the availability of stablelarge patches within a patch network, and with decreasinghabitat cover approaching the extinction threshold. For thewell-studied Glanville fritillary butterfly, Melitaea cinxia, inFinland, for example, Ovaskainen & Hanski (2004) suggestthat the period of transient metapopulation dynamicsfollowing habitat loss can be up to 5–10 generations.

(b ) Biogeographic factors controlling fragmentation responses

Biogeography and history may offer some clues as to thelikely long-term impacts of habitat fragmentation on speciesand communities. Species’ sensitivity to fragmentationdiffers between biomes, with particularly low sensitivityrecorded in the temperate zones of theNorthernHemisphere(Henle et al., 2004). One likely reason for this is thatanthropogenically-driven habitat loss and fragmentationoccurred long before scientists recognised it as a problem andbegan recording species responses (Balmford, 1996). Thus, itis possible that the most sensitive species in this biome havealready become extinct, leaving behind just a subset of theoriginal fauna that is resilient to the fragmented landscapesthat remain. This process is a type of ‘extinction filter ’(Balmford, 1996), and would explain why species in the morerecently degraded habitats of Oceania and many tropicalregions appear to be more vulnerable to fragmentation(Henle et al., 2004). It would also suggest that over longer time

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Fig. 5. The spatial attributes of habitat fragments have an important bearing on the time-lag in species loss following habitatloss (the ‘extinction debt ’). The y-axis represents the half-life to community relaxation, as the time in years that it took to lose 50%of bird species from forest fragments in Kakamega, Kenya. Figure reproduced from Brooks et al. (1999, p. 1146).


scales, humanmodification of natural habitats will lead to theextinction of many species that are presently considered to bevulnerable to fragmentation. Unfortunately, hypotheses suchas this are difficult, if not impossible, to test because we simplydo not have the required data on historical extinctions(Balmford, 1996).

( c ) Altered selection pressures and developmental instability

Morphological changes in individuals in response tofragmentation require time for natural selection to have anoticeable impact. Such phenotypic changes have seldombeen investigated, but may hold important clues aboutspecies traits that promote population persistence in frag-mented landscapes. For example, morphological changessuch as increased muscle mass for flight have been observedby comparing butterfly populations in historically frag-mented landscapes with those in recently fragmentedlandscapes (C. D. Thomas et al., 1998; Hill et al., 1999;Norberg & Leimar, 2002). Similar relationships betweenfragmentation and morphological characters that reflectthe dispersal power of individuals have been shown for thedamselfly, Calopteryx maculata in Canada (Taylor & Merriam,1995), two species of carabid beetles in western Europeansaltmarshes (Desender et al., 1998), two species of bushcricket in the UK (C. D. Thomas et al., 2001), and theGlanville fritillary butterfly, Melitaea cinxia, also in theUK (Norberg & Leimar, 2002). Several species of wing-dimorphic planthoppers also exhibit differences in therelative frequency of wing morphs in relation to fragmen-tation, with long-winged males more prevalent in frag-mented habitats (Denno et al., 2001; Langellotto & Denno,2001). Long wings confer an advantage over short-wingedmales when it comes to mate finding (Langellotto &Denno, 2001), but there is also a trade-off between flightcapability and reproductive output (Langellotto, Denno &Ott, 2000).

The above examples illustrate the role of habitatfragmentation in altering selection pressures for particulartraits of species. Typically, selection occurs on phenotypicvariation that occurs naturally within a species, but habitatfragmentation itself may also increase the amount and typesof phenotypic variation that are subject to natural selection.For instance, small fragments often contain poor-qualityhabitats that increase the environmental stresses experi-enced by individuals and populations (Lens, Van Dongen& Matthysen, 2002). These stresses can result in develop-mental instability of individuals, which is often shown inthe form of fluctuating asymmetry (Weishampel, Shugart &Westman, 1997). Fluctuating asymmetry (FA) was elevatedin populations of two gecko species inhabiting fragmentedversus continuous landscapes in western Australia (Sarre,1996) and FA rates for seven forest bird species in Kenyawere four to seven times greater for birds in the smallest,most degraded fragments sampled by Lens et al. (1999).Similarly, the bank vole Clethrionomys glareolus had greaterrates of FA in fragmented than in continuous landscapesin France (Marchand et al., 2003), as did centipedes infragmented Amazonian rainforests (Weishampel et al.,1997). Increased levels of FA have been correlated with

reductions in the growth rates and competitive ability ofa range of organisms (see reviews by Møller, 1997 andMøller & Thornhill, 1998), as well as reduced survivalprobabilities for the taita thrush Turdus helleri in east Africa(Lens et al., 2002). Furthermore, FA may also leave individ-uals more susceptible to predation and parasitism (Møller,1997; F. Thomas, Ward & Poulin, 1998). Interestingly, ameta-analysis by Møller & Thornhill (1998) indicated thatFA is a heritable trait, although the exact frequency withwhich FA is inherited is still being debated (Roff & Reale,2004). Moreover, it has been demonstrated that phenotypicchanges in symmetry can precede genetic changes that mayultimately lead to the fixation of asymmetrical traits in aspecies (Palmer, 2004). Hence, it now seems evident thatenvironmental stresses, such as those imposed by habitatfragmentation, can result in phenotypic changes thatmay ultimately lead to morphological divergence betweenisolated populations (Sarre, 1996).

(3 ) Synergies magnify the impacts offragmentation

(a ) Fragmentation and pollination

There are no data that unequivocally relate habitatfragmentation with long-term pollinator declines (Cane &Tepedino, 2001), perhaps because plant-pollinator systemsexhibit wide temporal variation (Roubik, 2001). However,habitat loss and fragmentation can significantly alter thenature of invertebrate pollinator communities and disruptplant-pollinator interactions (Rathcke & Jules, 1993; Kleinet al., 2003). For example, the number of social bee speciespollinating coffee crops decreased with isolation from forestedges (Klein et al., 2003), and the taxon richness of nativeinvertebrate pollinators in tropical forest fragments declinedwith fragment area (Aizen & Feinsinger, 1994). Pollinatorcommunities in small fragments were dominated instead bythe exotic honeybee Apis mellifera (Aizen & Feinsinger, 1994).Unfortunately, generalist pollinators that replace specialisednative species are frequently less effective pollinators, andmay result in reduced rates of outcrossing and hence lowergenetic variability of fragmented plant populations (Didhamet al., 1996; Steffan-Dewenter & Tscharntke, 2002). Thispoint was also demonstrated by Goverde et al. (2002), whofound that flowers in experimentally fragmented grasslandplots were visited less frequently by bumblebee pollinatorsthan were flowers in unfragmented control plots. Moreover,bumblebee foraging behaviour was altered by habitat frag-mentation, with lower visiting time per patch and greaterflight directionality and distance in fragments (Goverdeet al., 2002). However, in other cases introduced pollinatorsare able to replace sufficiently the loss of natives. Forinstance, the introduced African honeybee Apis melliferascutellata was a more efficient pollinator of a canopy tree infragmented Amazonian landscapes than were the nativespecies (Dick, 2001). Furthermore, the introduced honeybeedispersed pollen over greater distances, thereby expandingthe area of genetic neighbourhoods and possibly linkingfragmented with continuous populations (Dick, 2001; Dick,Etchelecu & Austerlitz, 2003).


Pollinators exhibit species- and scale-specific responsesto habitat loss and fragmentation. Steffan-Dewenter et al.(2002) showed that the abundance and species richness ofsolitary bees was positively correlated with the proportionof semi-natural habitat in the landscape at small scales ofup to 750 m (circular radius), whereas honeybee densitywas negatively correlated with semi-natural habitat in thelandscape at a much larger scale of 3000 m. These differ-ences occurred because of differences in individual specieslife histories. Solitary bees have more specific habitatrequirements and smaller foraging ranges than do honey-bees, leading to contrasting responses to habitat loss.These data clearly support the assertion of Cane (2001)that inter-patch movements and loss of nesting habitatmust be considered when investigating pollinator com-munities, rather than focusing solely on fragments of forageplants.

(b ) Fragmentation and disease

Deforestation has a significant effect on populations ofparasitic disease vectors, with anthropogenic conversionof forest to agricultural land-uses implicated in increasedabundances of the insect vectors for malaria, leishmaniasisand trypanosomiasis (Patz et al., 2000). Furthermore, habitatedges can strongly influence species interactions betweenhosts and pathogens (Fagan et al., 1999; Cantrell, Cosner& Fagan, 2001), but despite this the effect of habitatfragmentation on the dynamics of pathogens has receivedlittle attention (McCallum & Dobson, 2002). Nevertheless,it has been convincingly demonstrated that habitat frag-mentation can alter the prevalence of disease in a landscape.Langlois et al. (2001) found that deer mice Peromyscusmaniculatus in fragmented Canadian landscapes had ahigher hantavirus infection rate than in unfragmentedlandscapes, probably because habitat fragmentation forcesdeer mice to disperse over larger areas. In the northeasternU.S.A., Lyme disease also has a dramatically higher preva-lence in small forest fragments, because the vector, theblacklegged tick Ixodes scapularis, is exponentially moreabundant and has higher infection rates in small fragmentsthan in large fragments (Allan, Keesing & Ostfeld, 2003;Fig. 6). In model simulations, Hess (1994) showed thatgreater fragment isolation typically causes an increasedprobability of metapopulation extinction, but when host–pathogen interactions are important in host dynamics,then increasing landscape connectivity actually promoteddisease transmission, leading to an increased probability ofmetapopulation extinction. In these circumstances a morefragmented landscape of isolated patches would be prefer-able for restricting the spread of disease across a landscape(Hess, 1994). A similar conclusion was reached by Perkins& Matlack (2002), who found that increasing the degreeof fragmentation in Pinus spp. plantations could restrictthe spread of fusiform rust Cronartium quercuum (Holdenriederet al., 2004). However, later models by McCallum & Dobson(2002) have indicated that the benefits of corridors thatallow species to disperse throughout the landscape (e.g.increased colonisation of empty patches) typically outweighthe risks of increased disease transmission.

( c ) Fragmentation and climate change

Worryingly, recent models have indicated that habitatloss and fragmentation may increase a species’ susceptibilityto climate change, reducing their ability to survive simul-taneous changes in both factors (Travis, 2003). Duringperiods of climate change, insects typically shift their dis-tributions rather than adapt in situ (Hill et al., 2002). Forinstance, the northern distributional limits of manyEuropean butterflies have recently expanded northward asa result of 20th Century climate warming, and furtherexpansion is considered likely in the future (Hill et al., 2002;Parmesan et al., 1999). However, when populations areisolated by habitat fragmentation, range expansion isrestricted and populations may become more vulnerableto the effects of climate change and extreme weatherevents (Hill et al., 2002; McLaughlin et al., 2002; Opdam &

0 1 2 3 4 5 6 70.00

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Fig. 6. Synergistic interactions between habitat fragmentationand other drivers of population change, such as disease trans-mission, can magnify the impacts of fragmentation. Relation-ship between the prevalence of Lyme disease and forestfragment area in Dutchess County, New York. The density ofpotential disease vectors, nymphs of the tick Ixodes scapularis,is not only exponentially greater in small fragments (A), butthere is also a significant density-dependent increase in diseaseinfection rates of ticks in small fragments (B). Figure reproducedfrom Allan et al. (2003, p. 270).


Wascher, 2004). For example, in the western U.S.A., anincrease in yearly variability in precipitation rates amplifiedpopulation fluctuations in the checkerspot butterflyEuphydras editha bayensis and led to the local extinction of twoisolated populations (McLaughlin et al., 2002). Despite theobserved climatic changes over recent times, McLaughlinet al. (2002) considered that these checkerspot populationsmust have persisted through much larger historical vari-ations in climate, and have only recently become susceptibleto local extinction because of the greatly reduced distri-bution of suitable habitat. Similarly, metapopulations ofthe British tiger moth Arctia caja increased in variabilityand populations underwent a dramatic decline in abun-dance and distribution following a rise in winter tem-peratures (Conrad, Woiwood & Perry, 2002). In the U.K.,the synergistic effects of fragmentation and recent climatechange have led to a reduction in the geographic rangesizes of 30 out of 35 butterfly species in the last 30 years(Hill et al., 2002), with habitat specialist species exhibitingthe largest reductions in distribution and abundance(Warren et al., 2001). Similar effects have also been predictedfor butterflies in the Mediterranean (Stefanescu et al., 2004).

(d ) Fragmentation and human-modified disturbance regimes

The ecology of habitat fragments is often impacted byhuman-driven external disturbances that amplify theimpacts of fragmentation itself. Recent work suggests thatfocussing on changes in landscape configuration whileignoring these other anthropogenic effects is a dangerouslyinadequate strategy for conservation (Laurance &Cochrane, 2001). For instance, Amazonian forest remnantsare more accessible to hunters than continuous forest,perhaps because of the increased perimeter-area ratio offragments, but also because fragmentation is accompaniedby an influx of human migrants (Peres, 2001). Consequently,many large-bodied birds and mammals are persistentlyoverhunted in small fragments (Peres, 2001), leading directlyto their local extinction (Cullen, Bodmer & ValladaresPadua, 2000). In this case, the correlative link betweenfragmentation and species loss was indirect, and the directcause was over-exploitation due to a synergistic interactionbetween hunting and habitat fragmentation.

Similarly, fragments of woodland and shrubland inthe predominantly agricultural landscapes of southwestAustralia are more likely to be grazed and trampled bylivestock than continuous forest (Hobbs, 2001). These effectsare likely further amplified by the greater ease with whichsmall fragments and fragment edges are invaded byintroduced species (Robinson, Quinn & Stanton, 1995;Wiser et al., 1998; Hobbs, 2001; Yates, Levia & Williams,2004). For instance, trampling by cattle compacts soilstructure, reducing the regeneration ability of native treespecies that are already struggling with competition fromintroduced weeds (Hobbs, 2001). Moreover, the presenceof introduced animals may be essential for the persistence ofmany weeds that are unlikely to persist in fragments with-out the disturbances like external nutrient inputs fromcattle and increased soil turnover from rabbits (Hester &Hobbs, 1992; Hobbs, 2001).

Finally, forest fragments in the Brazilian Amazon arehighly susceptible to the penetration of fires that originate inthe surrounding agricultural matrix (Cochrane & Laurance,2002). This is because forest edges are associated withelevated rates of leaf litterfall (Sizer, Tanner & Kossmann-Ferraz, 2000) and tree damage and mortality (Lauranceet al., 1997, 1998), contributing to an increased standingfuel load (Cochrane & Laurance, 2002). Furthermore, theavailable fuel in forest fragments likely dries more rapidlyat edges than in forest interiors because of selective loggingthat opens the canopy, causing elevated desiccation rates(Cochrane & Laurance, 2002). Consequently, forest edgesare associated with increased fire frequency and intensity(Cochrane, 2001; Cochrane & Laurance, 2002). Unfor-tunately, the threat to forest remnants from fires in theBrazilian Amazon is amplified greatly by a positive feedbackmechanism between habitat loss and disturbance, wherebyforest fires increase the susceptibility of fragments to futurefires of greater intensity and cause elevated total defores-tation rates in the region (Cochrane et al., 1999).

VIII. IMPLICATIONS FOR FRAGMENTATION

RESEARCH

The amount of research being conducted on habitatfragmentation is increasing exponentially, as any simplebibliographic search will illustrate. Despite continued debateabout the relative importance of habitat fragmentation andhabitat loss (Fahrig, 2003; Hanski & Gaggiotti, 2004), it isabundantly clear that the size and spatial distribution ofhabitat remnants alters the patterns of species distributionand abundance within a landscape. Recent advances in ourunderstanding of habitat fragmentation, the importanceof landscape context and complex synergistic interactionswith other major drivers of biodiversity loss, have all addedconsiderably to a wider appreciation of the scope andmagnitude of the impacts of land use change. However,there are still many facets to the study of habitat frag-mentation that remain untested and only vaguely under-stood. Anthropogenic habitat fragmentation is a relativelyrecent phenomenon in evolutionary terms, and we stillhave little real understanding of its long-term implications.Species with certain traits, such as limited mobility orhigh trophic position, seem disproportionately affected byfragmentation and face the very real possibility of extinction.However, it remains unclear whether the long-term negativeeffects of fragmentation will be limited to a subset of specieswith a particular trait complex, or whether these suscep-tible species are merely the first to respond. Over largerspatial and temporal scales, species with quite differenttrait complexes may prove to be just as vulnerable tofragmentation.

While field experimental studies are becoming morecommon, controlled laboratory manipulations of micro-environments to investigate directly the physiological andbehavioural mechanisms underlying species responses tofragmentation have still not been widely undertaken. Trialsof this nature will be invaluable for determining the exact


process(es) underlying species responses, such as edgeavoidance, and will allow the development of specificmanagement actions to remedy, or at least alleviate, thespecies-level effects of habitat fragmentation in the field.These approaches could also be aided considerably bycontrolling statistically for the effects of phylogeneticallyrelated suites of traits.

Finally, a serious question must be asked about what weare doing with the knowledge we do have. The prevailingattitude toward reserve design is that we do not have achoice and must accept whatever conservation land isavailable (e.g. Saunders, Hobbs &Magules, 1991). This maybe true for most landscapes in temperate nations, but is nota viable argument when applied to many tropical nationswhere global concern about deforestation is currentlyfocussed (Laurance & Gascon, 1997). In these environmentsthere remains a significant biodiversity resource and theopportunity to plan and implement efficient reserve net-works based upon our current understanding of the effectsof habitat loss and fragmentation.

IX. CONCLUSIONS

(1) Habitat fragmentation is a pervasive feature ofmodern landscapes and has contributed to population de-cline in many species. Fragmentation impacts are effectedthrough changes in habitat area, the creation of habitatboundaries with their associated edge effects, and the iso-lation of habitat fragments. The relative intensity of each ofthese factors is mediated by the shape of the remnant habitatareas and the structure of the surrounding matrix habitat.

(2) Species responses to habitat fragmentation aregoverned by individual species’ traits. Species that arehighly susceptible to fragmentation are typically charac-terised by large body size, intermediate mobility, hightrophic level, high levels of habitat specialisation, and lowpre-fragmentation abundance. Synergies between thesetraits lead to a greater vulnerability of species with combi-nations of these traits in severely fragmented landscapes,than might otherwise be predicted from the simple additiveeffects of multiple traits considered individually.

(3) Habitat fragmentation does not occur in isolationfrom other threats to biodiversity. Synergistic interactionsamong multiple drivers of biodiversity loss may magnifythe detrimental impacts of fragmentation. For example,fragmentation can disrupt pollination systems, or increasethe rate of disease transmission, leaving populations inhabitat remnants susceptible to human encroachment, fireand introduced species, and may amplify the vulnerability ofspecies to climate change.

(4) There is a large literature that investigates theeffects of habitat fragmentation on species and communities.However, substantial questions remain unanswered. Whatrole does phylogeny play in determining species’ suscepti-bility to fragmentation? What are the physiological andbehavioural mechanisms underlying species responses tofragmentation? What are the long term implications ofhabitat fragmentation? Most importantly, can we predict

and mitigate the effects of habitat fragmentation in thefuture?

X. ACKNOWLEDGEMENTS

We thank Kendi Davies, Kath Dickinson, Lenore Fahrig,Jon Harding, Bill Laurance, Thomas Lovejoy, Ingolf Steffan-Dewenter, Amanda Todd, Teja Tscharntke and an anonymousreviewer for their comments on this manuscript. Tom Brooks,Kendi Davies, Felicia Keesing and Chris Thomas kindly gavepermission for us to reproduce figures from their publishedpapers.

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L E T T E RTemperature dependence of the functional response

Goran Englund,1* Gunnar Ohlund,1

Catherine L. Hein1,2 and Sebastian

Diehl1

1Department of Ecology and

Environmental Science, Umea

University, SE-901 87 Umea, Sweden2Climate Impacts Research Centre

(CIRC), Abisko Scientific Research

Station, SE-981 07 Abisko, Sweden

*Correspondence: E-mail:

[email protected]

AbstractThe Arrhenius equation has emerged as the favoured model for describing the temperature dependence of

consumption in predator–prey models. To examine the relevance of this equation, we undertook a meta-

analysis of published relationships between functional response parameters and temperature. We show that,

when plotted in lin-log space, temperature dependence of both attack rate and maximal ingestion rate exhibits a

hump-shaped relationship and not a linear one as predicted by the Arrhenius equation. The relationship

remains significantly downward concave even when data from temperatures above the peak of the hump are

discarded. Temperature dependence is stronger for attack rate than for maximal ingestion rate, but the thermal

optima are not different. We conclude that the use of the Arrhenius equation to describe consumption in

predator–prey models requires the assumption that temperatures above thermal optima are unimportant for

population and community dynamics, an assumption that is untenable given the available data.

KeywordsArrhenius, attack rate, functional response, handling time, optimum, parasitoid, predator, prey, response curve,

temperature.

Ecology letters (2011) 14: 914–921

INTRODUCTION

The relationship between the consumption rate of a predator and

the density of its prey, often referred to as the functional response,

is a mainstay in predator–prey theory. It was recognised early on

that this relationship is crucial for the dynamics of populations and

communities (Nicholson 1935; Holling 1959a), and subsequent

studies have explored a wide range of behaviours and environ-

mental conditions that influence functional responses (reviewed by

Jeschke et al. 2002). These studies have produced an impressive

diversity of functional response models: Jeschke et al. (2002) list as

many as 40 different types. One of these, the Holling�s type II

model (Holling 1959b), also known as the �disc equation�, has been

accorded the status of a �null-model�, and it is upon this that much

of modern predator–prey theory is built. This model describes the

number of prey eaten by a predator per time unit (E) as a

hyperbolic function of prey density (N), E = aN ⁄ (1 + ahN)

(Fig. 1a). The parameter a, often called the attack rate or search

efficiency, is the per capita prey mortality at low prey densities, and

h specifies the maximal intake rate (1 ⁄ h) that is observed at prey

densities high enough to cause satiation. Originally, h was defined

as the time needed to handle a prey item (Holling 1959b), but for

most predators the maximal intake is limited by the rate of gut

evacuation rather than the handling time (Jeschke et al. 2002).

Analogous equations have been proposed for parasitoids, but here,

the parameter h reflects the time needed for handling hosts (host

inspection, egg laying, etc.).

The effects of temperature on predator–prey dynamics received

little attention from theoretical population and community ecologists

during the twentieth century, and most published models that

included temperature dependence of consumption rates were detailed

and system specific (Wollkind & Logan 1978; Berry et al. 1991;

Petersen & Deangelis 1992; Collings 1995). More recently, predictions

of climatic warming have inspired a number of general theoretical

studies of temperature effects on predator–prey dynamics (Vasseur &

McCann 2005; van de Wolfshaar et al. 2008), interaction strength (Rall

et al. 2010) and food web connectance (Petchey et al. 2010).

Inspired by the Metabolic Theory of Ecology (MTE), these studies

have used the well-known Arrhenius equation to describe the

temperature dependence of functional response parameters. In its

original formulation, the Arrhenius equation describes the tempera-

ture dependence of chemical reactions. The reaction rate (y) is given

by y / e�Ea=Tk, where T is the absolute temperature, k is Boltzmann�sconstant, and Ea, which determines the strength of the temperature

dependence, is the activation energy of the reaction (Cornish-Bowden

2004). More recently, proponents of the MTE have suggested that the

Arrhenius equation also can serve as a mechanistic model for the

temperature dependence of basal metabolism and of a range of other

biological rates that are coupled to metabolism, including growth,

maximal consumption rate and development (Gillooly et al. 2001;

Brown et al. 2004; Savage et al. 2004). As all aerobic organisms, from

bacteria to mammals, share the same biochemistry of metabolism it

has been argued that a universal temperature dependence exists for all

ectothermic animals, and that this can be represented by the Arrhenius

equation. Gillooly et al. (2001) argued that the slope of this

relationship (Ea) should vary between 0.2 and 1.2. However, later it

was stated that the Ea value should be constrained between 0.6 and

0.7 (Gillooly et al. 2006; Allen & Gillooly 2007). Although the

mechanistic derivation of this prediction is unclear (see review by

Irlich et al. 2009), it was explicitly stated as being a prediction from

MTE by Gillooly et al. (2006) and Allen & Gillooly (2007).

Using the Arrhenius equation as a mechanistic representation for

the temperature dependence of physiological rates has been criticised

(Marquet et al. 2004; Clarke 2006; van der Meer 2006; Irlich et al.

2009), but the equation appears to be a useful empirical generalisation

for interspecific data concerning, for example, metabolism, digestion

rate and maximum population growth rate (Brown et al. 2004; Allen &

Gillooly 2007). Here, interspecific data refer to observations of the

performance of many different species, each studied at its optimal or

normal temperature. However, for population and community

Ecology Letters, (2011) 14: 914–921 doi: 10.1111/j.1461-0248.2011.01661.x

� 2011 Blackwell Publishing Ltd/CNRS

models, where the focus is usually on interactions between species

(e.g. van de Wolfshaar et al. 2008; Petchey et al. 2010), it is often more

relevant to consider intraspecific relationships (i.e. general patterns

describing the shape of species-specific response curves). For this type

of data, the relationship between temperature and the rate of

consumption or growth tends to be hump shaped rather than

exponential, as illustrated in Figs 1b–d (De Moed et al. 1998;

Angilletta 2009; Knies & Kingsolver 2010). Proponents of the

Arrhenius equation acknowledge this fact and argue that the equation

is valid for a �biologically relevant temperature range� (BTR) (Fig. 1d),

which is defined as spanning temperatures that are lower than the

optimal temperature, but high enough to yield positive growth (Savage

et al. 2004). In opposition to this approach, it can be argued that

temperatures outside the BTR are indeed relevant for ecological

interactions, especially if climate warming causes species to experience

temperatures higher than their optimum (Deutsch et al. 2008; Huey

et al. 2009). Moreover, a recent study of the temperature dependence

of intrinsic population growth rate suggests that relationships are not

exponential even at suboptimal temperatures (Knies & Kingsolver

2010).

Given that the Arrhenius equation is in the process of becoming

a generally accepted description of the temperature dependence of

parameters in models of trophic interactions (Savage et al. 2004;

Vasseur & McCann 2005; van de Wolfshaar et al. 2008; Petchey et al.

2010; Rall et al. 2010), it is important to evaluate it in relation to

available empirical data. Previous reviews of the temperature

dependence of consumption rates have focused on maximal intake

rates, often measured in the form of gut evacuation rates (He &

Wurtsbaugh 1993; Irigoien 1998), whereas attack rates have not been

reviewed. Here, we present a meta-analysis of studies that have

measured the temperature dependence of attack rates and maximal

intake rates of ectothermic animals. As the use of the Arrhenius

equation in dynamic population and community models has been

inspired by the MTE, we first test predictions from this theory, i.e. we

ask whether there is a universal exponential temperature dependence

of functional response parameters constrained within the range

10

100

0 10 20 30

Max

imum

inta

ke r

ate

Temperature (°C)

(b)

10

100

–42 –40 –38

Max

imum

inta

ke r

ate

Temperature (–1/kT)

(d)

I

BTRI

10

100

–42 –40 –38

Max

imum

inta

ke r

ate

Temperature (–1/kT)

(c)

0

5

10

15

20

0 25 50 75

Num

ber

of p

rey

eate

n

Prey density

25° C

20° C

30° C

15° C

10° C

(a)

Figure 1 The panels illustrate the different types of data and analyses used in the meta-analysis for one specific example. a) The functional response of the parasitoid Aphidius

matricariae to densities of the cotton aphid, Aphis gossypi at different temperatures (Zamani et al. 2006). Plotted lines represent type II functional responses fitted to the data using

the disc equation. Each marker (squares, triangles, etc.) denotes the mean of six replicates. Note that the lines for 20 �C and 25 �C are crossing at temperatures higher than

those shown in the graph. b) Maximal intake rates estimated as 1 ⁄ h from the functional responses fitted to the data in panel a and plotted against temperature (�C). Error bars

denote 1 standard error. c) Maximal intake rates plotted against inverse temperature (Kelvin) and scaled with the Boltzmann constant (k). The solid line represents the

Arrhenius model (eqn 1) and the dotted line represents the quadratic model (eqn 2), fitted to the data. d) The same data as in panel c with the horizontal bar indicating the

�biologically relevant temperature range� (BTR). The solid line represents the Arrhenius model (eqn 1) and the dotted line represents the quadratic model (eqn 2) fitted to

the data that fall within this range.

Letter Temperature dependence of consumption 915


predicted by the MTE (Ea = 0.6–0.7). Second, we examine whether

attack rate and maximal intake rate exhibit the same temperature

responses. This question is of interest because some models have

assumed that the two responses are equal (Vasseur & McCann 2005;

van de Wolfshaar 2006; van de Wolfshaar et al. 2008). Finally,

we examine whether the temperature responses of attack rate and

maximal intake rate vary between habitats, taxonomic groups, or

functional groups of predators and prey. We find that the temperature

dependence of attack rate and maximal intake rate is hump-shaped

rather than exponential and conclude that the Arrhenius equation

should not be used to describe the thermal dependence of functional

response parameters, especially in models exploring the influence of

temperature on population and community dynamics.

METHODS

Literature search

We searched the Web of Science and reference lists in published

papers and found 48 studies that could be used to estimate the effect

of temperature on attack rates and maximal intake rates. All studies

encountered that were published before 2010 were included. As some

studies reported data for several species or life stages (e.g. eggs and

adults), the total number of observations was 56. The studied

consumers included predators (N = 38), parasitoids (N = 15) and

filter feeders (N = 3). The majority of the consumers studied were

insects (N = 36), followed by fish (N = 8), crustaceans (N = 6) and

mites (N = 4). The studies included are listed in the Supporting

information, Table S1.

Several authors have noted that meta-analyses of the same body

of literature can reach different conclusions because different

criteria are used when selecting studies (Englund et al. 1999;

Whittaker 2010). There is no consensus on how to deal with this

problem (e.g. Lajeunesse 2010; Whittaker 2010), and we chose to

follow the recommendation of Lajeunesse (2010) to include all

relevant studies and use auxiliary information to evaluate variation

between studies.

Deriving attack rates and maximal intake rates from data

Some studies reported direct observations of attack rates and maximal

intake rates made at different temperatures, but in most cases, these

two parameters were estimated by fitting a functional response model

to data on consumption rates at different prey densities (see Fig. 1a

for an example). If the original study did not provide parameter

estimates or used an inappropriate functional response model, we

estimated attack rates and maximal intake rates using data extracted

from graphs or tables. For experiments without appreciable prey

depletion, we used Holling�s disc-equation, E = aN ⁄ (1 + ahN),

where E is the number of prey eaten, N is prey density, a is attack

rate, and h is handling time. For cases with prey depletion, the

integrated form of the disc equation, E ¼ N ð1� eaðhE�1ÞÞ, was used.

For data on parasitoids, we used either the disc equation or Rogers

(1972) random parasitoid equation, Ep ¼ N ð1� e�aP=ð1�ahN ÞÞ, where

P is the density of parasitoids and Ep is the number of hosts

parasitised. The former was used for cases involving superparasitism,

where the recorded response was the number of eggs laid. For data

with a pronounced sigmoid shape, we used the maximal attack rate as

defined by the slope of the steepest part of the response curve. This

slope was estimated by fitting a type III function to the data, that is,

E = aN 2 ⁄ (1 + ahN 2), and calculating the first derivative at the

inflection point.

Modelling temperature responses

We tested whether the slopes of temperature responses for attack

rates and maximal intake rates were within the range predicted by the

MTE (0.6–0.7). For each study, we described attack rates (a) and

maximal intake rates (Imax = 1 ⁄ h) as functions of )1 ⁄ (kT ), where k is

Boltzmann�s constant given in eV K)1 (= 8.617 * 10)5 eV K)1), and

T is temperature in Kelvin (see Gillooly et al. 2001). Although

)1 ⁄ (kT ) measures energy (the unit is eV)1), it is often referred to as

�Arrhenius temperature� and we follow this convention here.

�Arrhenius temperature� and untransformed temperature scale almost

identically (Figs 1b and c). Use of the former allowed us, however, to

fit the Arrhenius equation:

Y ¼ ceEað�1=kT Þ ð1Þ

to the data (Fig. 1c), where Y is the attack rate or maximal intake rate,

c is a fitted constant and Ea is the fitted activation energy (eV) that

describes the slope of the response (Gillooly et al. 2001).

In c. 40% of the studies, attack rate or maximal intake rate exhibited

a maximum (subsequently called a �thermal optimum�) within the

investigated temperature range. To restrict the analyses to the BTR,

we followed Irlich et al. (2009) and excluded all data points above the

temperature where the highest rate was observed. Subsequently, eqn 1

was fitted to these restricted data sets (Fig. 1d).

To examine whether the temperature responses of attack rates and

maximal intake rates deviated from the Arrhenius model, we fitted a

quadratic model:

Y ¼ cebð�1=kT Þþqð�1=kT Þ2 ð2Þto the data, where c, b and q were fitted parameters. We fitted eqn 2 to

three data sets: (1) the full data set (excluding studies that only

included two temperatures, n = 49); (2) the restricted BTR data set

(excluding data above the thermal optimum, n = 40); and (3) a data set

including only studies that exhibited a thermal optimum (hereafter

�optimum data�, n = 22 for attack rate and n = 23 for maximal intake

rate). When b is positive and q is negative, the quadratic model

describes a thermal optimum (Fig. 1c) or a downwards concave

relationship (Fig. 1d). In such cases, b can no longer be interpreted as

the activation energy.

Meta-analyses

We used the parameter estimates from the curve fitting exercises in

four types of meta-analyses:

(1) To test whether the temperature dependence of functional

response parameters is quantitatively constrained to the range

predicted by the MTE, we performed a meta-analysis using the

Ea values obtained from fitting the Arrhenius model (eqn 1) to

both the full data set and the BTR data set.

(2) To test whether temperature relationships deviated qualitatively

from the Arrhenius model, we performed a meta-analysis using

the values of b and q obtained from fitting the quadratic model

(eqn 2) to the full and the BTR data sets.

916 G. Englund et al. Letter


(3) To characterise the nonlinear temperature relationship found in

step 2 more accurately, we repeated the meta-analysis using b

and q, but only included studies where a thermal optimum was

observed over the investigated temperature range (�optimum

data�).(4) We tested whether heterogeneity in fitted activation energies

could be explained by the type of consumer (predator,

parasitoid or filter feeder), the taxonomic classifications of

predators and prey (Table S1 in the Supporting information), or

the type of habitat (aquatic or terrestrial).

Hypothesis tests were based on weighted means, as is common

in meta-analyses. This approach has two important advantages over

non-weighted analyses, which are normally used in tests of body

size and temperature scaling (Brown et al. 2004; Knies &

Kingsolver 2010). It allows the down-weighting of studies with

low precision, and it allows testing of the hypothesis that all studies

reflect the same underlying slope, even in situations where the

processes generating heterogeneity are unknown (Hedges & Olkin

1985). We chose not to use an analysis based on phylogenetic

relationships because the functional response is the result of the

interaction between two species, predators and prey, which are

often only distantly related.

The inverse of the sample variance was used to weight each

observation (Hedges & Olkin 1985). Observations for which the

sample variance could not be extracted were weighted using the mean

weight of the studies for which the variance could be extracted. Four

observations were excluded because the distance to the mean was

> 5.5 SD. If a study provided several estimates for the same predator–

prey combination, we formed a weighted mean using the inverse of

the sample variance as the weight. This mean value was then used as

an observation in the meta-analyses.

MetaWin (Rosenberg et al. 1997) was used for statistical analyses.

We used a fixed effects model and Cochran�s Q-statistic (Hedges &

Olkin 1985) to test the hypothesis that all studies estimated a single,

common slope. As the assumption of a common slope was rejected in

all tests, we used random effects models to test the significance of

differences between groups and to calculate confidence intervals

(Hunter & Schmidt 2000).

Visualising temperature responses

To visualise commonalities in the temperature dependencies of attack

rates and maximal intake rates across studies, we plotted the data

from all studies that included a thermal optimum (optimum data set)

in a single graph. As maximal attack rates, maximal intake rates and

the thermal optima varied between studies, we plotted all data on a

standardised scale while preserving the shapes of the original

response curves. To do so, we rescaled observed attack and intake

rates in relative units using Yi,s = Yi ⁄ Yi,max. Here, Yi and Yi,s are

vectors containing the observed and standardised rates at different

temperatures from study i (Fig. 1c), and Yi,max is the maximum rate

estimated from a second order polynomial fitted to the data in study

i. Temperatures were rescaled to the mean optimal temperature, that

is, the mean temperature at which the thermal optimum was

observed across studies. Temperatures were rescaled as

Ti;s ¼ Ti � Ti;opt þ Topt , where Ti and Ti,s are vectors containing the

observed and rescaled temperatures used in study i, Ti;opt is the

optimal temperature in study i, and Topt is the mean optimal

temperature across all studies. Only studies where the investigated

temperature range included the optimum could be standardised using

this method (N = 22 for attack rate and N = 23 for maximal intake

rate). To illustrate the central tendency of the rescaled data, we fitted

a LOWESS model, with the tension parameter set to 0.55 (Wilkinson

2000).

RESULTS

The temperature dependence of attack rates and maximal intake rates

did not fit the predictions of the MTE; fitted activation energies

covered a much wider range than that predicted, that is, 0.6–0.7, and

the relationships were not exponential. Using the BTR data set, the

mean estimate of the coefficient Ea for attack rate was higher than

predicted, whereas the mean coefficient for maximal intake rate did

not deviate significantly from the predicted range of 0.6–0.7 (Fig. 2b).

The variance around these means was, however, very large. Highly

significant between-study heterogeneity was noted for both attack rate

and handling time (Q = 373.6, d.f. = 48, P < 10)10 and Q = 1144.3,

–1 –0.5 0 0.5 1

Scaling coefficient

Imax

Attack rate

Linear coefficient

Quadratic coefficient

(a)

Attack rate

–1 –0.5 0 0.5 1

Scaling coefficient

Attackrate

Linear coefficient


(b)

Attackrate

–1.5 –1 –0.5 0

Scaling coefficient


(c)

Attackrate

All data BTR data Optimum data

ImaxImax

Imax

Imax

Figure 2 Scaling coefficients (mean ± 95% CI) for the temperature dependence of attack rates and maximal intake rates (Imax) calculated using a) all data, b) data at

temperatures below the thermal optimum (�BTR data�) and c) all data from studies in which a thermal optimum was observed (�optimum data�). The upper two bars in each

panel (labelled �linear coefficient�) represent estimates of the coefficient Ea in eqn 1 (Y ¼ ceEa ð�1=kT Þ). For comparison, the dotted lines indicate the range of Ea predicted by

the Metabolic Theory of Ecology (0.6–0.7). The lower two bars in each panel (labelled �quadratic coefficient�) represent estimates of the quadratic coefficient q in eqn 2

(Y ¼ cebð�1=kT Þþqð�1=kT Þ2 ). Estimates of the linear coefficient b in eqn 2 (not shown) were significant and positive. The sample sizes were: a) N = 56 for linear coefficients,

N = 49 for quadratic coefficients, b) N = 53 for linear coefficients, N = 40 for quadratic coefficients, c) N = 22 for maximal intake rate, N = 25 for attack rate.



d.f. = 48, P < 10)10), and most observations (95% for attack rate and

89% for maximal intake rate) fell outside the range 0.6–0.7 (Fig. 3).

Both temperature relationships were hump shaped as indicated by

significant positive linear terms b (data not shown) and negative

quadratic terms q (Figs 2a and b). This was true whether we used the

full data set (Fig. 2a) or the BTR data set (Fig. 2b). The magnitude of

q was smaller, but still significantly negative when we used the BTR

data set instead of the full data set (Fig. 2b).

The attack rate and the maximal intake rate depended similarly on

temperature. Both attack rate and maximal intake rate increased with

temperature (Figs 2a and b linear coefficients) and shared the same

thermal optimum (mean ± CI95% was 24.9 ± 2.5 �C for attack rate

and 26.1 ± 2.3 �C for maximal intake rate). The attack rate was,

however, more strongly affected by temperature than was the maximal

intake rate, both above and below the optimal temperature (Fig. 4).

The linear slope (Ea) of the attack rate estimated from eqn 1 was

significantly steeper than the maximal intake rate using either the full

data set (Q = 4.58, P < 0.05, Fig. 2a) or the BTR data set (Q = 9.86,

P < 0.005, Fig. 2b). Similarly, the weighted mean values of the

quadratic term q, which exclusively determines the steepness of the

function described by eqn 2 on both sides of its maximum, were

significantly higher for the attack rate than for the maximal intake rate

(Fig. 2c, Q = 6.92, P < 0.005).

Some of the variation we found in Ea (Fig. 3) could be explained by

the type of predator and by taxonomic differences between predators.

Using Ea values from the Arrhenius model (eqn 1) fitted to the BTR

data set, we found that the scaling coefficients for attack rate Ea varied

between taxonomic groups of predators (fish < insects < crustaceans

» mites), and both attack rate and maximal intake varied significantly

between different types of consumers (Table 1). However, scaling

coefficients did not differ between taxonomic groups of prey or

between aquatic and terrestrial habitats. It should be noted that sample

sizes were low for several of the groups, indicating that the observed

patterns may change if more data can be included.

DISCUSSION

The Arrhenius equation has emerged as the preferred model for

incorporating temperature dependence of consumption and growth

into general population and community models (Savage et al. 2004;

Vasseur & McCann 2005; van de Wolfshaar et al. 2008; Petchey et al.

2010; Rall et al. 2010). This practice has been inspired by recent

developments of the MTE. When evaluating the usefulness of the

Arrhenius model we, therefore, first examine the claims made by

MTE. According to this theory, there is a universal temperature

0

5

10

–0.2

–0.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Attack rate

0

5

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Scaling coefficient

Maximum intake rate

No

of o

bser

vatio

ns

Figure 3 Frequency distributions of the linear scaling coefficients for attack rates

and maximal intake rates estimated from the BTR data set using eqn 1. The shaded

bars indicate the range 0.6–0.7, which is that predicted by the Metabolic Theory of

Ecology.

0

0.5

1

1.5

0 10 20 30 40

Rate

Temperature (°C)

Maximum intake rate

Attack rate

Figure 4 Standardised attack rates (filled diamonds and solid, blue line) and

maximal intake rates (open diamonds and broken, red line). Data were standardised

as described in the Methods section and centred around the respective optimum

temperature (24.9 �C for attack rate and 26.1 �C for maximal intake rate). Only

studies from which the value for a thermal optimum could be estimated were

included. Lines were fitted using a LOWESS model.

Table 1 Temperature dependence of attack rate and maximal intake rate for

different types of predators and for predators and prey living in different habitats or

belonging to different taxonomic groups. Approximate 95% confidence intervals

are given within parentheses. Coefficients were estimated by fitting eqn 1 to data for

suboptimal temperatures (biologically relevant temperature range data). Q-values

refer to Cochran�s Q-statistic (Hedges & Olkin 1985), which is used to test for

differences between groups

Attack rate Q p Maximal intake rate Q p N

Predator type

Predator 0.74 (± 0.11) 7.55 0.02 0.45 (± 0.15) 6.82 0.03 37

Parasitoid 0.98 (± 0.25) 0.84 (± 0.33) 13

Filter feeder 1.15 (± 0.77) 0.82 (± 1.10) 3

Predator taxon

Insect 0.79 (± 0.12) 8.84 0.02 0.49 (± 0.15) 3.47 n.s. 35

Fish 0.59 (± 0.19) 0.80 (± 0.19) 8

Crustacean 1.12 (+0.51) 0.42 (± 0.50) 5

Mite 1.17 (± 0.67) 0.51 (± 0.64) 4

Prey taxa

Insect 0.75 (± 0.13) 5.85 n.s. 0.58 (± 0.16) 1.91 n.s. 34

Crustacean 0.69 (± 0.33) 0.29 (± 0.49) 7

Mite 0.98 (± 0.43) 0.53 (± 0.48) 6

Algae 1.15 (± 0.81) 0.82 (± 1.12) 3

Habitat

Aquatic 0.81 (± 0.16) 0.24 n.s. 0.60 (± 0.19) 0.74 n.s. 21

Terrestrial 0.76 (± 0.14) 0.49 (± 0.17) 32



dependence for biological rates that can be derived from the enzyme

kinetics of basal metabolism (Brown et al. 2004). Specifically, it is

hypothesised that temperature scaling coefficients are constrained to

the range 0.6–0.7 eV, with a mean value of 0.65 (Gillooly et al. 2006;

Allen & Gillooly 2007; see also the review by Irlich et al. 2009).

The existence of a universal temperature dependence for attack rates

and maximal intake rates was not supported by our data. All analyses

indicated that there was highly significant heterogeneity, and as many as

89–95% of the observations fell outside the 0.6–0.7 range of activation

energies predicted by the MTE (Fig. 3). Similar conclusions have been

reached for metabolic rate and development rate (Irlich et al. 2009), and

for fitness curves (Knies & Kingsolver 2010). More detailed analyses

showed that some of this heterogeneity occurred because the

temperature dependence varied between taxonomic groups and ⁄ or

types of consumers (Table 1). Significant heterogeneity remained,

however, after accounting for these effects (tests not shown).

An additional source of heterogeneity was suggested by our finding

that relationships were concave downwards rather than linear in plots of

log(rate) vs. inverse temperature, even when data were restricted to

temperatures below the optima. If the true response is concave, then the

slope of a fitted straight line will depend on the range of temperatures

investigated, relative to the position of the optimum. Thus, heteroge-

neity may occur because different studies investigated different

temperature ranges. The finding that maximal intake rate and attack

rate had different temperature responses also argues against the

existence of a universal temperature dependence.

Even though a universal temperature dependence was not

supported by the data, it can be argued that the Arrhenius equation

may be useful as a coarse empirical generalisation. For minimal or

strategic predator–prey models, tractability requires a high degree of

simplification. Thus, at least for very general research questions, it may

be reasonable to ignore the fact that the temperature response is

concave in lin-log space, or that it differs between attack rate and

maximal intake rate. However, using the Arrhenius equation as an

empirical generalisation can only be justified if we can ignore

interactions that occur at temperatures above the optimum, because in

this range, the Arrhenius model predicts an increasing response when

it is, in fact, decreasing.

A crucial question is therefore whether it is reasonable to consider

temperatures at and above the optimum as being outside of the BTR

(sensu Savage et al. 2004). The answer to this question depends on the

match between performance optima and the temperature experienced

in the habitat where the organisms occur. If thermal optima are, in

general, higher than environmental temperatures, then it makes sense

to use the Arrhenius equation. This question has recently received

interest because the effects of future warming on ecological

communities critically depend on its answer (Deutsch et al. 2008;

Huey et al. 2009; Asbury & Angilletta 2010). Several empirical data sets

do indeed suggest that thermal optima often are higher than

environmental temperatures (Deutsch et al. 2008; Huey et al. 2009).

However, there are important problems that complicate the interpre-

tation of these data. It is likely that, to some extent, these patterns

reflect experimental artefacts. Thermal optima of the most common

performance measures, that is, individual and population growth rates,

are usually estimated in laboratory experiments where organisms are

fed ad libitum and temperatures are kept constant. In contrast, natural

conditions are typically associated with scarcity of food and variable

temperatures. As reduced food intake rate lowers the thermal

optimum, it is likely that optima estimated in the laboratory are too

high (Elliott 1982; Boehlert & Yoklavich 1983). This effect can be

substantial; Elliott (1982) found that the thermal growth optimum of

brown trout varied from 4 oC to 14 oC, depending on food availability.

Also, the use of constant temperatures may lead to overestimated

thermal optima if response curves are skewed to the left (Martin &

Huey 2008).

The observed discrepancy between environmental temperatures and

thermal optima observed in laboratory experiments may also reflect

the fact that the mean annual temperature is not a relevant descriptor

of the temperature regime in habitats with seasonal temperature

variations. In high latitude habitats, the mean annual temperature

mainly reflects conditions during the long winter when many

ectotherms do not feed or experience much predation (Irlich et al.

2009). Activity is usually concentrated during a short period in the

summer, and it is the temperature regime during this period that is

most crucial for long-term population dynamics. A proper measure of

temperature, that accurately reflects the influence of temperature on

population dynamics in seasonal habitats, would be a weighted mean

temperature, where the weights describe the influence of different

temperatures on predator–prey dynamics. Performing such calcula-

tions requires information about the temperature dependence of birth

and mortality rates, which is lacking for most species. Thus, given that

we lack the data required to evaluate the match between thermal

optima and local temperature regimes in seasonal environments, we

suggest evaluation of this relationship in habitats with little seasonal

temperature variation. In both tropical insects (Deutsch et al. 2008)

and tropical lowland lizards (Huey et al. 2009), there is a good match

between habitat or body temperatures and thermal optima estimated

in laboratory experiments. Other studies show that even rather small

increases above the habitat mean temperature lead to decreased

performance, for example, in coral reef organisms (Baker et al. 2008;

Munday et al. 2008; Donelson et al. 2010) and in marine fish and

subtidal invertebrates in Antarctica (Peck et al. 2004a,b; Portner et al.

2007). These data suggest that we need to consider temperatures

higher than the optima when modelling predator–prey dynamics.

Thus, we cannot recommend the Arrhenius equation as a general

model for describing the thermal dependence of consumption.

We emphasise that our conclusion concerns intraspecific data. It is

not applicable to models of ecosystem processes, such as primary

production or decomposition, where it may be reasonable to use

scaling relations based on between-species data, because temperature

changes may lead to a succession of species. Note also that the

Arrhenius equation may serve well in models of species living at the

lower thermal limit of their range.

Irrespective of whether thermal optima have to be taken into

account, our results suggest that, as a generalisation across all studies,

attack rate has a steeper temperature response than maximal intake

rate (Fig. 4). For predators, but not parasitoids, the two parameters

often reflect fundamentally different processes (Jeschke et al. 2002).

Maximal intake rate is intimately coupled to the physiology of the

digestive apparatus for most predators. In contrast, attack rate

involves both predators and prey and largely reflects behavioural

processes such as search, attack, hiding and flight. Attack success will

often be influenced by the difference in behavioural performance

between the predator and its prey, and activities such as searching for

prey and attacking can cease if the expected pay-off is too low. Such

cost–benefit considerations may often involve three trophic levels.

For example, activity at temperatures where movement capacity is

reduced may expose ectothermic consumers to a high risk of



predation from birds and mammals. The ectothermic consumers�expected attack success may then be too low given this predation risk.

Thus, we hypothesise that behavioural decisions, rather than

differences in enzyme activity, cause the response curve to be steeper

for attack rate than for maximal intake rate.

The different thermal sensitivities of attack rate and maximal intake

rate imply that consumption is more temperature-sensitive at low prey

densities, where attack rate limits consumption, and less sensitive

at high prey densities, where digestion or handling limits consumption.

A second consequence of the steeper scaling of attack rate is that

warming will lead to increased specialisation and decreased connec-

tance, as long as temperatures are below the thermal optima (Petchey

et al. 2010).

As a final remark, we note that using hump-shaped temperature

response curves instead of the Arrhenius equation in predator–prey

models has important implications. Model results with respect to the

effects of temperature, which are based on Arrhenius scaling, will

often be reversed at temperatures higher than the thermal optima of

the organisms. For example, Vasseur & McCann (2005) investigated

temperature effects in a simple predator–prey model and found that

warming may push a system from a stable equilibrium to limit cycles.

The critical assumption underlying this result is that the temperature

relationship is steeper for consumption than for consumer metabo-

lism. Replacing the Arrhenius equation with a hump-shaped response

curve for consumption means that the original prediction may hold

for low temperatures, but that warming will stabilise dynamics at

temperatures near the optimum, where the temperature dependence

of consumption will inevitably be much shallower – or even exhibit

the opposite response – than that of metabolism. At even higher

temperatures, where ingestion is too low to meet metabolic demands,

consumer extinction can be expected. More generally, we expect that

the responses of communities to climate warming will, to a large

extent, reflect between-species differences in thermal optima. The

outcome of pair-wise competitive or predatory interactions will often

be reversed if warming pushes one of the interacting species above its

thermal optimum. Thus, we argue that our understanding of the

effects of warming on communities could be greatly enhanced by

incorporating hump-shaped temperature–response curves into general

models of species interactions (e.g. Mitchell & Angilletta 2009).

ACKNOWLEDGEMENTS

The study was made possible by a grant from the Swedish Research

Council for Environment, Agricultural Sciences and Spatial Planning

(FORMAS) to GE. We thank Barbara Giles, Andrew Clarke and three

anonymous reviewers for comments on the text.

AUTHORSHIP

GE and GO conceived the study. GE, GO and CLH extracted data.

GE performed meta-analyses and wrote the first draft of the parts

other than introduction. GO wrote the first draft of the introduction.

SB rewrote part of the first draft and suggested additional analyses.

All authors contributed substantially to the revision of the manuscript.

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SUPPORTING INFORMATION

Additional Supporting Information may be found in the online

version of this article:

Table S1 Studies included in the meta-analysis of temperature effects

on functional response parameters.

As a service to our authors and readers, this journal provides

supporting information supplied by the authors. Such materials are

peer-reviewed and may be re-organised for online delivery, but are not

copy-edited or typeset. Technical support issues arising from

supporting information (other than missing files) should be addressed

to the authors.

Editor, Andrew Liebhold

Manuscript received 30 March 2011

First decision made 2 May 2011

Second Decision made 7 June 2011

Manuscript accepted 10 June 2011



1575

Life is almost certainly the most complex and diversephysical system in the universe, covering more than 27 ordersof magnitude in mass, from the molecules of the genetic codeand metabolic process up to whales and sequoias. Organismsthemselves span a mass range of over 21 orders of magnitude,ranging from the smallest microbes (10–13·g) to the largestmammals and plants (108·g). This vast range exceeds that ofthe Earth’s mass relative to that of the galaxy (which is ‘only’18 orders of magnitude) and is comparable to the mass of anelectron relative to that of a cat. Similarly, the metabolicpower required to support life over this immense range spansmore than 21 orders of magnitude. Despite this amazingdiversity and complexity, many of the most fundamentalbiological processes manifest an extraordinary simplicitywhen viewed as a function of size, regardless of the class ortaxonomic group being considered. Indeed, we shall arguethat mass, and to a lesser extent temperature, is the primedeterminant of variation in physiological behaviour when

different organisms are compared over many orders ofmagnitude.

Scaling with size typically follows a simple power lawbehaviour of the form:

Y = Y0Mbb·, (1)

where Y is some observable biological quantity, Y0 is anormalization constant, and Mb is the mass of the organism(Calder, 1984; McMahon and Bonner, 1983; Niklas, 1994;Peters, 1986; Schmidt-Nielsen, 1984). An additionalsimplification is that the exponent, b, takes on a limited set ofvalues, which are typically simple multiples of 1/4. Amongthe many variables that obey these simple quarter-powerallometric scaling laws are nearly all biological rates, times,and dimensions; they include metabolic rate (b�3/4), lifespan(b�1/4), growth rate (b�–1/4), heart rate (b�–1/4), DNAnucleotide substitution rate (b�–1/4), lengths of aortas andheights of trees (b�1/4), radii of aortas and tree trunks

The Journal of Experimental Biology 208, 1575-1592Published by The Company of Biologists 2005doi:10.1242/jeb.01589

Life is the most complex physical phenomenon in theUniverse, manifesting an extraordinary diversity of formand function over an enormous scale from the largestanimals and plants to the smallest microbes andsubcellular units. Despite this many of its mostfundamental and complex phenomena scale with size in asurprisingly simple fashion. For example, metabolic ratescales as the 3/4-power of mass over 27 orders ofmagnitude, from molecular and intracellular levels up tothe largest organisms. Similarly, time-scales (such aslifespans and growth rates) and sizes (such as bacterialgenome lengths, tree heights and mitochondrial densities)scale with exponents that are typically simple powers of1/4. The universality and simplicity of these relationshipssuggest that fundamental universal principles underlymuch of the coarse-grained generic structure andorganisation of living systems. We have proposed a set of

principles based on the observation that almost all life issustained by hierarchical branching networks, which weassume have invariant terminal units, are space-filling andare optimised by the process of natural selection. We showhow these general constraints explain quarter powerscaling and lead to a quantitative, predictive theorythat captures many of the essential features ofdiverse biological systems. Examples considered includeanimal circulatory systems, plant vascular systems,growth, mitochondrial densities, and the concept of auniversal molecular clock. Temperature considerations,dimensionality and the role of invariants are discussed.Criticisms and controversies associated with this approachare also addressed.

Key words: allometry, quarter-power scaling, laws of life, circulatorysystem, ontogenetic growth.

Summary

Introduction

Review

The origin of allometric scaling laws in biology from genomes to ecosystems:towards a quantitative unifying theory of biological structure and organization

Geoffrey B. West1,2,* and James H. Brown1,3

1The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA, 2Los Alamos National Laboratory,Los Alamos, NM 87545, USA and 3Department of Biology, University of New Mexico, Albuquerque, NM 87131, USA

*Author for correspondence (e-mail: [email protected])

Accepted 14 March 2005

THE JOURNAL OF EXPERIMENTAL BIOLOGY

1576

(b�3/8), cerebral gray matter (b�5/4), densities ofmitochondria, chloroplasts and ribosomes (b=–1/4), andconcentrations of ribosomal RNA and metabolic enzymes(b�–1/4); for examples, see Figs·1–4. The best-known of thesescaling laws is for basal metabolic rate, which was first shownby Kleiber (Brody, 1945; Kleiber, 1932, 1975) to scaleapproximately as Mb

3/4 for mammals and birds (Fig.·1).Subsequent researchers showed that whole-organismmetabolic rates also scale as Mb

3/4 in nearly all organisms,including animals (endotherms and ectotherms, vertebrates andinvertebrates; Peters, 1986), plants (Niklas, 1994), andunicellular microbes (see also Fig.·7). This simple 3/4 powerscaling has now been observed at intracellular levels fromisolated mammalian cells down through mitochondria to theoxidase molecules of the respiratory complex, therebycovering fully 27 orders of magnitude (Fig.·2; West et al.,2002b). In the early 1980s, several independent investigators(Calder, 1984; McMahon and Bonner, 1983; Peters, 1986;Schmidt-Nielsen, 1984) compiled, analyzed and synthesizedthe extensive literature on allometry, and unanimouslyconcluded that quarter-power exponents were a pervasivefeature of biological scaling across nearly all biologicalvariables and life-forms.

Another simple characteristic of these scaling laws is theemergence of invariant quantities (Charnov, 1993). Forexample, mammalian lifespan increases approximately asMb

1/4, whereas heart-rate decreases as Mb–1/4, so the number of

heart-beats per lifetime is approximately invariant (~1.5�109),independent of size. A related, and perhaps more fundamental,

invariance occurs at the molecular level, where the number ofturnovers of the respiratory complex in the lifetime of amammal is also essentially constant (~1016). Understanding theorigin of these dimensionless numbers should eventually leadto important fundamental insights into the processes of agingand mortality. Still another invariance occurs in ecology, wherepopulation density decreases with individual body size asMb

–3/4 whereas individual power use increases as Mb3/4, so the

energy used by all individuals in any size class is an invariant(Enquist and Niklas, 2001).

It seems impossible that these ‘universal’ quarter-powerscaling laws and the invariant quantities associated with themcould be coincidental, independent phenomena, each a‘special’ case reflecting its own unique independent dynamicsand organisation. Of course every individual organism,biological species and ecological assemblage is unique,reflecting differences in genetic make-up, ontogeneticpathways, environmental conditions and evolutionary history.So, in the absence of any additional physical constraints, onemight have expected that different organisms, or at least eachgroups of related organisms inhabiting similar environments,might exhibit different size-related patterns of variation instructure and function. The fact that they do not – that the dataalmost always closely approximate a power law, emblematicof self-similarity, across a broad range of size and diversity –raises challenging questions. The fact that the exponents ofthese power laws are nearly always simple multiples of 1/4poses an even greater challenge. It suggests the operation ofgeneral underlying mechanisms that are independent of the

specific nature of individual organisms.We argue that the very existence of such

ubiquitous power laws implies the existenceof powerful constraints at every level ofbiological organization. The self-similarpower law scaling implies the existence ofaverage, idealized biological systems, whichrepresent a ‘0th order’ baseline or point ofdeparture for understanding the variationamong real biological systems. Realorganisms can be viewed as variations on, orperturbations from, these idealized normsdue to influences of stochastic factors,environmental conditions or evolutionaryhistories. Comparing organisms over largeranges of body size effectively averages overenvironments and phylogenetic histories.Sweeping comparisons, incorporatingorganisms of different taxonomic andfunctional groups and spanning many ordersof magnitude in body mass, reveal the moreuniversal features of life, lead to coarse-grained descriptions, and motivate the searchfor general, quantitative, predictive theories ofbiological structures and dynamics.

Such an approach has been very successfulin other branches of science. For example,

G. B. West and J. H. Brown

4.0

3.0

2.0

1.0

–1 0 1.0Body mass (kg)

logB

MR

2.0 3.0

Fig.·1. Kleiber’s original 1932 plot of the basal metabolic rate of mammals and birds(in kcal/day) plotted against mass (Mb in kg) on a log–log scale (Kleiber, 1975). Theslope of the best straight-line fit is 0.74, illustrating the scaling of metabolic rate asMb

3/4. The diameters of the circles represent his estimated errors of 10% in the data.


1577Allometric scaling laws

classic kinetic theory is based on the idea that generic featuresof gases, such as the ideal gas law, can be understood byassuming atoms to be structureless ‘billiard balls’ undergoingelastic collisions. Despite these simplifications, the theorycaptures many essential features of gases and spectacularlypredicts many of their coarse-grained properties. The originaltheory acted as a starting point for more sophisticatedtreatments incorporating detailed structure, inelasticity,quantum mechanical effects, etc, which allow more detailedcalculations. Other examples include the quark model ofelementary particles and the theories describing the evolutionof the universe from the big bang. This approach has also beensuccessful in biology, perhaps most notably in genetics. Again,the original Mendelian theory made simplifying assumptions,portraying each phenotypic trait as the expression of pairs ofparticles, each derived from a different parent, which assortedand combined at random in offspring. Nevertheless, this theorycaptured enough of the coarse-grained essence of thephenomena so that it not only provided the basis for the appliedsciences of human genetics and plant and animal breeding, butalso guided the successful search for the molecular genetic

code and supplied the mechanistic underpinnings for themodern evolutionary synthesis. Although the shortcomings ofthese theories are well-recognized, they quantitatively explainan extraordinary body of data because they do indeed capturemuch of the essential behavior.

Scaling as a manifestation of underlying dynamics has beeninstrumental in gaining deeper insights into problems acrossthe entire spectrum of science and technology, because scalinglaws typically reflect underlying general features andprinciples that are independent of detailed structure, dynamicsor other specific characteristics of the system, or of theparticular models used to describe it. So, a challenge in biologyis to understand the ubiquity of quarter-powers – to explainthem in terms of unifying principles that determine how life isorganized and the constraints under which it has evolved. Overthe immense spectrum of life the same chemical constituentsand reactions generate an enormous variety of forms,functions, and dynamical behaviors. All life functions bytransforming energy from physical or chemical sources intoorganic molecules that are metabolized to build, maintain andreproduce complex, highly organized systems. We conjecture

5

0

–5

–10

–15

–20

In vitro

Shrew

Mammals

Elephant

RC

CcO

In resting cell

Mitochondrion (mammalian myocyte)

Average mammalian cell,

in culture

–20 –15 –10 –5 0 5 10

log(mass)

log(

met

abol

ic p

ower

)

Fig.·2. Extension of Kleiber’s 3/4-power law for the metabolic rate of mammals to over 27 orders of magnitude from individuals (blue circles)to uncoupled mammalian cells, mitochondria and terminal oxidase molecules, CcO of the respiratory complex, RC (red circles). Also shownare data for unicellular organisms (green circles). In the region below the smallest mammal (the shrew), scaling is predicted to extrapolatelinearly to an isolated cell in vitro, as shown by the dotted line. The 3/4-power re-emerges at the cellular and intracellular levels. Figure takenfrom West et al. (2002b) with permission.


1578

that metabolism and the consequent distribution of energy andresources play a central, universal role in constraining thestructure and organization of all life at all scales, and that theprinciples governing this are manifested in the pervasivequarter-power scaling laws.

Within this paradigm, the precise value of the exponent,whether it is exactly 3/4, for example, is less important thanthe fact that it approximates such an ideal value over asubstantial range of mass, despite variation due to secondaryfactors. Indeed, a quantitative theory for the dominantbehaviour (the 3/4 exponent, for example) providesinformation about the residual variation that it cannot explain.If a general theory with well-defined assumptions predicts 3/4for average idealized organisms, then it is possible to erect andtest hypotheses about other factors, not included in the theory,which may cause real organisms to deviate from this value. Onthe other hand, without such a theory it is not possible to givea specific meaning to any scaling exponent, but only todescribe the relationship statistically. This latter strategy hasusually been employed in analyzing allometric data and hasfueled controversy ever since Kleiber’s original study (Kleiber,1932, 1975). Kleiber’s contemporary Brody independentlymeasured basal metabolic rates of birds and mammals,obtained a statistically fitted exponent of 0.73, and simply tookthis as the ‘true’ value (Brody, 1945). Subsequently a greatdeal of ink has been spilled debating whether the exponent is‘exactly’ 3/4. Although this controversy appeared to be settledmore than 20 years ago (Calder, 1984; McMahon and Bonner,1983; Peters, 1986; Schmidt-Nielsen, 1984), it was recentlyresurrected by several researchers (Dodds et al., 2001; Savageet al., 2004b; White and Seymour, 2003).

A deep understanding of quarter-power scaling based on aset of underlying principles can provide, in principle, a generalframework for making quantitative dynamical calculations ofmany more detailed quantities beyond just the allometricexponents of the phenomena under study. It can raise andaddress many additional questions, such as: How many oxidasemolecules and mitochondria are there in an average cell and inan entire organism? How many ribosomal RNA molecules?Why do we stop growing and what adult weight do we attain?Why do we live on the order of 100 years – and not a millionor a few weeks – and how is this related to molecular scales?What are the flow rate, pulse rate, pressure and dimensions inany vessel in the circulatory system of any mammal? Why dowe sleep eight hours a day, a mouse eighteen and an elephantthree? How many trees of a given size are there in a forest,how far apart are they, how many leaves does each have andhow much energy flows in each or their branches? What arethe limits on the sizes of organisms with different body plans?

Basic principlesAll organisms, from the smallest, simplest bacterium to the

largest plants and animals, depend for their maintenance andreproduction on the close integration of numerous subunits:molecules, organelles and cells. These components need to be

serviced in a relatively ‘democratic’ and efficient fashion tosupply metabolic substrates, remove waste products andregulate activity. We conjecture that natural selection solvedthis problem by evolving hierarchical fractal-like branchingnetworks, which distribute energy and materials betweenmacroscopic reservoirs and microscopic sites (West et al.,1997). Examples include animal circulatory, respiratory, renal,and neural systems, plant vascular systems, intracellularnetworks, and the systems that supply food, water, power andinformation to human societies. We have proposed that thequarter-power allometric scaling laws and other features of thedynamical behaviour of biological systems reflect theconstraints inherent in the generic properties of these networks.These were postulated to be: (i) networks are space-filling inorder to service all local biologically active subunits; (ii) theterminal units of the network are invariants; and (iii)performance of the network is maximized by minimizing theenergy and other quantities required for resource distribution.

These properties of the ‘average idealised organism’ arepresumed to be consequences of natural selection. Thus, theterminal units of the network where energy and resources areexchanged (e.g. leaves, capillaries, cells, mitochondria orchloroplasts), are not reconfigured or rescaled as individualsgrow from newborn to adult or as new species evolve. In ananalogous fashion, buildings are supplied by branchingnetworks that terminate in invariant terminal units, such aselectrical outlets or water faucets. The third postulate assumesthat the continuous feedback and fine-tuning implicit in naturalselection led to ‘optimized’ systems. For example, of theinfinitude of space-filling circulatory systems with invariantterminal units that could have evolved, those that have survivedthe process of natural selection, minimize cardiac output. Suchminimization principles are very powerful, because they lead to‘equations of motion’ for network dynamics.

Using these basic postulates, which are quite general andindependent of the details of any particular system, we havederived analytic models for mammalian circulatory andrespiratory systems (West et al., 1997) and plant vascularsystems (West et al., 1999b). The theory predicts scalingrelations for many structural and functional components ofthese systems. These scaling laws have the characteristicquarter-power exponents, even though the anatomy andphysiology of the pumps and plumbing are very different.Furthermore, our models derive scaling laws that account forobserved variation between organisms (individuals and speciesof varying size), within individual organisms (e.g. from aortato capillaries of a mammal or from trunk to leaves of a tree),and during ontogeny (e.g. from a seedling to a giant sequoia).The models can be used to understand the values not only forallometric exponents, but also for normalization constants andcertain invariant quantities. The theory makes quantitativepredictions that are generally supported when relevant data areavailable, and – when they are not – that stand as a priorihypotheses to be tested by collection and analysis of new data(Enquist et al., 1999; Savage et al., 2004a; West et al., 1997,1999a,b, 2001, 2002a,b).




Metabolic rate and the vascular networkMetabolic rate, the rate of transformation of energy and

materials within an organism, literally sets the pace of life.Consequently it is central in determining the scale of biologicalphenomena, including the sizes and dimensions of structuresand the rates and times of activities, at levels of organizationfrom molecules to ecosystems. Aerobic metabolism inmammals is fueled by oxygen whose concentration in blood isinvariant, so cardiac output or blood volume flow rate throughthe cardiovascular system is a proxy for metabolic rate. Thus,characteristics of the circulatory network constrain the scalingof metabolic rate. We shall show how the body-size dependencefor basal and field metabolic rates, B�Mb

3/4, where B is totalmetabolic rate, can be derived by modeling the hemodynamicsof the cardiovascular system based on the above generalassumptions. In addition, and just as importantly, this whole-system model also leads to analytic solutions for many otherfeatures of the blood supply network. These results are derivedby solving the hydrodynamic and elasticity equations for bloodflow and vessel dynamics subject to space-filling and theminimization of cardiac output (West et al., 1997). We makecertain simplifying assumptions, such as cylindrical vessels, asymmetric network, and the absence of significant turbulence.Here, we present a condensed version of the model that containsthe important features pertinent to the scaling problem.

In order to describe the network we need to determine howthe radii, rk, and lengths, lk, of vessels change throughout thenetwork; k denotes the level of the branching, beginning withthe aorta at k=0 and terminating at the capillaries where k=N.The average number of branches per node (the branchingratio), n, is assumed to be constant throughout the network.

Space-filling (Mandelbrot, 1982) ensures that every localvolume of tissue is serviced by the network on all spatial scales,including during growth from embryo to adult. The capillariesare taken to be invariant terminal units, but each capillarysupplies a group of cells, referred to as a ‘service volume’, vN,which can scale with body mass. The total volume to beserviced, or filled, is therefore given by VS=NNvN, where NN isthe total number of capillaries. For a network with many levels,N, space-filling at all scales requires that this same volume, VS,be serviced by an aggregate of the volumes, vk, at each level k.Since rk<<lk, vk�lk3, so VS�Nkvk�Nklk3 for every level, k. Thuslk+1/lk�n–1/3, so space-filling constrains only branch lengths, lk.

The equation of motion governing fluid flow in any singletube is the Navier–Stokes equation (Landau and Lifshitz,1978). If non-linear terms responsible for turbulence areneglected, this reads:

where v is the local fluid velocity at some time t, p the localpressure, ρ, blood density and µ, blood viscosity. Assumingblood is incompressible, then local conservation of fluidrequires ∇•v=0. When combined with Eq.·2, this gives:

∇2p = 0·. (3)

The beating heart generates a pulse wave that propagates downthe arterial system causing expansion and contraction ofvessels as described by the Navier equation, which governs theelastic motion of the tube. This is given by:

where ξ is the local displacement of the tube wall, ρw itsdensity, and E its modulus of elasticity. These three coupledequations, Eq.·2–4, must be solved subject to boundaryconditions that require the continuity of velocity and force atthe tube wall interfaces. In the approximation where the vesselwall thickness, h, is small compared to the static equilibriumvalue of the vessel radius, r, i.e. h<<r, the problem can besolved analytically, as first shown by Womersley (Caro et al.,1978; Fung, 1984), to give:

where Jn denotes the Bessel function of order n. Here, ω isthe angular frequency of the wave, α�(ωρ/µ)1/2r is adimensionless parameter known as the Womersley number,c0�(Eh/2ρr)1/2 is the classic Korteweg–Moens velocity, and Zis the vessel impedance. Both Z and the wave velocity, c, arecomplex functions of ω so, in general, the wave is attenuatedand dispersed as it propagates along the tubes. The characterof the wave depends critically on whether |α| is less than orgreater than 1. This can be seen explicitly in Eq.·5, where thebehavior of the Bessel functions changes from a power-seriesexpansion for small |α| to an expansion with oscillatorybehavior when |α| is large. In humans, |α| has a value of around15 in the aorta, 5 in the arteries, 0.04 in the arterioles, and 0.005in the capillaries. When |α| is large (>>1), Eq.·5 gives c~c0,which is a purely real quantity, so the wave suffers neitherattenuation nor dispersion. Consequently, in these large vesselsviscosity plays almost no role and virtually no energy isdissipated. In an arbitrary unconstrained network, however,energy must be expended to overcome possible reflections atbranch junctions, which would require increased cardiac poweroutput. Minimization of energy expenditure is thereforeachieved by eliminating such reflections, a phenomenonknown as impedance matching. From Eq.·5, Z~ρc0/πr2 forlarge vessels, and impedance matching leads to area-preservingbranching: πrk

2=nπrk+12, so that rk+1/rk=n–1/2. For small

vessels, however, where |α|<<1, the role of viscosity andthe subsequent dissipation of energy become increasinglyimportant until they eventually dominate the flow. Eq.·5 thengives c~(1/4)i1/2αc0→0, in quantitative agreement withobservation (Caro et al., 1978; Fung, 1984). Because c now hasa dominant imaginary part, the traveling wave is heavilydamped, leaving an almost steady oscillatory flow whoseimpedance is, from Eq.·5, just the classic Poiseuille formula,Zk=8µlk/πrk

4. Unlike energy loss due to reflections at branchpoints, energy loss due to viscous dissipative forces cannot be

(5)co

2ρπr2c

,and Z ~J2(i3/2α)J0(i3/2α)

~ –⎛⎜⎝

⎞⎟⎠

c

c0

2

(4)∂2ξ∂t2

= E�2ξ – �p ,ρw

(2)∂v

∂t= µ�2v – �p ,ρ


1580

entirely eliminated. It can be minimized, however, using theclassic method of Lagrange multipliers to enforce theappropriate constraints (Marion and Thornton, 1988; West etal., 1997). To sustain a given metabolic rate in an organism offixed mass with a given volume of blood, Vb, the cardiac outputmust be minimized subject to a space-filling geometry. Thecalculation shows that area-preserving branching is therebyreplaced by area-increasing branching in small vessels, soblood slows down allowing efficient diffusion of oxygen fromthe capillaries to the cells. Branching, therefore, changescontinuously down through the network, so that the ratio rk+1/rk

is not independent of k but changes continuously from n–1/2 atthe aorta to n–1/3 at the capillaries. Consequently, the networkis not strictly self-similar, but within each region (pulsatile inlarge vessels and Poiseuille in small ones), self-similarity is areasonable approximation that is well supported by empiricaldata (Caro et al., 1978; Fung, 1984; Zamir, 1999).

In order to derive allometric relations between animals ofdifferent sizes we need to relate the scaling of vesseldimensions within an organism to its body mass, Mb. A naturalvehicle for this is the total volume of blood in the network,Vb, which can be shown to depend linearly on Mb if cardiacoutput is minimized, i.e. Vb�Mb, in agreement with data (Caroet al., 1978; Fung, 1984). This is straightforwardly given byVb=ΣNkVk=Σnkπrk

2lk, where Nk=nk is the number of vessels atlevel k. Provided there are sufficiently large vessels in thenetwork with |α|>1 so that pulsatile flow dominates, theleading-order behavior for the blood volume is Vb�n4N/3VN.Conservation of blood requires that the flow rate in the aorta,Q0= NNQN, where QN is the flow rate in a capillary andNN�nN, the total number of capillaries. But Q0�B, the totalmetabolic rate, so putting these together we obtainB�(Vb/VN)3/4QN. However, capillaries are invariant units, soVN and QN are both independent of Mb, whereas fromminimization of energy loss, Vb�Mb, so we immediatelyobtain the seminal result B�Mb

3/4.The allometric scaling of radii, lengths and many other

physiological characteristics, such as the flow, pulse anddimensions in any branch of a mammal of any size, can bederived from this whole-system model and shown to havequarter-power exponents. Quantitative predictions for all thesecharacteristics of the cardiovascular system are in goodagreement with data (West et al., 1997). For example, even theresidual pulse wave component in capillaries is determined: itis predicted to be attenuated to 0.1% with its velocity being~10·cm·s–1, compared to ~580·cm·s–1 for the unattenuatedwave in the aorta, both numbers being invariant with respectto body size.

To summarise: there are two independent contributions toenergy expenditure: viscous energy dissipation, which isimportant only in smaller vessels, and energy reflected atbranch points, which is important only in larger vessels and iseliminated by impedance matchings In large vessels (arteries),pulse-waves suffer little attenuation or dissipation, andimpedance matching leads to area-preserving branching, suchthat the cross-sectional area of daughter branches equals that

of the parent; so radii scale as rk+1/rk=n–1/2 with the bloodvelocity remaining constant. In small vessels (capillaries andarterioles) the pulse is strongly damped since Poiseuille flowdominates and substantial energy is dissipated. Hereminimization of energy dissipation leads to area-increasingbranching with rk+1/rk=n–1/3, so blood slows down, almostceasing to flow in the capillaries. Consequently, the ratio ofvessel radii between adjacent levels, rk+1/rk, changescontinuously from n–1/2 to n–1/3 down through the network,which is, therefore, not strictly self-similar. Nevertheless, sincethe length ratio lk+1/lk remains constant throughout the networkbecause of space-filling, branch-lengths are self-similar and thenetwork has some fractal-like properties. Quarter-powerallometric relations then follow from the invariance ofcapillaries and the prediction from energy optimization thattotal blood volume scales linearly with body mass.

The dominance of pulsatile flow, and consequently of area-preserving branching, is crucial for deriving power laws,including the 3/4 exponent for metabolic rate, B. However, asbody size decreases, narrow tubes predominate and viscosityplays an ever-increasing role. Eventually even the majorarteries would become too constricted to support wavepropagation, blood flow would become steady and branchingexclusively area-increasing, leading to a linear dependence onmass. Since energy would be dissipated in all branches of thenetwork, the system is now highly inefficient; such animpossibly small mammal would have a beating heart (with aresting heart-rate in excess of approximately 1000·beats·min–1)but no pulse! This provides a framework to estimate thesize of the smallest mammal in terms of fundamentalcardiovascular parameters. This gives a minimum massMmin~1·g, close to that of a shrew, which is indeed the smallestmammal (Fig.·3; West et al., 2002b). Furthermore, thepredicted linear extrapolation of B below this mass to the massof a single cell should, and does, give the correct value for the


1.01.21.41.61.82.02.22.42.62.83.0

0 842 6logMb

log

fH

y=–0.251x+3.072r2=0.95

Fig.·3. Plot of heart rates (fH) of mammals at rest vs body mass Mb

(data taken from Brody, 1945). The regression lines are fitted to theaverage of the logarithms for every 0.1 log unit interval of mass, butboth the average (squares) and raw data (bars) are shown in the plots.The slope is –0.251 (P<0.0001, N=17, 95% CI: –0.221, –0.281),which clearly includes –1/4 but excludes –1/3. Figure taken fromSavage et al. (2004b) with permission.



metabolic rate of mammalian cells growing in culture isolatedfrom the vascular network (Fig.·2).

The derivation that gives the 3/4 exponent is only anapproximation, because of the changing roles of pulsatile andPoiseuille flow with body size. Strictly speaking, the theorypredicts that the exponent for B is exactly 3/4 only wherepulsatile flow completely dominates. In general, the exponentis predicted to depend weakly on M, manifesting significantdeviations from 3/4 only in small mammals, where only thefirst few branches of the arterial system can support a pulsewave (West et al., 1997, 2002b). Since small mammalsdissipate relatively more energy in their networks, they requireelevated metabolic rates to generate the increased energyexpenditure to circulate the blood. This leads to the predictionthat the allometric exponent for B should decrease below 3/4as Mb decreases to the smallest mammal, as observed (Doddset al., 2001; Savage et al., 2004b).

If the total number of cells, Nc, increases linearly with Mb,then both cellular metabolic rate, Bc(�B/Nc), and specificmetabolic rate, B/Mb, decrease as Mb

–1/4. In this sense,therefore, larger animals are more efficient than smaller ones,because they require less power to support unit body mass andtheir cells do less work than smaller animals. In terms of ourtheory this is because the total hydrodynamic resistance of thenetwork decreases with size as Mb

–3/4. This has a furtherinteresting consequence that, since the ‘current’ or volume rateof flow of blood in the network, Q0, increases as Mb

3/4, whereasthe resistance decreases as Mb

–3/4, the analog to Ohm’s law(pressure=current�resistance) predicts that blood pressuremust be an invariant, as observed (Caro et al., 1978; Fung,1984). This may seem counterintuitive, since the radius of theaorta varies from approximately 0.2·mm in a shrew up toapproximately 30·cm in a whale!

Scaling up the hierarchy: from molecules to mammalsAt each organisational level within an organism, beginning

with molecules and continuing up through organelles, cells,tissues and organs, new structures emerge, each with different

physical characteristics, functional parameters, and resourceand energy network systems, thereby constituting a hierarchyof hierarchies. Metabolic energy is conserved as it flowsthrough this hierarchy of sequential networks. We assume thateach network operates subject to the same general principlesand therefore exhibits quarter-power scaling (West et al.,2002b). From the molecules of the respiratory complex up tointact cells, metabolic rate obeys 3/4-power scaling.Continuity of flow imposes boundary conditions betweenadjacent levels, leading to constraints on the densities ofinvariant terminal units, such as respiratory complexes andmitochondria, and on the networks of flows that connectthem (West et al., 2002b). The total mitochondrial massrelative to body mass is correctly predicted to be(Mminmm/mcMb)1/4�0.06Mb

–1/4, where mm is the mass of amitochondrion, Mmin is minimum mass, mc is average cellmass and Mb is expressed in g. Since mitochondria areassumed to be approximately invariant, the total number in thebody is determined in a similar fashion. This shows why thereare typically only a few hundred per human cell, whereas thereare several thousand in a shrew cell of the same type.

As already stressed, a central premise of the theory is thatgeneral properties of supply networks constrain the coarse-grained, and therefore the scaling properties, of biological

5.0

5.5

6.0

6.5

7.0

7.5

8.0

–15 –14 –13 –12 –11 –10 –9

log(cellular mass)

log(

geno

me

leng

th)

Slope=0.24±0.02Intercept=9.4±0.2

Non-photosynthetic prokaryotesCyanophyta

Fig.·4. Plot of genome length (number of base pairs) vs mass (in g)for a sequence of unicells on a log–log scale. The best straight-line fithas a slope very close to 1/4.

–13

–12

–11

–10

–9

0 2 4 6 8

log(mass of organism)lo

g(po

wer

per

cel

l)

Cells in vivo, B�Mb–1/4

Cultured cellsin vitro, B�Mb

0

M=µ

Fig.·5. Metabolic rates (in W) of mammalian cells in vivo (blue line)and cultured in vitro (red line) plotted as a function of organism mass(Mb in g) on a log–log scale. While still in the body and constrainedby vascular supply networks cellular metabolic rates scale as Mb

–1/4.When cells are removed from the body and cultured in vitro, theirmetabolic rates converge to a constant value predicted by theory(West et al., 2002b). The two lines meet at the mass of the smallestmammal (the shrew with mass ~1·g, as predicted). Figure taken fromWest et al. (2002b) with permission.


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systems. An immediate qualitative consequence of thisidea is that, if cells are liberated from the networkhegemony by culturing them in vitro, they are likely tobehave differently from cells in vivo. An alternativepossibility is that cellular metabolic rates are relativelyinflexible. This, however, would be a poor design,because it would prevent facultative adjustment inresponse to variation in body size over ontogeny and inresponse to the varying metabolic demands of tissues.If the metabolic rate and number of mitochondria percell are indeed tuned facultatively in response tovariations in supply and demand, the theory makes anexplicit quantitative prediction: cells isolated fromdifferent mammals and cultured in vitro underconditions of unlimited resource supply shouldconverge toward the same metabolic rate (predicted to be~6�10–11·W), rather than scaling as M–1/4 as they do in vivo(Fig.·5); cells in vitro should also converge toward identicalnumbers of mitochondria, losing the M–1/4 scaling that theyexhibit in vivo. The in vivo and in vitro values are predicted tocoincide at Mmin, which we estimated above to beapproximately 1·g. So cells in shrews work at almost maximaloutput, which, no doubt, is reflected in their high levels ofactivity and the shortness of their lives. By contrast cells inlarger mammals are constrained by the properties of vascularsupply networks and normally work at lower rates.

All of these results depend only on generic networkproperties, independent of details of anatomy and physiology,including differences in the size, shape and number ofmitochondria among different tissues within a mammal. Sincequarter-power scaling is observed at intracellular, as well aswhole-organism and cellular levels, this suggests thatmetabolic processes at subcellular levels are also constrainedby optimized space-filling, hierarchical networks, which havesimilar properties to the more macroscopic ones. A majorchallenge, both theoretically and experimentally, is tounderstand quantitatively the mechanisms of intracellulartransport, about which surprisingly little is known.

ExtensionsOntogenetic growth

The theory developed above naturally leads to a generalgrowth equation applicable to all multicellular animals (Westet al., 2001, 2002a). Metabolic energy transported through thenetwork fuels cells where it is used either for maintenance,

including the replacement of cells, or for the production ofadditional biomass and new cells. This can be expressed as:

where Nc is the total number of cells in the organism at time tafter birth and Ec the energy needed to create a new cell. SinceNc=m/mc, where m is the ontogenetic mass and mc the averagecell mass, this leads to an equation for the growth rate of anorganism:

where B0 is the taxon-dependent normalization constant for thescaling of metabolic rate: B�B0m3/4. The parameters of theresulting growth equation are therefore determined solely byfundamental properties of cells, such as their metabolic ratesand the energy required to produce new ones, which can bemeasured independently of growth. The model gives a naturalexplanation for why animals stop growing: the number of cellssupplied (Nc�m) scales faster than the number of supply units(since B�NN�m3/4), and leads to an expression for theasymptotic mass of the organism: Mb=(B0mc/Bc)4. Eq.·7 can besolved analytically to determine m as a function of t, leadingto a classic sigmoidal growth curve. By appropriately rescalingm and t as prescribed by the theory, the solution can be recastas a universal scaling curve for growth. When rescaled in thisway, growth data from many different animals (includingendotherms and ectotherms, vertebrates and invertebrates) all

(7)m ,m3/4 –⎛⎜⎝

⎞⎟⎠

Bc

Ec

dm

dt=

⎛⎜⎝

⎞⎟⎠

B0mc

Ec

(6),B = NcBc + Ec

⎛⎜⎝

⎞⎟⎠

dNc

dt


0

0.25

0.50

0.75

1.00

1.25

0 2 4 6 8 10

Dim

ensi

onle

ss m

ass

ratio

(m

/M)1/

4

(at/4Mb1/4) – ln [1–(m0/Mb)1/4]

Dimensionless time

Swine

Shrew

Rabbit

Cod

Rat

Guinea pig

Shrimp

Salmon

Guppy

Chicken

Robin

Heron

Cow

Fig.·6. The universality of growth is illustrated by plotting thedimensionless mass ratio (m/M)1/4 against a dimensionlesstime variable, as shown. When data for mammals, birds, fishand crustacea are plotted this way, they are predicted to lie ona single universal curve; m is the mass of the organism at aget, m0 its birth mass, Mb its mature mass, and a a parameterdetermined by theory in terms of basic cellular properties thatcan be measured independently of growth data. Figure takenfrom West et al. (2001) with permission.



closely fit a single universal curve (Fig.·6). Ontogenetic growthis therefore a universal phenomenon determined by theinteraction of basic metabolic properties at cellular and whole-organism levels. Furthermore, this model leads to scaling lawsfor other growth characteristics, such as doubling times forbody mass and cell number, and the relative energy devoted toproduction vs maintenance. Recently, Guiot et al. (2003)applied this model to growth of solid tumors in rats andhumans. They showed that the growth curve derived fromEq.·7 gave very good fits, even though the parameters theyused were derived from statistical fitting rather than determinedfrom first principles, as in ontogenetic growth. This is just oneexample of the exciting potential applications of metabolicscaling theory to important biomedical problems.

Temperature and universal biological clocks

Temperature has a powerful effect on all biological systemsbecause of the exponential sensitivity of the Boltzmann factor,e–E/kT, which controls the temperature dependence ofbiochemical reaction rates; here, E is a chemical activationenergy, T absolute temperature, and k Boltzmann’s constant.Combined with network constraints that govern the fluxes ofenergy and materials, this predicts a joint universal mass andtemperature scaling law for all rates and times connectedwith metabolism, including growth, embryonic development,

longevity and DNA nucleotide substitution in genomes. Allsuch rates are predicted to scale as:

R � Mb–1/4e–E/kT ·, (8)

and all times as:

t � Mb1/4eE/kT ·. (9)

The critical points here are the separable multiplicative natureof the mass and temperature dependences and the relativelyinvariant value of E, reflecting the average activation energyfor the rate-limiting biochemical reactions (Gillooly et al.,2001). Data covering a broad range of organisms (fish,amphibians, aquatic insects and zooplankton) confirm thesepredictions with E~0.65·eV (Fig.·7). These results suggest ageneral definition of biological time that is approximatelyinvariant and common to all organisms: when adjusted for sizeand temperature, determined by just two numbers (1/4 andE~0.65·eV), all organisms to a good approximation run by thesame universal clock with similar metabolic, growth, andevolutionary rates! (Gillooly et al., 2005).

Metabolic scaling in plants: independent evolution of M3/4

One of the most challenging facts about quarter-powerscaling relations is that they are observed in both animals andplants. Our theory offers an explanation: both use fractal-like

3.0 3.83.4–6

2

–2

ln(B

MD

–3/4

)

Temperature–1 (1000/°K)

G

y=–9.10x+29.49r2=0.88N=142

Birds and mammals

3.0 3.83.4–8

0

–4

Temperature–1 (1000/°K)

E

y=–5.76x+16.68r2=0.56N=64

Amphibians

3.0 3.83.4–8

0

–4

F

y=–8.78x+26.85r2=0.75N=105

Reptiles

3.0 3.83.4–8

0

–4

D

y=–5.02x+14.47r2=0.53N=113

Fish

3.0 3.83.4–8

0

–4

B Plants

3.0 3.83.4–8

0

–4

C

y=–9.15x+27.62r2=0.62N=20

Multicellular invertebrates

3.0 3.83.4–8

0

–4

A

y=–8.79x+25.80r2=0.60N=30

y=–7.61x+21.37r2=0.75N=67

Unicells

Fig.·7. Plot of mass-corrected resting metabolic rate, ln(B Mb–3/4) vs inverse

absolute temperature (1000/°K) for unicells (A), plants (B), multicellularinvertebrates (C), fish (D), amphibians (E), reptiles (F), and birds and mammals(G). Birds (filled symbols) and mammals (open symbols) are shown at normalbody temperature (triangles) and during hibernation or torpor (squares). Figuretaken from Gillooly et al. (2001) with permission.


1584

branching structures to distribute resources, so both obey thesame basic principles despite the large differences in anatomyand physiology. For example, in marked contrast to themammalian circulatory system, plant vascular systems areeffectively fiber bundles of long micro-capillary tubes (xylemand phloem), which transport resources from trunk to leaves,driven by a non-pulsatile pump (Niklas, 1994). If themicrocapillary vessels were of uniform radius, as is oftenassumed in models of plants, a serious paradox results: thesupply to the tallest branches, where most light is collected,suffers the greatest resistance. This problem had to becircumvented in order for the vertical architecture of higherplants to have evolved. Furthermore, the branches thatdistribute resources also contain substantial quantities of deadwood which provide biomechanical support, so the modelmust integrate classic bending moment equations with thehydrodynamics of fluid flow in the active tubes.

Assuming a space-filling branching network geometry withinvariant terminal units (petioles or leaves) and minimization ofenergy use as in the cardiovascular system, the theory predictsthat tubes must have just enough taper so that the hydrodynamic


–2

–1

0

1

2

3

4

–2 0 2 4 6log(mass)

log(

xyle

m f

lux)

y=0.736x–0.022r2=0.91

Fig.·8. Plot of maximum reported xylem flux rates (liters of fluidtransported vertically through a plant stem per day) for plants (Enquistand Niklas, 2001). The RMA regression line is fitted to the averageof the logarithm for every 0.1 log unit interval of plant biomass, butboth the average (circles) and raw data (bars) are shown in the plot.The slope is 0.736 (P<0.0001, N=31, 95%CI: 0.647, 0.825). Theregression fitted to the entire unbinned data set gives a similarexponent of 0.735 (P<0.0001, N=69, 95% CI: 0.682, 0.788). Figuretaken from Enquist and Niklas (2001) with permission.

0.1 1 10 100

Pinus edulis - Los Alamos dataPinus monophylla - Tausch (1980)

0.1

1

10

100

1000

10000

A

y=–2.077x+4.962

y=–1.946x+4.737

Mean branch diameter (cm) within given branch order

Num

ber

of b

ranc

hes

with

in o

rder

B

C DSlope = –2.2(S.D. = 0.1) Slope = –2.4

(S.D. = 0.1)

0.5 1.0 1.5 2.0 2.5 3.0

1981

1947

0.5

1.0

1.5

2.0

2.5

3.0

log(trunk diameter)

log(

num

ber

of s

tem

s)

Fig.·9. (A) A typical tree. (B) A page from Leonardo’s notebooks illustrating his discovery of area-preserving branching for trees. (C) A plotof the number of branches of a given size in an individual tree versus their diameter (in cm) showing the predicted inverse square law behaviour.(D) A plot of the number of trees of a given size vs their trunk diameter (in cm) showing the predicted inverse square law behaviour. Thedata are from a forest in Malaysia taken at times separated by 34 years, illustrating the robustness of the result. Even though the individualcomposition of the forest has changed over this period the inverse square law has persisted. Figure taken from West and Brown (2004), withpermission.



resistance of each tube is independent of path length. Thistherefore ‘democratises’ all tubes in all branches, therebyallowing a vertical architecture. As in the mammalian system,many scaling relations can be derived both within and betweenplants, and these make quantitative testable predictions formetabolic rate (the 3/4 exponent), area-preserving branching,xylem vessel tapering and conductivity, pressure gradients,fluid velocity, and the relative amount of non-conducting woodto provide biomechanical support (Figs·8, 9).

Of particular relevance here is the fact that these two systems,in plants and mammals, which have evolved independently bynatural selection to solve the problem of efficient distributionof resources from a central ‘trunk’ to terminal ‘capillaries’ andwhich have such fundamentally different anatomical andphysiological features, nevertheless show identical Mb

3/4

scaling of whole-organism metabolic rate, and comparablequarter-power scaling of many structures and functions. Ourmodel accurately predicts scaling exponents for 17 parametersof trees (West et al., 1999b). These sets of comparable quarter-power scaling laws reflect convergent solutions of trees andmammals to the common problems of vascular network designsatisfying the same set of basic principles.

The fourth dimension

We have shown that power law scaling reflects genericproperties of energy and resource distribution networks: space-filling, invariant terminal units and minimization of energyexpenditure are sufficient to determine scaling properties,regardless of the detailed architecture of the network. Forexample, area-preserving branching and the linearity of thenetwork volume with body mass both follow from optimisingthe solution to the dynamical equations for network flow andare sufficient to derive quarter-powers in both mammals andplants. Nevertheless, one can ask why it is that exponents aredestined to be quarter-powers in all cases, rather than someother power, and why should this be a universal behaviourextending even to unicellular organisms with no obviousbranching network. Is there a more general argument,independent of dynamics and hierarchical branching thatdetermines the ‘magic’ number 4? This question was addressedby Banavar et al. (1999) who, following our work, alsoassumed that allometric relations reflect network constraints.They proposed that quarter-powers arise from a more generalclass of directed networks that do not necessarily have fractal-like hierarchical branching. They assumed that the networkvolume scales linearly with body mass Mb and claimed ongeneral grounds that a lower bound on the overall network flowrate scales as Mb

3/4. Although intriguing, the biologicalsignificance of this result is unclear, not only because it is alower bound rather than an optimization, but more importantly,because it was derived assuming that the flow is sequentialbetween the invariant terminal units being supplied (e.g. fromcell to cell, or from leaf to leaf) rather than hierarchicallyterminating on such units, as in most real biological networks.Whether their result can be generalized to general networks ofmore relevance in biology is unclear.

A general argument (West et al., 1999a) can be motivatedfrom the observation that in d dimensions our derivations ofthe metabolic exponent obtained from solving the dynamicalequations leads to d/(d+1), which in three dimensions reducesto the canonical 3/4. Thus, the ubiquitous ‘4’ is actually thedimensionality of space (‘3’) plus ‘1’. In our derivations thiscan be traced partially to the space-filling constraint, whichtypically leads to an increase in effective scalingdimensionality (Mandelbrot, 1982). For example, the total areaof two-dimensional sheets filling three-dimensional washingmachines clearly scales like a volume rather than an area. Inthis scaling sense, organisms effectively function as if in fourspatial dimensions. Natural selection has taken advantage ofthe generalised fractality of space-filling networks to maximisethe effective network surface area, A, of the terminal unitsinterfacing with their resource environments. This can beexpressed heuristically in the following way: if terminal unitsare invariant and the network space-filling, then metabolic rate,B�A, which scales like a volume, rather than an area; that is,B�A�L3 (rather than �L2), where L is some characteristiclength of the network, such as the length of the aorta in thecirculatory system of mammals or the length of the stem inplants. However, the volume of the network, Vnet�AL�L4. So,if we assume that Vnet�M (proven from energy minimisationin our theory), we then obtain Vnet�M�L4. Thus, L�M1/4

leading to B�A�L3�M3/4. This therefore provides ageometrical interpretation of the quarter-powers, and, inparticular, a geometrical ‘derivation’ of the 3/4 exponent forbasal metabolic rate (West et al., 1999a).

Criticisms and controversiesSince our original paper was published (West et al., 1997),

there have been several criticisms (Darveau et al., 2002; Doddset al., 2001; White and Seymour, 2003). Some of these revolvearound matters of fact and interpretation that still need to beresolved – such as the scaling of maximal metabolic rates inmammals or the precise value of the exponent. Others claim toprovide empirical information or theoretical calculations thatrefute our models. We have not found any of these lattercriticisms convincing for two reasons. First, most of them reston single technical issues, for which there are at least equallysupportable alternative explanations, and some that are simplyincorrect. Furthermore, most of these have been concernedsolely with mammalian metabolic rate, so they fail toappreciate that our theory offers a single parsimoniousexplanation, rooted in basic principles of biology, physics andgeometry, for an enormous variety of empirical scalingrelations. None of the criticisms offer alternative models forthe complete design of vascular networks or for the Mb

3/4

scaling of whole-organism metabolic rate. Here, we addresssome of the more salient issues.

Scaling of metabolic rate: is it 3/4, 2/3 or some othernumber?

Some of the recent criticisms have centered around whether


1586

whole-organism metabolic rate really does scale as Mb3/4

(Dodds et al., 2001; White and Seymour, 2003). Indeed,Kleiber himself (Kleiber, 1932, 1975) and many others (Brody,1945; Calder, 1984; McMahon and Bonner, 1983; Niklas,1994; Peters, 1986; Schmidt-Nielsen, 1984) had expected thatbasal mammalian metabolic rates (BMR) should scale as Mb

2/3,reflecting the role of body surface area in heat dissipation.Heusner (1982) presented a statistical analysis focusing onintra-specific comparisons and suggested that the exponent wasindeed 2/3 rather than 3/4, indicative of a simple Euclideansurface rule. The statistical argument was strongly counteredby Feldman and McMahon (1983), and by Bartels (1982), afterwhich the debate subsided and the ubiquity of quarter powerswas widely accepted (Calder, 1984; McMahon and Bonner,1983; Peters, 1986; Schmidt-Nielsen, 1984). In his syntheticbook on biological scaling, Schmidt-Nielsen seemed to havesettled the argument when he declared that ‘the slope of themetabolic regression line for mammals is 0.75 or very close toit, and most definitely not 0.67’ (Schmidt-Nielsen, 1984).

Arguments that the scaling of whole-organism metabolicrate is effectively a Euclidean surface phenomenon wereovershadowed by two lines of opposing evidence. First,metabolic rates of many groups of ectothermic organisms,whose body temperatures fluctuate closely with environmentaltemperatures, so that control of heat dissipation is not an issue,were also shown to scale as Mb

3/4. Second, extensive work ontemperature regulation in endotherms elucidated powerfulmechanisms for heat dissipation, in which body surface areaper se played an insignificant role (Schmidt-Nielsen, 1984).

Recently, however, this controversy was resurrected byDodds (2001) and by White and Seymour (2003), whoconcluded that a reanalysis of data supported 2/3, especiallyfor smaller mammals (<10·kg). These and earlier authors(Heusner, 1982) argued for an empirical exponent of 2/3 basedon their reanalyses of large data sets, using various criteria forexcluding certain taxa and data, and employing non-standardstatistical procedures. For every such example, however, it ispossible to generate a counter-example using at least equallyvalid data and statistical methods (Bartels, 1982; Feldman andMcMahon, 1983; Savage et al., 2004b). Observed deviationsfrom perfect Mb

3/4 seems attributable to some combination ofelevated rates for the smallest mammals, as first observedempirically by Calder (1984) and predicted theoretically by ourmodel (see above; West et al., 1997), and statistical artefactsdue to small errors in precisely estimating the characteristicbody masses of species. Ironically, one might argue thatdeviations from the 3/4 exponent for small mammals is anotherof the successful predictions of our theory.

More telling than repeated reanalyses of the largelyoverlapping data on basal metabolic rates of mammals wouldbe a reanalysis of all of the multiple studies of scaling ofwhole-organism metabolic rate in different groups oforganisms. Peters (1986) published such a meta-analysis of thelarge number of studies available at the time of his syntheticmonograph. He obtained an approximately normal-shapedfrequency distribution of exponents, with a sharp peak at

almost exactly 3/4. Savage et al. (2004b) recently performed asimilar analysis, incorporating data from additional studies,


0.1 0.15 0.2 0.25 0.3 0.33 0.40

1

2

3

4

5

6

7

Num

ber

mea

sure

d to

hav

e α

Allometric exponent, α

C Biological times

–0.5–0.55 –0.4–0.45 –0.33 –0.25 –0.20

2

4

6

8

10

12

14

16

18

20B Mass-specific

biological rates

–0.15 –0.1 –0.05 0 0.10.05

0 0.2 0.4 0.5 0.67 0.75 0.9 1 1.2 1.40

10

20

30

40

50

60

70A Biological rates

Fig.·10. Histograms of the exponents of (A) biological rates, (B)mass-specific biological rates (Peters, 1986) and (C) biological times(Calder, 1984). Note that the peak of the histogram for biological ratesis very close to 0.75 (0.749±0.007) but not close to 0.67. Moreover,the histogram for mass-specific rates peaks near –0.25 (–0.247±0.011)but not –0.33, and the histogram for biological times peaks at 0.25(0.250±0.011) and not 0.33. All errors quoted here are the standarderror from the mean for the distribution. In all cases, the majority ofbiological rates and times exhibit quarter-power, not third-power,scaling. Figure taken from Savage et al. (2004b) with permission.



and obtained virtually identical results: the mean value of theexponent is 0.749±0.007, so the 95% confidence intervalsinclude 3/4 but exclude 2/3 (Fig.·10). This analysis wasextended to a variety of other rates and times leading to similarresults: the mean value of the exponent for mass-specific rateswas found to be –0.247±0.011 and for times, 0.250±0.011, soboth of these clearly exclude a 1/3 exponent. It is worthemphasizing that these meta-analyses include studies of a widevariety of processes in a broad range of taxa (includingectotherms, invertebrates, and plants, as well as birds andmammals) measured in a very large number of independentstudies by many different investigators working over more than50 years. This kind of evidence had earlier led Calder (1984)to conclude that ‘Despite shortcomings and criticisms[including the lack of a theoretical model], empirically mostof the scaling does seem to fit M1/4 scaling.…..’, and Peters(1986) to remark that ‘.…..one cannot but wonder why thepower formula, in general, and the mass exponents of 3/4, 1/4,and –1/4, in particular, are so effective in describing biologicalphenomena.’ We see no reason to change this assessment inthe light of the very few recent studies that have once againargued for Mb

2/3 scaling.

Ours are whole-system models: how do other parametersscale?

Many critics lose sight of the fact that our theory generatesa complete, whole-system model for the structure and functionof the mammalian arterial system as well as quantitativelypredicting many other unrelated biological phenomena. Themodel quantifies the flow of blood from the heart to thecapillaries. It predicts the scaling exponents for 16 variables,including blood volume, heart rate, stroke volume, bloodpressure, radius of the aorta, volume of tissue served by acapillary, number and density of capillaries, dimensions ofcapillaries and oxygen affinity of hemoglobin (Fig.·3; West etal., 1997). No alternative whole-system model has beendeveloped that makes different predictions.

The most serious theoretical criticism, by Dodds et al.(2001), took issue with our derivation of the 3/4 exponent formammals based on an analysis of the pulsatile circulatorysystems Their calculation, however, naively minimized thetotal complex impedance of the network, which includesanalogs to capacitance and inductance effects not directlyassociated with energy dissipation. This is a subtle, butimportant, point. The meaningful, physical quantity associatedwith energy dissipation due to viscous forces is the real part ofthe impedance, and it is only this that must be minimized inorder to minimize the total energy dissipated. In addition, andas already emphasized above, the total energy expended in apulsatile system is the sum of two contributions: the viscousenergy dissipated (determined from the real part of theimpedance) and the loss due to reflections at branch points.Dodds et al. neglected, however, to consider this critical lattereffect and so failed to impose impedance matching, therebyallowing arbitrary reflections at all branch points, so the totalenergy expended is no longer minimised. Consequently, they

did not obtain area-preserving branching in large vessels nor,therefore, a 3/4 exponent nor a realistic description of the flow.Put simply, their criticism is invalid because they failed tocorrectly minimize the total energy expended in the network.

For those who would have mammalian BMR scale as M2/3,the onus is on them to explain the scaling of other componentsof the metabolic resource supply systems In particular, theyneed to explain why cardiac output and pulmonary exchangealso scale as M3/4 in mammals (Schmidt-Nielsen, 1984). Heartrate (fH), stroke volume (VS), respiration rate (Rl) and tidalvolume (VT) can all be measured with at least as muchprecision and standardization as metabolic rates It is wellestablished that fH�Rl�M–1/4, and VS�VT�M, so the cardiacoutput, fH�VS, scales as M–1/4M=M3/4, and similarly for therate of respiratory ventilation, Rl VT, again scaling as M3/4. Ofcourse this is not surprising if metabolic rate scales as M3/4,because the rate of respiratory gas exchange in the lungs andthe rate of blood flow from the heart with its contained oxygenand fuel must match the rate of metabolism of the tissues.There is, however, a serious unexplained inconsistency in thequarter-power scalings of these components of the circulatoryand respiratory systems if metabolic rate scales as M2/3.

Supply and demand at the cellular level: why do the cells careabout the size of the body?

Darveau et al. (2002) and Suarez et al. (2004) criticized ourtheory as being ‘flawed’ for implying that ‘there is a singlerate-limiting step or process that accounts for the b value inequation (1)’ (i.e. the allometric exponent for metabolic rate).As an alternative, they suggested a much more complicated,multiple-causes, allometric cascade model, in which metabolicrate is the sum of all ‘ATP-utilising processes’, Bi:B=ΣBi. Thissum simply represents overall conservation of energy, so itmust be correct if it is carried out consistently. Therefore, itcannot be in conflict with our theory. Darveau et al.incorporated many details of metabolic processes both atwhole-organism and at cellular–molecular levels in their sum:from pulmonary capacity, alveolar ventilation and cardiacoutput to Na+,K+-ATPase activity, protein synthesis andcapillary–mitochondria diffusion. All were added as if theywere independent and in parallel. However, many of theseprocesses are primarily in series, thereby leading to multiple-counting and therefore to a violation of energy conservation.Each Bi was assumed to scale allometrically as Bi=aiMbi soB=aΣciMbi�aMb, where the ci(=ai/a) were identified withconventional control coefficients defined as ‘the fractionalchange in organismal flux divided by the fractional change incapacity’ of the ith contributing process. As such, the ci aredimensionless. Unfortunately, however, it is obvious that theci as used by Darveau et al. in the above equations cannot bedimensionless since the bi that were used all have differentvalues. Consequently, their results are inconsistent andincorrect (West et al., 2003).

Even without this fatal flaw, their model makes no a prioripredictions about the scaling of metabolic rate, since noexplanation is offered for the origin or values of the scaling


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exponents for the contributing processes, bi. If the sum iscarried out correctly, it simply verifies the conservation ofmetabolic energy. From the Darveau et al. point of view the bi

are simply inputs; from ours, they are potentially outputsdetermined from network constraints. It is surely no accidentthat almost all of the bi cluster around 0.75.

Although we take issue with the characterization of our theoryas ‘single-cause’ – and point out that it predicts the scaling of16 variables for the mammalian cardiovascular system inaddition to metabolic rate and, in addition, makes similarpredictions for plants – we regard its relative simplicity as astrength rather than a weakness. We contend that for a givenmetabolic state, scaling of metabolic rate between different-sized organisms (that is, its relative value: M varying, but witha and ai fixed) is indeed constrained by the network and this isthe origin of quarter-powers. However, the absolute rate ofresource flow and power output (given by a and ai) within anindividual organism (that is, with fixed M) is not rate-limited bythe network: as in any transport system, changes in supply anddemand cause the network flow to change accordingly. Theconcept of an absolute ‘single-cause’ as used by Darveau et al.simply does not arise. Because of this, our model deliberatelyleaves out much of what is known about the biochemistry andphysiology of metabolism at cellular-molecular levels.

More generally, analytic models are typically deliberateoversimplifications of more complex realities. They areintended to ignore many details, to capture just the mostfundamental essence of a phenomenon, to provide a usefulconceptual framework, and to make robust testable predictions.To make an analogy, the basic theory of Mendelian geneticsstill provides the conceptual foundation for most of modernpopulation and evolutionary genetics, even though it does notincorporate much of what is known about genetics at thecellular (chromosomal) and molecular level. Indeed, for at leasta century Mendel’s laws have helped to guide the research intothe structure and function of the genetic material. Mendel’slaws ignore linkage, epistasis and crossing over, not to mentionsuch features of genomic architecture as regulatory regions,introns and transposons. They can now be amended orextended to account for these phenomena if and when it isimportant to incorporate such details into a conceptualframework or an empirical analysis.

We therefore find it surprising that certain features ofmetabolic processes at molecular and cellular levels (Darveauet al., 2002) are viewed as irreconcilable alternatives toour model. We view them as generally consistent andcomplementary. So, for example, cellular–molecular processesrelated to BMR generally scale close to M3/4 (but with higherexponents for some processes linked more directly to maximalmetabolic rate (Weibel et al., 2004). This is used as input tothe ‘allometric cascade model’ of Darveau et al. (2002), whoclaim that the M3/4 scaling of metabolic rate is determined bydemand-generated processes at the cellular–molecular levelrather than by supply-generated processes at the whole-organism level. We fail to see the logic of this argument, whichmakes an explicit distinction between supply- and demand-

driven processes. We conjecture that metabolic systems at themolecular, organelle and cellular levels, and the circulatory,respiratory, and other network systems that supply metabolicrequirements at the whole-organism level, are co-adjusted andco-evolved so as to match supply to demand and vice versa.More importantly, if whole-organism metabolic rate isdetermined entirely by cellular and molecular processes, whyshould it scale at all and why should it scale as M3/4? Thesimplest design would be to make the cells and molecules inmammals of different sizes identical building blocks so thatcellular metabolic performance is invariant. Whole-organismmetabolic rate would then simply be the sum of the rates of allthe identical cells, and so would scale linearly with mass. Ourtheory shows, however, that the constraints on blood volume,cardiac output, etc resulting from generic properties of networkdesign naturally lead to M3/4 scaling. But given this scaling ofwhole-organism metabolic rate, it is completely consistent –indeed it is predicted by our theory – that in vivo the cellularand molecular processes of metabolism also scale as M3/4

(West et al., 2002b).Although we disagree with the dichotomous supply- and

demand-driven views of metabolic regulation, our model doesmake predictions about the consequences of altering therelationship between the cells that perform the work ofmetabolism and the vascular networks that supply theresources. Specifically, it predicts that since the cellularmetabolic rates of large mammals are downregulated to obeythe constraints of reduced resource supply, their rates shouldincrease and converge on the cellular rates of small mammalswhen they are grown in culture with abundant resources. Thisis indeed observed (Fig.·5). Metabolic rates of cells derivedfrom different species and body sizes of mammals converge tonear maximal rates after being grown for multiple generationsin tissue culture under conditions of abundant resource supply(West et al., 2002b). A complementary result consistent withthis is reported by Else et al. (2004), who found that whenavian liver cells were disassociated and maintained in culturefor short periods, the allometric exponent decreased: fromapproximately –1/3 in vivo (the exact value is complicated bythe fact that the study used both passerine and non-passerinebirds, which likely have different normalization constants) toapproximately –0.1 in vitro. Although Else et al. state that thisresult ‘undoubtedly supports the allometric cascade model,’ itironically is exactly what would be expected in our theory ifthe cells have only partially compensated for isolation from thevascular supply network, because they had been maintained inculture without division for only a few hours. We conjecturethat, if they had been cultured for many days and had theopportunity to divide and adjust the numbers of mitochondria,the exponent would continue to decrease and eventuallyasymptote near zero.

Scaling of other biological rates and times: are quarterpowers universal?

Nearly all biological rates scale as M–1/4, although these varyfrom milliseconds for twitch frequencies of skeletal muscle




to decades for periods of population cycles (Calder, 1984;Lindstedt and Calder, 1981). Similarly, biological times tendto scale as M1/4, although these again vary from millisecondsfor turnover times of ATP to decades for lifespans ofindividuals. Recently, we (Savage et al., 2004b) collected dataand performed a meta-analysis of many of these rates andtimes. The results were very clear: average exponents for ratesand times showed clear peaks very close to 1/4 and –1/4,respectively, and the 95% confidence intervals excluded thevalues of –1/3 and 1/3 that would be predicted on the basis ofEuclidean geometric scaling (Fig.·10). So, the scaling of thesemany other attributes contributes to a synthetic body ofevidence providing overwhelming support for quarter-powerallometric scaling. This is a pervasive feature of biology acrossan enormous range of mass, time and space.

Our recent work has involved extensions of metabolic theoryto explain scaling of other attributes of biological structureand function at the levels of individuals, populations andecosystems. Beyond ontogenetic growth and development ofindividuals discussed above (Gillooly et al., 2001; West et al.,2002a), these have focused on individual-level production ofbiomass in animals and plants (Gillooly et al., 2001, 2002),population growth rates and related life history attributes(Savage et al., 2004a), rates of carbon flux and storage and fluxin ecosystems (Allen et al., 2005), and rates of molecularevolution (Gillooly et al., 2005).

BMR, FMR and VO∑max: what is optimized by naturalselection?

Most of the historical and recent discussion about theallometric scaling of metabolic rate, especially when appliedto mammals, has focused on basal metabolic rate (BMR). BMRis used as a standardized measure of physiological performancebecause it can be rigorously defined and quite accuratelymeasured as the metabolic rate of a resting, fasting, post-absorbtive mammal within its thermoneutral zone. However,since the animal is not in an energetic steady-state, let alone ata normal level of activity, BMR is of questionable biologicalsignificance.

Of much more biological relevance is the field metabolicrate (FMR), which is the rate of energy expenditure of ananimal during ‘normal’ activity in nature (Nagy et al., 1999).This immediately raises the question of standardization. Whatdoes normal activity mean? FMR is typically determined usingdoubly-labeled water or a similar technique to obtain anintegrated measure of metabolic rate over a period of severaldays. So it includes the costs of locomotion, grooming,foraging and other ‘maintenance’ activities, but usually not thegreater costs of reproduction or of thermoregulation tocounteract severe cold or heat stress, and not the energeticsavings accrued by entering hibernation, aestivation or torpor.Natural selection has presumably operated to maximize theperformance of the mammalian metabolic processes – and ofthe cardiovascular system that supplies resources formetabolism – over the entire life history, thereby incorporatingthe costs of reproduction, thermoregulation, hibernation,

migration, and other such activities throughout an annual cycle.There are few studies on such a scale, however, so FMRsprobably provide the most relevant measures of metabolicperformance.

Some physiologists (Taylor et al., 1988; Weibel et al., 2004,1991) have emphasized the maximal sustained aerobicmetabolic rate (MMR) or VO∑max. Such levels of performanceare typically measured in non-volant mammals as rates ofenergy utilization or oxygen consumption while running athigh speed. They are undoubtedly of great adaptivesignificance, especially during predator avoidance, preycapture and reproductive activity. There are, however, someproblems of standardization. One concerns how long and atwhat speed the mammals are run. Since both maximal speedand endurance scale positively with body size (Calder, 1984;Schmidt-Nielsen, 1984), there is the issue of how this shouldbe incorporated into experimental protocols. Additionally,there is substantial variation in performance among species,even those of the same body size. ‘Athletic’ mammals suchas cheetahs, dogs, horses, antelopes and hares, which haveevolved to run at high speeds, have several-fold higher VO∑max

and factorial aerobic scope than ‘sedentary’ species of similarsize.

Nevertheless, we are convinced, especially by the recentwork of Weibel et al. (2004), that the athletic species define anupper boundary for the scaling of VO∑max, which has anexponent significantly greater than 3/4 and perhaps evenapproaching 1. We are quick to point out, however, that whilethis raises important questions, it does not invalidate ourtheory. There are several issues. First, the high metabolic ratesof these athletic mammals are still supplied by thehierarchically branching arterial network, so many of theprinciples embodied in our model must still apply. Second,there is a reallocation of blood flow during exercise. Heart rateincreases and blood flow is shunted to the metabolically activetissues, chiefly cardiac and skeletal muscle, to supply theincreased oxygen demand. But since total blood volumeremains virtually unchanged, blood is diverted from othertissues, such as digestive organs, and they are temporarilyoxygen-deprived. Third, it is unlikely that the steep scaling ofMMR can hold over the entire mammalian size range,including the great whales. Simple extrapolation of twoallometric relationships, one with an exponent of 3/4 for BMRand FMR, and the other with a much higher exponent forMMR, would require a very large factorial aerobic scope andprevent any of the largest mammals from being athletic.

Lastly, our theory predicts that the allometric exponentshould change between BMR and MMR because of thesensitivity of impedance matching to heart beat frequency.Recall that an important ingredient to our derivation of the 3/4was that reflections be eliminated at branch junctions, leadingto area-preserving branching. However, all the importantphysiological variables, including heart-rate, are ‘tuned’ tobody size. If heart rate is increased because of increasedactivity, but the dimensions of the large vessels are kept fixed,there is a mis-match and reflections result. We speculate that


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while the scalings of BMR and FMR reflect minimization ofenergy loss (thereby requiring impedance matching), scalingof MMR reflects maximization of power output, which isachieved by several changes in the cardiovascular system,including giving up impedance matching. Such an effect wouldindeed drive the exponent larger, but it is difficult to calculatethe exact value without a formal model.

We suggest that what is needed is an effort to model theperformance of the cardiovascular and skeleton–muscularsystems of athletic mammals performing under standardizedconditions of VO∑max. Such a model would retain many featuresof our model for the arterial system, but would also incorporatewhat is known about changes in heart rate, blood flow andtissue metabolism. To the extent that not all of the data desiredmay be available, such a model would help to motivateempirical studies by comparative physiologists to betterunderstand how the mammalian cardiovascular system adjustsdynamically to the shifting demands imposed by differentlevels of activity. Some features of our original model mayneed to be changed. For example, natural selection has likelymaximized blood flow to certain tissues so as to maximizepower output for speed or endurance rather than to minimizeexpenditure of energy within the arterial network.Nevertheless, such a whole-system model would demand basicconstraints, such as conservation of blood volume within thenetwork and sufficient oxygen supply to meet aerobicmetabolic demand. Ultimately this could lead to a completemodel that would quantitatively predict the scaling exponentsand normalizations for many relevant parameters of thesystem, including how they deviate from quarter-powers in theactive state.

Concluding remarksWe are very much aware that the philosophy of our

theoretical research program on biological scaling runs counterto recent trends in comparative and mammalian physiology.Although not a major theme of current research, analyticalmathematical models and general theory based on firstprinciples have in the past played an important role inphysiology. As examples, we cite applications ofthermodynamics to body temperature regulation (Scholanderet al., 1950), electrical and chemical potentials to nerveconduction (Hodgkin and Huxley, 1952), countercurrentexchange principles to thermoregulation (Scholander andSchevill, 1955), aerodynamic theory to flying animals(Greenwalt, 1975), and hydrodynamic principles to aquaticorganisms (Vogel, 1981).

Recently, however, most research programs have had astrong empirical emphasis. They have sought to explainvariation in performance of organisms from differentenvironments and phylogenetic lineages in terms of details ofstructure and function at cellular and molecular levels. Theyhave accumulated and organized a vast store of information. Apowerful theme in basic and comparative physiology has beento understand the molecular basis, including characterizing

enzyme kinetics and identifying genes, for variation in whole-organism function. This trend mirrors similar reductionistthemes in many branches of science, from atomic physics tohuman psychology, during the last few decades.

While we recognize the scientific merit and importance ofthis approach, we also believe that general theory andmathematical models can play an important role. Sciencestypically cycle between periods of empiricism and theory,reductionism and holism. Empirical advances are typicallyunified and synthesized by theoretical contributions that usebasic principles and idealized, simplified models to obtaingeneralized insights. Reductionist studies that discovercomponents and processes at microscopic levels are givenadditional meaning by holistic studies that show how thesephenomena contribute to structure and function of large,complex systems at higher levels of organization. Theoreticaland empirical, reductionist and holistic studies are typicallyconducted by different individuals, motivated by differentquestions and predilections. Both are equally necessary forscientific progress.

We believe that new theories of biology can play a majorrole in synthesizing recent empirical advances and elucidatinguniversal features of life. We see the prospects for theemergence of a general theory of metabolism that will play arole in biology similar to the theory of genetics. Genetic theoryis increasingly successful in explaining the development of thephenotype and the dynamics of evolutionary change in termsof the heritable traits of individual organisms, and inunderstanding how those individual-level traits are coded andregulated by the molecular structure and function of thegenome. Genetic theory is successful in part because there isa universal molecular genetic code. The code operatesaccording to certain basic principles of structure and functionto direct the ontogeny and determine the phenotype ofindividual organisms, and these individuals live, die, and leaveoffspring according to additional rules of population geneticsand ecology to determine the evolutionary dynamics ofpopulations and lineages.

Similarly, all organisms share a common structural andfunctional basis of metabolism at the molecular level. Thebasic enzymes and reactions are universal, at least across theaerobic eukaryotes. Additional general rules based on firstprinciples determine how this molecular-level metabolism issupplied and regulated at higher levels of organization: fromorganelles, to cells, to organisms, to ecosystems. The mostimportant of these rules are those relating to the size of thesystems, including the body size of the individual organisms,and the temperature at which they operate. Our theory ofquarter-power scaling offers a unified conceptual explanation,based on first principles of geometry, biology, physics andchemistry for the size-dependence of the metabolic process.The theory is based on generic properties of the metabolicdistribution networks in simplified, idealized organisms. Itprovides a 0th order quantitative explanation for manyobserved phenomena at all of the hierarchical levels oforganization.




Quarter-power scaling theory is not the only ingredient of ageneral theory of metabolisms Thermodynamics and, inparticular, temperature are clearly another critical ingredient.As already emphasised, quarter-power allometry and simpleBoltzmann kinetics together account for the body size andtemperature dependence of metabolic rates and other relatedbiological structures, rates, and times across all levels oforganization from molecules to ecosystems (Gillooly et al.,2001, 2002; Savage et al., 2004a). For example, these two basiccomponents of metabolic theory account for more than 99% ofthe variation in rates of whole-organism biomass productionacross an enormous diversity of organisms spanning 16 ordersof magnitude in body mass from unicellular algae and protiststo trees and mammals (Ernest et al., 2003).

There is much work still to be done, but we look forward tothe development of universal theories of biology that integrateacross levels of organization from molecules to populationsand ecosystems and across the diverse taxonomic andfunctional groups of organisms. Such theories will incorporaterecent empirical discoveries, especially the recent advances atcellular to molecular levels of organization. Ultimately theymay provide for biology the kinds of unifying conceptualframeworks, based on first principles and expressedquantitatively in the language of mathematics, that similartheories do for physics and chemistry. This is a bold butexciting vision for the 21st Century, which many are calling theCentury of Biology.

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Temperature control of larval dispersal and theimplications for marine ecology, evolution,and conservationMary I. O’Connor*†‡, John F. Bruno†, Steven D. Gaines§, Benjamin S. Halpern¶, Sarah E. Lester§, Brian P. Kinlan§,and Jack M. Weiss*

*Curriculum in Ecology, CB 3275, University of North Carolina, Chapel Hill, NC 27599; †Department of Marine Sciences, CB 3300, University of NorthCarolina, Chapel Hill, NC 27599; §Department of Ecology, Evolution, and Marine Biology and the Marine Science Institute, University of California,Santa Barbara, CA 93106; and ¶National Center for Ecological Analysis and Synthesis, 735 State Street, Santa Barbara, CA 93101

Edited by James H. Brown, University of New Mexico, Albuquerque, NM, and approved November 13, 2006 (received for review April 27, 2006)

Temperature controls the rate of fundamental biochemical pro-cesses and thereby regulates organismal attributes including de-velopment rate and survival. The increase in metabolic rate withtemperature explains substantial among-species variation in life-history traits, population dynamics, and ecosystem processes.Temperature can also cause variability in metabolic rate withinspecies. Here, we compare the effect of temperature on a keycomponent of marine life cycles among a geographically andtaxonomically diverse group of marine fish and invertebrates.Although innumerable lab studies document the negative effect oftemperature on larval development time, little is known about thegenerality versus taxon-dependence of this relationship. Wepresent a unified, parameterized model for the temperature de-pendence of larval development in marine animals. Because theduration of the larval period is known to influence larval dispersaldistance and survival, changes in ocean temperature could havea direct and predictable influence on population connectivity,community structure, and regional-to-global scale patterns ofbiodiversity.

metabolic scaling ! population connectivity ! temperature dependence !larval development ! survival

Through a general effect on metabolic rate, variation inenvironmental temperature can influence population, spe-

cies, and community-level processes (1–3). Recently, evidencefor a universal temperature dependence has linked individualmetabolism to community-wide productivity, which in turn leadsto predictable rates of population growth, carbon flux, andpatterns of regional diversity (4–7). Although less appreciated inthis context, the universal temperature dependence of metabo-lism implies an inverse relationship between temperature andlife-stage duration (8). For marine animals whose offspringdevelop in the water column, the duration of the larval life stagedetermines the length of time that larvae are subject to move-ment by currents and exposed to sources of mortality. Therefore,a general and quantitative influence of temperature on larvalduration potentially implies a mechanistic link between oceantemperature and the biogeographic patterns mediated by theecological processes of larval dispersal and survival.

Two aspects of the influence of temperature on larval durationare well documented. First, Thorson’s rule describes the latitu-dinal gradient of a decreasing proportion of marine species withplanktonic larval development toward the poles (9, 10). Second,temperature is known to cause among-species variation in larvaldevelopment and duration (10, 11). Studies in this vein haveemphasized between-species comparisons without accountingfor within-species relationships between temperature and plank-tonic larval duration (PLD); therefore, these studies reportstrong relationships only within narrower taxonomic groupings.Numerous other studies have documented the temperaturedependence of the larval development period within species.

Typically this relationship has been described as exponential(e.g., ref. 12) with species-specific parameter values. Therefore,the generality of the temperature-dependence of larval durationremains untested. If general for a wide variety of animals, aquantitative model of the effect of temperature on planktoniclarval duration could enhance hypotheses and existing models toevaluate the ecological and evolutionary consequences of tem-perature change in the ocean.

We tested the generality of the temperature-dependence ofplanktonic larval duration for 72 species of marine animals [seesupporting information (SI) Tables 3 and 4]. We synthesized theeffect of temperature on PLD by comparing results from 62laboratory experiments in which vertebrate and invertebratelarvae were reared at multiple, nonlethal temperatures (SI Text1 and SI Table 4). We used a multilevel model to estimateparameter values that describe the influence of temperature ondevelopment of marine larvae (SI Appendix) (13). We then usedour results to formulate models of the effect of temperature ondispersal and survival.

ResultsThe quantitative relationship between planktonic larval dura-tion and temperature is highly predictable across taxa, latitudes,and oceans (Figs. 1 and 2). Using Akaike Information Criteria(AIC) for model selection, we determined that an exponentialmodel quadratic in temperature on a log–log scale, hereaftercalled the exponential-quadratic model (methods: Eq. 2), bestdescribes the general temperature dependence of PLD withinspecies (SI Table 5 and SI Appendix).

An analysis of species-level (level-2) residuals using caterpillarplots (14) suggests that a species-specific model with randomintercepts but constant linear and quadratic coefficients fitsnearly all species under consideration (Fig. 1 and SI Appendix).However, a few species deviate significantly from this overallpattern (Fig. 1A and SI Appendix). We identified these speciesby constructing 95% confidence intervals for species-level re-siduals of the model parameters (Fig. 1). Sequential removal ofthe most deviant species reveals that only three species (Limuluspolyphemus, Laqueus californianus, and Callianassa tyrrhena, Fig.

Author contributions: M.I.O., J.F.B., and S.D.G. designed research; B.S.H., B.P.K., and J.M.W.contributed new reagents/analytic tools; M.I.O., B.P.K., and J.M.W. analyzed data; andM.I.O., J.F.B., S.D.G., B.S.H., S.E.L., B.P.K., and J.M.W. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS direct submission.

Freely available online through the PNAS open access option.

Abbreviations: PLD, planktonic larval duration; UTD, universal temperature dependence.‡To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/cgi/content/full/0603422104/DC1.

© 2007 by The National Academy of Sciences of the USA

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2A) are driving the need for random linear and quadratic termsin the log–linear formulation of the model. When these threespecies are removed from the analysis, a multilevel model withonly random intercepts adequately fits the remaining 69 species.Therefore, we present a population-averaged model for a dataset that excludes the three outliers (Fig. 2B).

We find that PLD shows essentially the same relationship withtemperature across species (Fig. 1A) and differs only in how thecurve is scaled (as determined by the factor !0 in Eq. 2; Fig. 1B).Individual intercept values (!0i) are highly species-specific and mostare not well represented by the population-averaged estimate (Figs.1B and 2B). Thus, most of the variation among species is withrespect to the magnitude of the larval duration at a given temper-ature but not its relationship to changing temperature.

The nearly uniform temperature sensitivity of larval-development time is consistent with a model derived from firstprinciples of physics and biology (2, 5) (Fig. 3 and SI Fig. 7).Gillooly et al. (5) described the universal temperature depen-dence (UTD) of biological processes, a mechanistic theory thatlinks whole-organism metabolic rates to the effects of temper-ature on biochemical processes. Although the UTD model was

not the best fit of the models we tested (SI Table 5), thefunctional forms of the mechanistic UTD model (Eq. 3) and thepurely descriptive exponential–quadratic model (Eq. 2) aresimilar over most of the temperature range (SI Fig. 8). Theprimary difference is that the exponential model predicts asteeper slope to the temperature dependence below !7°C. Thissimilarity suggests that the mechanistic basis of the UTD modelmay be relevant to the temperature dependence of PLD. An-other important difference between the two models is theirtreatment of larval mass: the UTD model assumes mass-normalized development durations (8), whereas the exponential–quadratic model (Eq. 2) does not. Although sufficient larvalmass data were not available for this analysis, the omission ofmass could explain why Eq. 2 is a better fit for these data.

The within-species temperature dependence of PLD matchesthe predicted effect of temperature based on among-species

Fig. 1. Caterpillar plots comparing ranked species-level residuals (randomeffects) for 72 species along with 95% confidence intervals, for two of thethree level-1 parameters. Confidence intervals that do not intersect zeroidentify species whose species-specific value for that parameter is significantlydifferent from the corresponding population-averaged value. The caterpillarplot graphically identifies those species poorly represented by the population-averaged model (see SI Appendix). (A) Predictions and 95% confidence inter-vals (black triangles and gray error bars) for the random effect component (u1i)of the linear scaling parameter !1i for each species (Eq. 15). Confidenceintervals do not include 0 for seven species (red points): L. polyphemus, C.tyrrhena, H. americanus, G. morhua, S. spirorbis, S. balanoides, and L. cali-fornianus. After removing the three most-deviant outliers, L. polyphemus, L.californianus, and C. tyrrhena, there is no longer a need for random effects forthe linear and quadratic scaling parameters. (B) Caterpillar plot for species-level residuals u0i. Because the majority (46 of 72) of the confidence intervalsfail to include 0, we conclude that the species-specific intercept parameters !0i

are significantly different from the population-averaged value !0 for mostspecies. No adjustments for multiple testing were made.

Fig. 2. The relationship between water temperature and PLD based onresults from published experimental laboratory studies on the effect of tem-perature on larval duration for 72 species (six phyla: 6 fish, 66 invertebrates; SITables 3 and 4). (A) Mean recorded larval duration at each temperature foreach species; two to six data points per species connected by gray lines.Subsequent analyses identified three outliers (black diamonds). (B) Popula-tion-averaged (black) and species-specific (gray) trajectories obtained from amultilevel exponential model quadratic in temperature on a log–log scalewith random intercepts displayed here on an arithmetic scale. Estimatedpopulation-averaged curve: ln(PLD) " 3.17 # 1.34 $ ln(T/Tc) # 0.28 $ (ln(T/Tc))2, which yields the plotted estimated geometric mean curve: PLD "exp(3.17) $ (T/Tc)(#1.40#0.27$ln(T/Tc)), Tc " 15°C (SI Appendix). The parameterestimates !1 " #1.34 and !2 " #0.28 adequately describe 69 species, whereas!0 is highly variable among species (see SI Text for model application). Shownhere is the population-averaged trajectory for PLD about which individualspecies-level trajectories are assumed to vary randomly. !0 " 3.17 is interpret-able as the value of ln(PLD) at 15°C. Three outliers were excluded in estimatingthe model (data not shown); dashed lines represent the 95% confidence bandfor the population-averaged trajectory.

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analyses (5, 8). Gillooly et al. (5) predicted that the averageactivation energy (i.e., temperature scaling) for metabolic pro-cesses in ectotherms is !0.62 eV, which matches our estimate fordeveloping larvae that used the UTD model (95% CI: 0.59–0.69,Fig. 3 and SI Fig. 7). To date, the UTD hypothesis has generallybeen tested by making among-species comparisons of mass-normalized resting metabolic rates (5, 15). In contrast, ourestimate of the temperature sensitivity of PLD focuses onwithin-species temperature dependence. This similarity betweenthe within- and among-species patterns (Fig. 3 and SI Fig. 7)suggests that the effect of temperature on larval development isuniversal and not species-specific. Our result is consistent withthe only other test of this hypothesis (16).

In colder water, increased temperature dependence and gen-erally longer development times (Fig. 2) may affect the evolutionof molecular processes and life history traits. Because highcumulative mortality rates are associated with very long larvalduration, there may be selection to reduce planktonic larvalduration in animals that evolve in cold climates (17). We testedwhether home-range temperature could explain variation inPLD among species by adding a species-level regional temper-ature variable to the multilevel model (Fig. 4; Eq. 7). Theaddition of this variable significantly improved the ability of themodel to predict species-specific PLD (SI Table 6) and explains17% of the variation in intercepts among species (SI Text).Species from colder climates tend to have shorter PLDs (lowervalues of !0i) compared with species from warmer regions (Fig.4). Adding a variable for developmental mode (lecithotrophic vs.planktotrophic) to the model increases the explained variance inintercepts to 27%; planktotrophs tend to have longer PLDs thanlecithotrophs (Fig. 4).

DiscussionOur results demonstrate a strong effect of temperature onplanktonic larval duration that is quantitatively constant acrossnearly all species tested. A single, parameterized model describesthe temperature dependence of the planktonic larval period for

a diverse group of species from six phyla over a range of bodysizes and habitats. A general temperature dependence of larvalduration implies common and predictable effects of oceantemperature on larval dispersal distance and survival.

The universal form of the temperature dependence emergesdespite enormous differences in larval size and other life-history traits among species. Conceptually, the remainingvariation in PLD among species can be thought of as parti-tioning into three categories: (i) variation in PLD amongspecies at any particular temperature (the intercept parameter!0i in Eq. 4; Figs. 1B and 4), (ii) variation among species in thescaling effect of temperature (parameters !1i and !2i in Eq. 4;SI Appendix), and (iii) scatter of measured PLD around theindividual regression lines because of measurement error orother unmeasured variation (SI Text). Variation among speciesin PLD at any given temperature (variation type 1), asobserved in Figs. 1 and 2, could be due to life-history traitssuch as development mode, larval size at hatching or compe-tency, or assimilation efficiency. For example, lecithotrophic(nonfeeding) larvae tend to be larger and generally haveshorter PLDs than planktotrophic (feeding) larvae (18) (Fig.4). There are contrasting predictions for how larval size affectsplanktonic duration. Large eggs and larvae can result fromincreased parental investment before release, allowing forshorter planktonic periods (19–21). Alternatively, metabolicecological theory predicts that development time and body sizeshould be positively correlated such that species with largerlarvae require longer larval durations (2, 8). Metabolic theorymight accommodate this apparent contradiction. Part of thesolution may lie in appropriately separating the disparateeffects of variation in larval size at hatching from larval size atcompetency. In addition, lecithotrophs may have higher foodquality than planktotrophs, or may be more efficient atassimilating energy. Food quality and assimilation efficiencyare held constant in the general metabolic scaling model (8)

Fig. 3. Arrhenius plot of Universal Temperature Dependence model (Eq. 3)for within-species variation in PLD with temperature (n " 72). Temperature(°C) is expressed as its reciprocal adjusted to Kelvin and multiplied by theBoltzmann constant (k). Population-averaged trajectory for the temperatureeffect within species as estimated from a multilevel model with random slopesand intercepts: ln(PLD) " #22.47 % 0.64 $ (1/(k $ (T % 273))) for temperature(T) in °C (solid line), or PLD & exp(0.64/(k $ (T % 273))). The model-basedempirical Bayes trajectories shown here differ from the ordinary least-squares-fitted trajectories that would be obtained from fitting individual tempera-ture-dependence models to each species one species at a time (SI Appendix).Metabolic theory predicts that on average the slope is 0.62 eV (5) (dashed line)and within the range 0.60–0.70 eV (2). As with the linearized power lawmodel, a random slopes and intercepts UTD model is required for this data setof 72 species (SI Table 9).

Fig. 4. Effect of climate and developmental mode on the temperaturedependence of PLD for 69 species. We used mean ln(test temperature) for eachspecies as a proxy for the average temperature in each species’ geographicrange. The best model among those we examined was one in which therandom intercepts model (Eq. 4) was extended to allow ln(PLD) to varyadditively with mean ln(test temperature) and developmental mode (SI Table6). In the multilevel modeling framework, these two species-level variables areconsidered predictors of the species-specific intercept, !0i. In the centeredlevel-1 model presented here (SI Table 7), this intercept is interpretable asln(PLD) at 15°C. The predicted intercepts from a random intercepts multilevelmodel (Eq. 4) are plotted here against mean ln(test temperature) (Left) anddevelopmental mode (Right). (Left) The lowess (solid curve) and linear trend(dashed line) suggest that larvae tested at colder temperatures tend to havesmaller predicted intercepts than do larvae tested at warmer temperatures.(Right) Schematic boxplots, following standard conventions for such graphs,of predicted intercepts for each developmental mode are displayed, withmeans indicated by asterisks. Lecithotrophs (L, filled circles) tend to havesmaller predicted intercepts than do planktrophs (P, open circles).

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but may, in fact, vary systematically among lecithotrophs andplanktotrophs.

We observed very little variation among species in the scalingeffect of temperature (type 2 variance above). Residual analysissuggests that a single model fits 69 of 72 species (Fig. 2A; and seeSI Appendix). We suggest three hypotheses for the species withunique temperature dependence: (i) unique evolutionary history,(ii) unique selective environments, or (iii) metabolic cold adapta-tion. Regarding hypothesis i, two of the species are the solerepresentatives of their taxonomic order in this data set (thebrachiopod L. californianus and the horseshoe crab L. polyphemus).Because the temperature dependence parameter estimates forthese species deviate in different directions, their selective envi-ronment may have driven their unique temperature dependence(hypothesis ii). These hypotheses do not appear to explain the thirdoutlier, the ghost shrimp C. tyrrhena. A common species in thewarm-temperate eastern Atlantic Ocean, adult C. tyrrhena arewidely distributed among shallow sand flat environments, andlarvae are commonly found in the plankton (22).

Common and predictable temperature control of larval du-ration may have important implications for many ecologicalprocesses and applied issues, including larval dispersal, larvalmortality, population connectivity, and recruitment dynamics.For many marine species, the planktonic larval phase is the onlylife stage in which individuals disperse away from the parentalpopulation. Unless oceanographic retention processes or larvalbehaviors change radically in concert with water temperature(23), an increased development rate effectively shortens theduration of the planktonic larval phase (24). Syntheses of marinedispersal data show that PLD is, in turn, positively correlatedwith larval dispersal distance (25, 26). Although a variety ofother factors may also influence realized dispersal distances,including active larval behavior and complex oceanography (27),on average, the more time larvae spend in the planktonic phase,the farther they tend to travel before they settle (25).

To illustrate the potential influence of water temperature onlarval dispersal, we used a simple, idealized model of therelationship between PLD and passive larval dispersal distance(25). This ‘‘null model’’ of larval dispersal predicts the averagedispersal distance of passive larvae along a linear coastline as afunction of two-dimensional near-shore current velocity statis-tics and the larval competency period. Despite its simplicity,predictions of this model correspond well with available empir-ical measures of marine larval dispersal for currents typical ofcoastal oceans (25). Our results suggest that water temperaturemay have a striking effect on the dispersal distance of marinelarvae (Fig. 5A). Because dispersal distance scales nonlinearlywith PLD, maximum predicted dispersal distances for larvae incolder water are much greater than those in warmer water. Usingthe temperature-PLD model (Fig. 2B), we predict that, all elsebeing equal, mean dispersal distance should vary by over anorder of magnitude (20 versus 225 km) as temperature variesfrom warm tropical conditions (30°C) to cold temperate waters(5°C). More detailed numerical models tailored to the ocean-ography of particular regions and investigations into how larvalbehavior and life history traits may modulate the temperatureeffect on dispersal will lead to further insight on the impacts ofchanging temperature on connectivity in actual populations.

By controlling larval duration, temperature also mediates theduration of exposure to important sources of larval mortality(10, 28). Larval survival is generally very low, often '1% (28,29), and decreases exponentially with time when mortalitysources such as predation or the likelihood of encountering harshenvironmental conditions are relatively constant over the lifes-pan of a larva (28, 29). Assuming that mortality remains constantwith temperature, the exponential loss of larvae with increasingPLD (30) should lead to much lower cumulative larval survivalrates in cold water than in warmer water (Fig. 5B). Some sources

of mortality, however, such as starvation, oxygen limitation, orpredation, are not constant through the larval developmentperiod and may change either with larval density, age (31), ortemperature (24). Survival of a larval cohort reflects mortalitydue to both these temperature sensitive factors and to constantfactors.

Reduced survival over long larval periods may select forshorter PLDs in colder climates than expected based on tem-perature (Fig. 4) (17). There are two adaptive explanations forshorter than expected cold water PLDs: either organisms haveadapted life history traits that reduce time spent in the plankton,or molecular processes have evolved to be faster at cold tem-peratures (32). Within some taxa, life-history traits correlatedwith reduced PLD are more common in cold regions. There isa greater proportion of species with either lecithotrophic ornonplanktonic development in polar regions for some taxa (17,28, 30, 31), consistent with Thorson’s rule (17, 33). Because weobserve declining PLD with home-range ocean temperature inboth lecithotrophs and planktotrophs (Fig. 4), we suggest thatlecithotrophy and larval size are two distinct strategies forreducing PLD that can occur separately or together.

The general influence of temperature on marine larval dis-persal has fundamental implications for the understanding and

Fig. 5. The predicted effects of ocean temperature on two importantecological and evolutionary parameters: larval dispersal distance (A) andlarval survival (B). The predicted effect on dispersal distance is based on ourpopulation-averaged temperature-PLD model (Fig. 1B) and on a publishedmodel relating PLD to dispersal (25) that used mean current velocity (U) " 0cm/s and with standard deviation (s) " 15 cm/s to reflect typical near-shorecoastal ocean currents. Species-specific projections are shown (gray lines) toconvey the range of variability. Confidence band (95%) is for prediction ofmean temperature effect on PLD, as in Fig. 1B. Predicted effects on cumulativesurvival assume a constant density- and temperature-independent daily mor-tality rate of 15% (18).


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management of marine populations and ecosystems. Effectivemanagement requires knowledge of population size, geneticdiversity, and connectivity; these properties depend on prop-agule and gene flow maintained by both frequent, medium-range, and rare, long-distance, dispersal events. Because larvalduration influences both medium- and long-range dispersal (34),and dispersal distances can be far greater in cold water, popu-lation connectivity and effective population size should, ingeneral, be inversely related to ocean temperature. Conse-quently, the spacing among individual reserves in networks ofmarine protected areas (MPAs) (35) may need to be far closerin the tropics than in high-latitude regions to ensure connectiv-ity. The degree of connectivity and openness also affects localand landscape-scale processes, including predator–prey interac-tions, local community composition, and metacommunity dy-namics (24, 36, 37).

Temperature effects on planktonic larval duration may alsoexplain some interannual variation in recruitment. It has longbeen hypothesized that events or factors that influence vital ratesduring early life-history stages are linked to recruitment varia-tion (24, 38). Whether increased temperature results in increasedor decreased recruitment depends on the species’ ecology, thespatial arrangement of essential habitat, and how larval durationrelates to recruitment. The effect of temperature on recruitmentthrough its effect on planktonic larval duration may help explainrecruitment variation in commercially important or invasivespecies.

Temperature is one of several factors that influence larvalduration, dispersal, and survival in the field. For example,changes in nutrient availability or ocean current dynamics areoften associated with change in ocean temperature, and theirinfluence on larval dispersal would ultimately need to be ac-counted for in a species- or system-specific model of larvaldispersal and recruitment. Nonetheless, two lines of evidencesuggest that the temperature-dependent dispersal model wepresent here will be a useful tool for dispersal models: (i) mostlaboratory studies that factorially tested the effect of tempera-ture and another environmental variable, such as salinity or foodavailability, found temperature to have the greatest effect ondevelopment time (e.g., ref. 39), and (ii) the quantitative modelwe present here is applicable to nearly all species and so caneither serve as a null model for the effects of changing oceantemperature, or can be combined with other quantified effects.

This research provides a context for understanding the effectof environmental temperature on the patterns and processes thatinfluence population dynamics and species diversity. The uni-versal temperature dependence of metabolism previously doc-umented extends to the larval development of ectothermicmarine organisms and, hence, to their PLD. Recognition thatthis temperature effect is common to the most motile life stageof many marine organisms will improve our ability to predict theeffects of variation in temperature on demographic and evolu-tionary processes and to incorporate the effects of temperatureinto marine species and ecosystem management. Our resultssuggest that a fundamental constraint of enzyme kinetics canexplain a remarkable degree of variation in local, regional, andglobal patterns and processes and possibly even macroevolution-ary processes that take place over geological time scales.

MethodsData Transformation. The temperature dependence of larval de-velopment time typically follows a power law (9, 24). To linearizethis relationship and satisfy statistical assumptions, both PLDand temperature were ln-transformed (SI Appendix, Section II).To aid interpretation and improve numerical stability of themodel, we express temperature as ln(T/Tc), where T is temper-ature (°C) and Tc " 15°C. This is equivalent to subtracting ln(Tc)from each temperature observation on a log scale and thus is a

form of centering (SI Appendix). Statistical results from centeredand uncentered models are identical (SI Appendix). All statisticalanalyses were performed in R 2.4.0 (40).

Statistical Analyses. To estimate the relationship between PLDand temperature and to compare that effect among species, weused a random-effects (multilevel) model [also called a hierar-chical model (13)]. Because observations are nested withinspecies, we treat this as a two-stage sample and fit a random-effects model in which parameters are allowed to vary acrossspecies. A multilevel model allowed us to explore intra- andinterspecific patterns while respecting the inherent structure ofthe data. Different models were possible depending on whichparameters were allowed to vary across species. We treatedmodel parameters for each species as random effects at thespecies level, treating these species as random representatives ofall species. Because the analysis fits the model to all species atonce, we were able to include in the analysis even those speciesthat provided only two data points. See SI Appendix for a moredetailed description of statistical methods.

Model Selection. We compared ln-transformed versions of threetheoretical models of temperature effects on PLD. In eachmodel, !0 is the intercept, and !1 and !2 are linear andquadratic scaling parameters, respectively. T " temperature(°C) and Tc " 15°C.

(i) A linearized power law model that has traditionally beenused to approximate the effect of temperature on PLD (41):

ln(PLD) " !0 # !1 $ ln(T"Tc); [1]

(ii) A linearized power law model that is quadratic in tem-perature (42). We are calling this the exponential-quadraticmodel:

ln(PLD) " !0 # !1 $ ln(T"Tc) # !2 $ ( ln(T"Tc))2;

[2]

(iii) The UTD equation (5), where k is the Boltzmann constant(8.62 $ 10#5 eV K#1), and (T (°C) % 273) is absolute temper-ature (K):

ln(PLD) " !0 # !1"(k $ (T # 273)) . [3]

We assumed that individual observations were realizationsfrom a normal distribution with constant variance %2 and thatconditional mean was given by the respective theoretical models.Within each model type (Eqs. 1–3), we first investigated the needfor including random effects that allow the intercepts, slopes,and/or quadratic coefficients to vary among species. We usedmodified likelihood ratio tests, adjusted for boundary condi-tions, to compare nested models that differed in the number ofrandom effects they contained (SI Table 8 and SI Appendix).Having chosen the best random-effects model of each type (e.g.,Eq. 1, 2, or 3), the winners were then compared by using Akaike’sInformation Criterion (AIC) (43) (SI Table 5). We conclude thata multilevel linearized power-law model with a quadratic tem-perature term (Eq. 2) best approximates the relationship be-tween temperature and PLD. Based on model diagnostics (SIAppendix) we identified those species not well described by ourchosen model (Figs. 1A and 2A). With these outliers removed,the model requires random effects only for the intercept (!0i)(Eq. 4). Our final model written in statistical form, where iindexes species and j indexes observations, is the following:

Level 1: ln(PLDij) " !0i # !1 $ ( ln(Tij"Tc))%!2

$(ln(Tij"Tc))2%&ij [4]

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Level 2: !0i " !0 # u0i; u0i # N (0,'2) , & ij # N(0, %2) .

!1 and !2 are fixed for all species (Fig. 2B). u0i is a random effectthat allows !0i to vary across species.

Variation in PLD with Climate. We estimated species’ normaltemperature range by calculating the mean of the ln(tempera-tures) tested for each species, and considered this value to be aproxy for the average temperature in the species’ normal geo-graphic range. In the majority of studies, test temperaturesspanned the range of temperatures experienced by the organismduring most of the year.

Projection of Temperature Scaling of Dispersal Distance and Survival.We used a model linking nearshore current velocity and flowpatterns to average passive larval dispersal distance. The modelprojects larval movement in coastal surface currents and ac-counts for serial correlation in larval trajectories introduced bylarge turbulent eddies. See Kinlan et al. (34) for further discus-sion of this use of the Siegel et al. (25) model. The modelpresented in Fig. 5A is:

Dd " 0.695 $ (PLD) $ U # 0.234 $ (PLD) $ s . [5]

Terms are the current velocity (U in km/d), its standarddeviation (s in km/d), and the temperature-dependent larvalduration model presented in Fig. 1B (PLD in days). Numericconstants in Eq. 5 are fit parameters for dispersal kernels asfunctions of the flow parameters for near-shore coastal envi-ronments (25).

To calculate the survival of a cohort based on temperatureeffects on PLD, we used the exponential decay model:

Sc " SdPLD. [6]

Terms are the percent of a cohort surviving through meta-morphosis (Sc), daily survival rate (Sd " 1 # Md, where Md is thedaily mortality rate), and the temperature-dependent larvalduration model presented in Fig. 2B (PLD in days).

We thank S. V. McNally for data collection and W. Eaton, S. Lee, K.France, N. O’Connor, E. Selig, A. Steen, A. Allen, J. Brown, and twoanonymous reviewers for comments that improved this manuscript. Thiswork was funded in part by National Science Foundation GrantsOCE0326983 and OCE0327191 (to J.F.B.), the National Center forEcological Analysis and Synthesis, The Nature Conservancy, the Davidand Lucile Packard Foundation, the Gordon and Betty Moore Foun-dation, the Fannie and John Hertz Foundation, the Andrew W. MellonFoundation, the Pew Charitable Trusts, University of California (SantaBarbara), and University of North Carolina, Chapel Hill, NC.

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Theoretical Predictions for How Temperature Affects the Dynamics of Interacting Herbivoresand Plants.Author(s): Mary I. O’Connor, Benjamin Gilbert, and Christopher J. BrownReviewed work(s):Source: The American Naturalist, Vol. 178, No. 5 (November 2011), pp. 626-638Published by: The University of Chicago Press for The American Society of NaturalistsStable URL: http://www.jstor.org/stable/10.1086/662171 .Accessed: 20/08/2012 16:49



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vol. 178, no. 5 the american naturalist november 2011

Theoretical Predictions for How Temperature Affects the

Dynamics of Interacting Herbivores and Plants

Mary I. O’Connor,1,*,† Benjamin Gilbert,2,†,‡ and Christopher J. Brown3,4

1. National Center for Ecological Analysis and Synthesis, 735 State Street, Suite 300, Santa Barbara, California 93101; 2. Ecology,Evolution and Marine Biology Department, University of California, Santa Barbara, California 93106; 3. Ecology Centre, University ofQueensland, St. Lucia, Queensland 4072, Australia; 4. Climate Adaptation Flagship, Commonwealth Scientific and Industrial ResearchOrganisation, Cleveland, Queensland 4163, Australia

Submitted January 5, 2011; Accepted July 5, 2011; Electronically published October 7, 2011

Online enhancement: appendix.

abstract: Concern about climate change has spurred experimentaltests of how warming affects species’ abundance and performance.As this body of research grows, interpretation and extrapolation toother species and systems have been limited by a lack of theory. Toaddress the need for theory for how warming affects species inter-actions, we used consumer-prey models and the metabolic theory ofecology to develop quantitative predictions for how systematic dif-ferences between the temperature dependence of heterotrophic andautotrophic population growth lead to temperature-dependent her-bivory. We found that herbivore and plant abundances change withtemperature in proportion to the ratio of autotrophic to heterotro-phic metabolic temperature dependences. This result is consistentacross five different formulations of consumer-prey models and overvarying resource supply rates. Two models predict that temperature-dependent herbivory causes primary producer abundance to be in-dependent of temperature. This finding contradicts simpler exten-sions of metabolic theory to abundance that ignore trophicinteractions, and is consistent with patterns in terrestrial ecosystems.When applied to experimental data, the model explained 77% and66% of the variation in phytoplankton and zooplankton abundances,respectively. We suggest that metabolic theory provides a foundationfor understanding the effects of temperature change on multitrophicecological communities.

Keywords: consumer-resource models, herbivore, primary produc-tion, metabolic theory, temperature, mesocosm, plankton.

Introduction

Climate change is driving directional trends in environ-mental factors including temperature, precipitation, and

* Corresponding author. Present address: Department of Zoology, University

of British Columbia, 2370-6270 University Boulevard, Vancouver, British Co-

lumbia, Canada V6T 1Z4; e-mail: [email protected].†

Authors contributed equally.‡

Present address: Department of Ecology and Evolutionary Biology, Uni-

versity of Toronto, Toronto, Ontario M5S 3G5, Canada.

Am. Nat. 2011. Vol. 178, pp. 626–638. � 2011 by The University of Chicago.

0003-0147/2011/17805-52731$15.00. All rights reserved.

DOI: 10.1086/662171

water chemistry. This abiotic variation can be modeledwith growing confidence and precision, but the ecologicalconsequences are far less clear. Projecting ecological effectsof climate change requires quantitatively linking environ-mental variation to the rates and outcomes of ecologicalprocesses in a framework that incorporates general mech-anisms with specific conditions of particular ecological sys-tems. Such a framework would produce testable hypoth-eses for how environmental change affects ecologicalstructure and function and would foster an approach toglobal change science that would be more easily integratedwith basic ecological and evolutionary theory.

A promising framework for joining abiotic environ-mental change and population- and community-structur-ing processes can be developed by extending general re-lationships between temperature, metabolism, anddemographic rates (Robinson et al. 1983; Gillooly et al.2001). The acceleration of metabolic rate with increasingtemperature has been empirically described for diverse tax-onomic groups by simple mathematical functions (Rob-inson et al. 1983; Pepin 1991; Gillooly et al. 2001; Roseand Caron 2007). General temperature-dependence ofgrowth and reproduction rates suggests potential effectsof temperature on population abundance. Direct exten-sions of temperature-dependent metabolic models to pop-ulation abundance produce quantitative predictions forhow warming should affect populations. Savage et al.(2004) demonstrated that the maximum growth rate( ) of populations is temperature dependent, and thermax

slope of the temperature effect is consistent with an un-derlying constraint of temperature on respiratory pro-cesses. Allen et al. (2002) used the energetic equivalencerule (Damuth 1987) to predict that mass-corrected pop-ulation abundance declines with warming in direct pro-portion to the temperature dependence of heterotrophicmetabolism, assuming that the total energy flux of a pop-ulation per unit area is invariant with respect to body size.

mailto:[email protected]

Theory for Temperature and Herbivory 627

Vasseur and McCann (2005) considered effects of tem-perature on consumer and prey abundance and founddecreases in abundance with warming. The most straight-forward extensions of metabolic theories predict thatabundance declines with temperature. However, these ex-tensions typically ignore biotic feedbacks, resource supplyrates, and how different temperature dependencies of met-abolic rates influence species interactions.

Though general temperature-dependent demographicmodels can inform expectations for how temperature af-fects abundance, previous applications have not includeda critical difference between primary and secondary pro-ducers. Heterotrophs and autotrophs respond differentlyto nonlethal temperature shifts as a result of differencesbetween metabolic complexes that cause respiration-lim-ited metabolism to be more sensitive to temperature thanphotosynthesis-limited metabolism (Dewar et al. 1999; Al-len et al. 2005; Lopez-Urrutia et al. 2006; Rose and Caron2007). This systematic difference implies a general tem-perature dependence of herbivory that could drive pre-dictable responses of multitrophic systems to changes inenvironmental temperature. For example, general differ-ences in the effects of warming on consumer and plantmetabolism may be sufficient to shift food web structure,as has been observed in natural and experimental systems(Thompson et al. 2004; Lopez-Urrutia et al. 2006; Vaz-quez-Dominguez et al. 2007; O’Connor et al. 2009; Woh-lers et al. 2009). However, general predictions for meta-bolic temperature dependence on the abundance ofherbivores and their prey have not been articulated.

We analyzed a set of consumer-prey models that in-corporate temperature-dependent rates for heterotrophicand autotrophic processes and resource-based carrying ca-pacities for autotrophs. Our goal was to determine whethertemperature-dependent herbivory could produce new andgeneral predictions for the effects of temperature on theabundance of populations in food webs. We used meta-bolic theory and consumer-prey models to answer threequestions: (1) Is there a simple relationship between tem-perature and abundance, or does trophic context introduceenough complexity to obscure detectable and predictabletemperature effects? (2) Can temperature-dependent con-sumer-prey models relate the short-term effects of tem-perature typically observed in experiments to longer-termeffects that are more relevant to natural impacts of climatechange? (3) Do these predictions differ from predictionsderived for single trophic level systems? To answer thesequestions, we evaluate the effects of temperature on modelequilibria for herbivore and plant abundance. We showthat long-term predictions for herbivores are consistentfor all consumer-prey models developed, while predictionsfor primary producers varied among models. These dy-namic models are also well suited to testing short-term

dynamics, and we use the models to relate experimentalresults to predictions for natural systems. Our approachbuilds upon well-studied models of consumer-prey dy-namics to link the effects of environmental temperatureon fundamental metabolic processes to the outcome ofspecies interactions, and it generates quantitative hypoth-eses for the effects of environmental temperature changein natural environments.

Model Formulation

Choosing Models

We modeled the dynamics of autotrophic primary pro-ducers (P) and heterotrophic secondary producers (H),using a general consumer-prey model that relates changesin abundance over time to rates of autotroph growth (g),heterotroph consumption (c), conversion efficiency (e)and heterotroph mortality (h):

dPp g(P) � c(P, H),

dt (1)

dHp ec(P, H) � h(H).

dt

We modeled the temperature dependence of the ratesin equation (1). Several formulations for the relationshipbetween temperature and metabolic rate have been re-peatedly supported by empirical tests (Robinson et al.1983; Gillooly et al. 2001). A general formulation thatcaptures two competing relationships can be expressed as

E#tI p I e (2)0

in which a metabolic rate (I) scales exponentially withtemperature (t) according to the factor E. The normali-zation constant (I0) captures variation in I due to factorsother than temperature. The generic temperature term tcan take either the form T (�C or �Kelvin) in a simpleexponential model, or it can take the form in the�1/kTArrhenius relationship. In the Arrhenius formulation of ametabolic model, E is denoted as Ea and represents theactivation energy of metabolic processes (Gillooly et al.2001). In this formulation, a metabolic rate (I) is relatedto temperature (T in �Kelvin) by the Boltzmann constant(k).

The difference between the temperature dependence asmodeled by and by is subtle over the biologicalE#T �E /kTae erange of temperatures ( C; Arrhenius 1915; Bele-0�–35�hradek 1928), and tests of these models against empiricaldata often reveal that each model performs well (Robinsonet al. 1983; O’Connor et al. 2007). Though either for-mulation could be used to relate body temperature to rateparameters (intrinsic rate of increase, herbivore attack, and

628 The American Naturalist

Table 1: Model parameters and their average temperature dependence as characterized by activation energies (Ea) ineV, according to the general predictions of metabolic theory using the Arrhenius formulation in equation (2) andempirical data

Parameter Variable Ea Reference

Primary producer growth rate (based on primaryproductivity rate) r .32 Allen et al. 2005; Lopez-Urrutia et al. 2006;

Rose and Caron 2007Primary producer carrying capacity K �.32 Savage et al. 2004Herbivore attack rate (inclusive of capture and

ingestion rates and handling time) a .65 Gillooly et al. 2001Herbivore mortality rate m .65 Gillooly et al. 2001; Savage et al. 2004Transfer efficiency � 0 del Giorgio and Cole 1998; Vazquez-Domin-

guez et al. 2007Half saturation constant for herbivore feeding

response b 0

mortality rates) and carrying capacity (K) in the subse-quent analysis, we used the Arrhenius formulation( ) in equation (2). This model has been used by�E /kTaebiologists for a century and is a cornerstone of the met-abolic theory of ecology (MTE), which provides a usefulframework for applying the metabolic effects of temper-ature to more complex community and ecosystem pro-cesses (Gillooly et al. 2001; Brown et al. 2004; Allen et al.2005). We apply equation (2) assuming that body tem-perature is known for consumer and prey. For aquaticectotherms, which represent the vast majority of taxa onEarth (Ruppert and Barnes 1994), body temperature isstrongly influenced by environmental (water) temperature.For endotherms, variation in body temperature is highlyconstrained. For terrestrial and intertidal organisms, bodytemperatures can be decoupled from environmental tem-peratures (Helmuth 1998), and these relationships needto be known to relate the metabolic model to environ-mental temperature.

To test the effect of differential temperature dependenceof primary and secondary production on consumer-preymodel predictions, we assigned rates of primary producer-and consumer-driven processes the activation energies thatreflect specific rates of increase with warming (table 1).To obtain a first-order prediction of how temperature de-pendent rates affect abundance, we assume that con-sumption rate is related to the body temperature of theherbivore. This approach is robust to the inclusion of en-dotherms or any organism with a known relationship be-tween body temperature and consumption rates. Transferefficiency has repeatedly been shown emprically to be tem-perature independent (del Giorgio and Cole 1998; Vaz-quez-Dominguez et al. 2007), so we leave this term in-dependent of temperature. In addition, we used therelationship between constant nutrient supply, autotrophmetabolism, and temperature to assign an activation en-ergy to the carrying capacity (K; table 1; Savage et al. 2004).

All of our models implicitly assume that body size distri-butions remain constant. Although there is evidence thatchanges in body size may occur with temperature (Dau-fresne et al. 2010; Atkinson 1994), there is no consistentpattern or theoretical prediction for this phenomenon thatfacilitates its inclusion in our model. Nonetheless, bodysize could easily be included in this framework by devel-oping size classes that are scaled at , where mass is3/4massthe average body mass for a given size class.

Our goal was to determine whether, taking into accountdifferences between heterotrophs and autotrophs, a generaltemperature dependence of metabolism leads to generaleffects on abundance when considered in a context oftrophic interactions. An alternative hypothesis is that dif-ferent trophic dynamics interact with metabolic temper-ature dependence to create numerous possible outcomesthat are difficult to anticipate or interpret without sub-stantial information about a particular system. We there-fore considered five different common versions of the con-sumer-prey model (eq. [1]). The simplest model is onewith primary producers only, and we modeled maximumgrowth (r) and carrying capacity (K) in a logistic growthmodel to capture effects of resource limitation (model 1,table 2). To this model, we added an herbivore populationwith constant per capita mortality and a nonsaturating(type I) feeding response (model 2), or a saturating feedingresponse (type II, modeled using a Monod function, model3). We also considered a version of model 2 with density-dependent herbivore mortality, which could reflect den-sity-dependent predation or disease (model 4). Finally, weconsidered a model with exponential primary producergrowth, a nonsaturating herbivore response, and density-dependent herbivore mortality (model 5). This last model,while unrealistic in the absence of herbivores, representsa scenario where autotrophs grow at maximum rates underthe range of conditions they encounter. Other combina-tions of these basic functional forms do not produce stable


Table 2: Equilibrium conditions for five consumer-resource models

Model g(P) c(H, P) h(H) Equilibria Temperature-dependent equilibria

1P

rP 1 �( )K ... ... P p KEPˆln (P) p � ln (K )0kT

2P

rP 1 �( )K aPH mH ,P p KEPˆln (P) p � ln (K )0kT

;H p 0

,m

P p�a

m0ˆln (P) p ln ( )�a0

r mH p 1 �( )

a �aK

�E /kTPE �E r m eH P 0 0ˆln (H) p � ln 1 �[ ( )]kT a a �K0 0 0

3P

rP 1 �( )K

PaH( )P�b mH P p K,

EPˆln (P) p � ln (K )0kT

H p 0;

,mb

P p�a�m

m b0ˆln (P) p ln ( )�a �m0 0

�rb(K�a�Km�mb)H p 2K(�a�m)

�E /kTPE �E b�r [K (�a �m )�bm e ]H P 0 0 0 0 0ˆln (H) p � ln 2{ }kT K (�a �m )0 0 0

4P

rP 1 �( )K aPH 2mH P p K,EPˆln (P) p � ln (K )0kT

H p 0;

,Krm

P p 2�Ka �rm

E �E K r mH P 0 0 0ˆln (P) p � ln 2 (E �2E /kT)H P( )kT �K a �m r e0 0 0 0

K�arH p 2�Ka �rm

E �E K r a �H P 0 0 0ˆln (H) p � ln 2 (E �2E /kT)H P( )kT �K a �m r e0 0 0 0

5 rP aPH 2mHmr

P p ( )2�a

E �E m rH P 0 0ˆln (P) p � ln ( )2kT �a0

rH p ( )

a

E �E rH P 0ˆln (H) p � ln ( )kT a0

Note: Models use different functions to relate abundance (P, H) to primary producer growth f(P), herbivore consumption h(H), and

mortality h(H). The temperature dependence of these rates is modeled with an Arrhenius function using equation (2). General, stable

equilibrium conditions (eq. [1]) are given and are restated with temperature-dependence terms for autotrophic (EP) or heterotrophic (EH)

processes to give general formulations for the temperature dependence of equilibrium abundance. These temperature-dependent equilibria

are presented in the form of equation (3a), , in which the first term includes the predominant temperatureˆln (N) p (�E /kT) � ln (B)ab

dependence and the second term (B) captures all other model terms.

equilibrium solutions under any conditions or they haveequilibria that are too complex to be interpreted biolog-ically, and we therefore did not consider them in thisanalysis.

Modeling the Effect of Temperature on Abundance

To compare effects of temperature on abundance amongmodels and determine whether a general temperature-dependent equilibrium solution is possible, we express so-lutions for equilibrium abundance N as a function of tem-perature using the Arrhenius relationship:

�Eabˆln (N) p � ln (B), (3a)kT

where temperature is expressed as , captures all�1/kT B

other drivers of variation in abundance other than tem-perature including growth, consumption, and mortalityrate parameters (r, , m) and carrying capacity (K). Thea

term represents the slope of the effect of temperatureEab

on the abundance N. When used to model abundancerather than a metabolic process, is a calculation basedEab

on the activation energies that determine the net effect ofmetabolic temperature dependence on abundance of her-bivores ( ) and primary producers ( ). Equation (3a)E EH P

models a change in abundance N with a change in tem-perature. To compare abundance at two specific temper-atures ( , ), we solved for the ratio of abundances:T T1 2

( )�E T � Tˆ ab 2 1N BT2 T2ln p � ln . (3b)( ) ( )N kT T BT1 1 2 T1


By combining equation (3a) for two different temper-atures and simplifying algebraically, equation (3b) predictsabundance at ( ) based only on a known pair ofT N2 T2

temperatures ( , ), abundance at ( ) and . Im-T T T N E1 2 1 T1 ab

portantly, this solution does not require additional param-eters comprising for a wide range of conditions (ap-Bpendix, available online) because the main effects oftemperature have been moved algebraically to the firstterm.

Modeling Effects of Changes in Resource Supply

In natural systems, temperature often changes in con-junction with resource supply rates. To determine howchanges in resource supply could modify the effects oftemperature change, we modeled K as a linear functionof resource supply, R, so that

K R0(R2) 2 ˙∝ p R. (4)K R0(R1) 1

A change in with temperature could affect either theKslope or intercept of a temperature-dependent abundancesolution expressed as in equation (3a) or (3b). When Kappears in the second term but is not multiplied by T, achange in K affects the intercept only. In other words,change in abundance with concurrent changes in tem-perature and resource supply could be considered as achange in the slope (due to temperature) and the intercept(due to resource supply). In contrast, for solutions whereK is multiplied by T in the second term of equation (3a),a change in resource supply would also affect the slope ofabundance against temperature. To explore the potentialimportance of changing K in modifying the slope from atemperature-only prediction, we added the term to equi-Rlibrium solutions expressed as in equation (3b) to capturea change in resource supply correlated with a change intemperature from to (appendix). To test the con-T T1 2

ditions under which increasing resources changed the ratioof abundances, we ran a sensitivity analysis that was similarto that run for the change in abundance with temperature(appendix), except that it included changes in resourcesfrom 1 (no change) upward to 50 times the base level anddownward to 0.1 times the base level. In particular, wetested the conditions under which a change in causedRthe slope of the line of log change in abundance versus

to differ by more than 1% from modelDT/(1 � DT/T )1

predictions. Because the effect of on the slope decreasesRwith larger changes in temperature, we tested a smallchange in temperature, from 4� to 7�C. Simulations withlarger changes in temperature (from 15� to 25�C) producedqualitatively similar results.

Analytical Methods

For each model, equilibrium conditions were identifiedand tested for stability using Routh-Hurwitz conditionsfor equilibria that included both herbivores and plants(Otto and Day 2007; appendix). The Routh-Hurwitz con-ditions specify when equilibria are locally stable, withoutrequiring explicit solving of the eigenvalues of the stabilitymatrix, and are therefore useful for complicated stabilitymatrices. We determined the conditions for stability andinvasibility (the ability of each trophic level to establish inthe community when one or both trophic levels were ini-tially absent), and also determined whether periodic fluc-tuations occurred over any parameter values (followingOtto and Day 2007). For each consumer-prey model, weanalyzed the effect of temperature on the equilibriumabundance of herbivores and plants.

To visualize the model results and to test model pre-dictions, we chose specific parameter values based on thetemperature dependences of photosynthesis and respira-tion ( eV and eV, respectively; AllenE p 0.32 E p 0.65P H

et al. 2005; Lopez-Urrutia et al. 2006; Lopez-Urrutia 2008;table 1). These values have been empirically estimated inseveral independent investigations using very large samplesizes (Gillooly et al. 2001; Lopez-Urrutia et al. 2006, 2008).It is important to note that the values used for EP and EH

do not influence the general result that abundance is apredictable function of temperature. Rather than a par-ticular value for E in equation (2), the models simplyrequire that a general scaling relationship be estimated bya value of E. For example, the effect of a steeper slope forheterotrophs, as found by Frazier et al. (2006) for insectrmax, could be solved for by substituting their value of

into the appropriate equations.E p 0.97H

To determine the utility of the activation energy of me-tabolism for predicting how temperature affects abun-dance, we explored the sensitivity of the model outputs toa wide range of consumer-prey parameter values (appen-dix). In particular, we determined the range of parametervalues under which the first half of equation (3a) wassufficient to determine the effect of temperature changeon abundance. Using a similar sensitivity analysis as forchanges in temperature, we tested the range of resourcechanges and parameter values that caused model predic-tions to deviate from the first half of equation (3a)(appendix).

Relating Short- and Long-Term Effects of Temperature

The dynamical models that we developed are equally usefulfor exploring short-term dynamics as they are for long-term equilibria. We explored the utility of our modelingapproach for explaining short-term dynamics by testing


model predictions against abundance data from an ex-periment measuring the response of phyto- and zooplank-ton abundance to factorial manipulations of temperature(four levels at 2�C intervals) and nutrient supplies (controland addition of nitrogen and phosphorus; O’Connor etal. 2009). At the end of the 8-day experiment, the densityof multispecies assemblages of zooplankton and phyto-plankton had responded to warming and nutrient addi-tion: phytoplankton abundance declined despite increasedprimary productivity (C14 uptake), and zooplankton abun-dance increased.

We identified a priori the model formulation that wasmost appropriate for the experimental system. In partic-ular, we assumed that zooplankton feeding rates were bestmodeled with a saturating (type II) functional response,that nutrient supply rates determined phytoplankton car-rying capacity and that zooplankton mortality was notstrongly density dependent over the range of densitiesfound within the experiment. This model is commonlyrelated to the dynamics of spatially and temporally con-fined experimental conditions (Norberg and DeAngelis1997). Because the phytoplankton and zooplanktonshowed no change in size distribution, we fitted our model3 (table 2) after incorporating equation (4) with two re-source supply rates (full model in appendix).

We used a differential equation solver (fitOdeModel,Simecol library, R 2.8.1) to fit the model to the data. Weset the initial phytoplankton and zooplankton abundanceto the starting conditions in the experiment and then de-termined the maximum likelihood estimates for param-eters by fitting modeled abundance after 8 days to exper-imental results. The basal rates of parameters were heldconstant across all temperatures but the rate of resourcesupply (and therefore the carrying capacity) varied be-tween resource treatments. Realized rates of temperature-dependent parameters varied according to equation (2)(using activation energy values chosen a priori; table 1).

Although the model that we fit to the short-term dy-namics was constrained by our a priori choices for tem-perature dependencies (table 1), we used maximum like-lihood to solve for other model parameters

. To assess the sensitivity of the model(a , r , b, K , m , �)0 0 0 0

results, we used a cross-validation analysis. In particular,we fit the model using all but one data point (i.e., resultsfrom one replicate mesocosm), and then used the modelto predict the abundances of zooplankton and phytoplank-ton in the removed mesocosm. This procedure was thenrepeated for each mesocosm, so that the predicted valueswere always determined without the focal mesocosm usedin the model fit. We then compared the predicted fit tothe observed data.

Results

A Simple Relationship between Temperatureand Abundance

We found that the effect of temperature on herbivore andplant abundance can be represented by one or two modelparameters (EP, EH), regardless of the trophic dynamics inthe model. More specifically, in all models the log of her-bivore abundance responds to temperature according to

when expressed as equation (3a) (table 2;E p E � Eab H P

see table A1, available online, for solutions expressed aseq. [3b]). This result is not intuitive based on simple con-ceptual extensions of temperature-dependent demo-graphic models, because each consumer-prey model so-lution differs markedly in the term B (eq. [3a]), which insome cases even includes a temperature-dependent pa-rameter (table 2). However, numerical analyses of theseequilibrium solutions indicate that the B term has virtuallyno influence on the overall slope of the relationship, andthe temperature dependence of the log of herbivore abun-dance can therefore be accurately represented simply by

(appendix).E � EH P

In the absence of herbivores, primary producer abun-dance declined directly in proportion to the temperature-dependence of the carrying capacity (fig. 1; table 2). In allmodels, herbivores declined in abundance with warming.In the presence of herbivores, primary producer abun-dance declined at a rate identical to herbivore abundancewhen herbivore mortality was dependent on density (fig.1D, 1E). In contrast, primary producer abundance wasindependent of temperature when per capita herbivoremortality was not density dependent (fig. 1B, 1C).

In addition to the decline in equilibrium herbivoreabundance predicted by the consumer-prey models (fig.1), models 2 and 3 predict that warming can cause her-bivore populations to become dynamically unstable andbecome extinct (1F; table A2). For herbivores to invadeand persist in these models, the carrying capacity must beabove a threshold determined by the parameter values andequilibrium conditions. Specifically, for model 2,

, and for model 3, is necessarym/�a ! K mb/(�a � m) ! Kfor viable equilibria and invasion of H into the systems.For model 3, additional criteria for K determine whetherequilibria are stable points or oscillations (1F). A changein temperature can affect model stability because K de-creases with temperature (tables 1 and 2), but the stabilityconditions remain constant (e.g., for model 2;K 1 m/�a

table A2). Thus, if the carrying capacity is close to thethreshold herbivores require for persistence, warmingcould cause herbivore extinction. Similarly, model 3 maystop cycling and move to a stable point equilibrium withan increase in temperature (1F). This pattern could appearas a stabilizing effect of warming.


Figure 1: Predicted temperature dependence of herbivore and primary producer equilibrium abundance (N) for different model structures,plotted against temperature expressed as 1/kT (T in �Kelvin, �C also shown; both axes present increasing T from left to right). A–E, Herbivoreabundance (dashed lines) declines with increasing temperature in most cases, while primary producer abundance (solid lines) either declinesor does not change. Slopes are determined by net activation energy in the temperature-dependent equilibrium formulas in table 2. Fillustrates how a change in temperature can change the range of possible stable values for carrying capacity for model 3. Viable equilibriaK0

and invasion of H requires (dark gray region). Stable equilbria with H and P occur whenmb/(�a � m) ! K mb/(�a � m) ! K ! b(�a �(light gray region), and stable periodic cycles occur when (white region). Parameter values are thosem)/(�a � m) b(�a � m)/(�a � m) ! K

fit to emprical data, except for (fig. 3). For comparison, estimated for experimental nutrient addition ( ) and nutrient controlK K K0 0 �N

( ) are shown.KCont

The effect of a change in temperature on the log ofabundance can be captured by a simple term ( ),E � EH P

despite consumer-prey dynamics, when no change in re-source supply is assumed. Adding a change in resourcesupply to the model changes the carrying capacity and, inturn, herbivore and primary producer abundance. Thelargest effects of changing K occur in the intercept. How-ever, in models 2–4, the second term in the equilibriumsolution (B in eq. [3b]), includes K multiplied by T (table2), indicating an effect of K on the relationship betweenT and abundance (table A2). A sensitivity analysis showedthat when controlling for temperature, changes in resourcesupply had a nonlinear effect on abundance. A resource-driven change in abundance per unit change in resourcewas greatest with small changes in resources, and addi-tional change was less influential (fig. A1). As a result,decreases in resource supply, rather than increases, havethe greatest effect on abundance (fig. 2). Increases in re-source supply and warming have opposite effects onabundance.

Relating Short- and Long-Term Dynamics

The consumer-prey model that we chose a priori to modelmesocosm dynamics (model 3 with eq. [4] incorporated)was highly consistent with the observed effects of warmingand nutrient addition on plankton abundance (fig. 3). Themodel accurately simulated the decline in phytoplanktonabundance and the increase in zooplankton abundancewith warming at high resource levels and captured thehighly constrained temperature effects at low resource lev-els ( for phytoplankton and for zoo-2 2r p 0.77 r p 0.66plankton, both ; fig. 3). These results were robustP ! .001when tested with cross-validation analysis: when planktonabundances were fit to replicates that were not includedin the model-fitting analysis, values for phytoplankton2rand zooplankton remained high ( and , respec-0.74 0.62tively). As predicted from our model, the decline in phy-toplankton abundance occurred even though primary pro-ductivity increased with temperature (O’Connor et al.2009).


Figure 2: Changes in the primary producer carrying capacity K caninteract with temperature to affect herbivore and plant abundance.A, A change in K can alter the intercept of a modeled change in logabundance with temperature if K appears in the solution for equi-librium abundance but is not multiplied by T (e.g., models 1 and 2,table 2). In this case, the effect of a concurrent warming ( )T 1 T2 1

and increase in resources ( ; eq. [4]) on population trajectoriesR2 1 R1(solid lines, as in fig. 1) would lead to an increase in abundance(arrow i). In contrast, a decline in resource supply with warmingleads to a more severe decline in abundance than expected fromtemperature alone (arrow ii). B, A change in K can also change theslope of log abundance with temperature, when the equilibrium so-lution contains K multiplied by T (as in models 2–5, table 2). Therelative abundance of herbivores at temperature along the X-axisT2

and relative to C (vertical line) is shown (model 3, table A3,T p 5�1

available online). Resources have the maximum effect at parametervalues near the boundary for stable equilibrium (appendix, availableonline), so for these values (e.g., , , ,m p 0.1 � p 0.1 a p 2 b p0

, and ), changes in resource supply of a 10-, 20- or100 K p 5,680200-fold increase ( , , , respectively; solid gray˙ ˙ ˙R p 10 R p 20 R p 200lines overlap and appear as one line) do not have a large effect relativeto no change ( , black line) or a 10-fold decrease in resourceR p 1supply ( , dashed line).R p 0.1

Discussion

Consumer-prey models that incorporated general tem-perature-dependence functions for heterotrophs and au-totrophs produced a small set of testable predictions forthe effects of temperature on the abundances of interactingherbivores and primary producers. Across five differentmodel formulations and a wide range of parameter values,slopes of the log of abundance as a function of temperature

converge on a single difference of temperature-dependenceterms for herbivore abundance, and three possible slopesfor primary producer abundance (table 2; fig. 1). The find-ing that trophic dynamics can cause primary producerpopulation abundance to be independent of temperatureis new and highlights the importance of considering pop-ulation dynamics in the context of trophic interactions.These models that relate temperature to abundance viagrowth, consumption, and mortality rates can informbroader hypotheses about effects of environmental change.

General Predictions

Despite the complexity of consumer-prey models, modelpredictions for effects of temperature on abundance aresurprisingly simple and general across different formula-tions. Each consumer-prey model produced a unique gen-eral solution (table 2), yet these models predict virtuallyidentical temperature dependences of herbivore and plantabundances. These solutions suggest negative or null ef-fects of temperature on abundance, despite positive effectsof temperature on growth and consumption rates. Further,the ability to characterize the temperature dependence ofabundance simply as the temperature dependence (Ea) ofprimary productivity or as the difference in Ea betweenprimary and secondary productivity means that the so-lutions are inclusive of taxa for which the values of EH

and EP deviate from those given in table 1 (Kerkhoff etal. 2005; de Castro and Gaedke 2008). Deviations mayoccur because Ea is an average of observed temperaturedependencies for relevant rates, and for particular cases,Ea may deviate from the mean. In other cases, acclimationor changes in species composition of metabolism maymodify the relationship between photosynthesis and netprimary production (Enquist et al. 2007). The Ea may notcapture the relationship between environmental temper-ature and metabolic rates, as for endotherms.

In addition to gradual declines in abundance with tem-perature, temperature-dependent consumer-prey modelscan explain sudden shifts in food web dynamics. Warmingcan destabilize some models, or drive a transition fromperiodic cycling to a stable point equilibrium (fig. 1). Thus,despite the continuous scaling of metabolic rates with tem-perature, changes in relative rates within certain modelformulations can alter the stability of their equilibria, man-ifesting in sudden changes to dynamics that can lead toextinction of herbivores (Murdoch and McCauley 1985;Beisner et al. 1997; Vasseur and McCann 2005) or, alter-natively, lead to more steady conditions. In an empricalstudy, Beisner et al. (1997) found that warming caused aclosed planktonic system to transition into unstable con-ditions that led to herbivore extinction, as is predicted by


Figure 3: Comparison of model predictions for consumer and prey abundance as a function of general constraints on metabolism andknown initial conditions (eq. [1]) with experimental data (O’Connor et al. 2009). Final abundance (open symbols) of phytoplankton (PP,A) and zooplankton (ZP, B) are plotted along with simulated abundance after 8 days (filled circles), given dynamics in model 3, parametervalues fit to the data, and temperature dependence according to the metabolic theory of ecology (eq. [2]; table 1). Experimental treatmentsfor increased resource (N, P) supply (circles) and resource limitation (squares) are plotted. Observed means (SE) are plotted againstpredictions for phytoplankton (C) and zooplankton (D), and the line indicates the 1 : 1 relationship. Parameter values are ,3.08a p 10

, , , , , and at 21�C.6.62 6.00 �3.42 ˙r p 0.62 K p 10 b p 10 m p 0.05 � p 10 R p 5.90

our models when primary producer carrying capacity isinitially low (fig. 1F).

Like changes in stability conditions, changes in resourcesupply to autotrophs can occur simultaneously with warm-ing and potentially obscure a gradual scaling of abundancewith temperature (fig. 2). Relationships between temper-ature change and supply of resources can be complicatedin nature. In pelagic systems, warmer surface waters aretypically more stratified and nutrient-poor than colder wa-ters. For this kind of situation, our models would predicta severe effect of nutrient limitation to autotrophs thatwould reduce the carrying capacity of the system beyondthe temperature-driven reductions alone. A predictionbased only on how warming affects abundance might bethat phytoplankton abundance does not change consumerabundance declines (fig. 1B or 1C), but when resourcesare taken into account, the revised prediction should in-clude declines in phytoplankton abundance (fig. 2). In-deed, this pattern is consistent with trends in oceanic sys-tems (Roemmich and McGowan 1995; McGowan et al.1998). Resource supply does not always change with tem-perature, however. Light is an important resource for au-totrophs, and while environmental temperature may

change with climate change, light availability generallyshould not.

The temperature dependence of herbivore and plantdynamics that we present is an important first step inmodeling the overall impacts of temperature change. Innature, realized temperature effects on abundance coulddeviate from these predictions for numerous reasons, suchas temperature-dependent changes in resource supply thatare not driven by metabolic rates (appendix), evolutionarychange and changes in body size distributions. We andothers have shown how some of these variations can bebuilt into this modeling framework (e.g., Savage et al. 2004;Vasseur and McCann 2005; Lopez-Urrutia et al. 2006;Arim et al. 2007; de Castro and Gaedke 2008). For ex-ample, several authors have included body size in MTEdemographic predictions (Vasseur and McCann 2005;Arim et al. 2007), but unless there is a known, causalrelationship between body size and temperature, suchmodeling does not facilitate predictions about the effectsof changing temperature. Although there are several ex-amples of reductions in body size with environmentalwarming, general quantitative predictions for this trendare lacking (Atkinson 1994; Daufresne et al. 2010; Moran


Figure 4: Dynamics of model 3 over time at two temperatures. Tem-peratures are reflected in parameter values. The “cold” parameters(black lines) are those fit to the experimental data in figure 3 for21�C, except was adjusted to to meet conditions for a6.00K K p 10stable point equilibrium rather than stable periodic cycles (fig. 1F).The “warm” parameters (gray lines) are predicted parameters usingmodel 3 (fig. 1C) for 27�C. Transient dynamics can explain an in-creased herbivore abundance (A) concurrent with a decline in pri-mary producer abundance (B) in the short-term and long-term de-clines in herbivore abundance but no change in primary producerabundance (fig. 1C).

et al. 2010). Similarly, exceptions occur when herbivoresare endotherms or exist in complex thermal environments(Helmuth et al. 2006), in which case models would requireadditional terms (Kearney and Porter 2009).

Relating the Model to Empirical Data andLong-Term Studies

Relating simple theory to field data is a challenge, in partbecause the information needed to rigorously test modelsis often different from the measurements taken by em-pirical ecologists. We have tested our model against em-pirical data from a short-term experiment, and the modelsuccessfully captured short-term dynamics in a simple sys-tem (figs. 3, 4). These models may also inform predictionsfor long-term trends in herbivore and primary producerabundance and in doing so may relate short-term exper-iments to long-term patterns. For example, phyto- andzooplankton abundance has generally declined with en-vironmental warming (Roemmich and McGowan 1995;Richardson and Schoeman 2004), and such trends mightbe interpreted as contradictory to short-term increases inabundance with temperature observed in experiments.Our analysis shows that exactly the same underlying con-sumer-prey dynamics and temperature dependencies canexplain both patterns, suggesting that short-term trendscould actually be compatible with long-term declines (fig.4). Though the consistency of mesocosm results and the-ory do not imply that temperature-dependent abundancealone explains long-term patterns, their congruence doessuggest that the underlying mechanisms should not beignored.

The model predictions presented in table 2 are straight-forward to test in systems where equilbrium dynamics canbe assumed. Effects of temperature on equilibrium abun-dance might be meaningful when demographic rates arevery slow or very fast relative to temperature change. Forexample, for long-lived primary producers, the averagegrowing season temperature may be representative of theeffect of temperature on productivity. Alternatively, forfast-growing plankton systems in aseasonal (tropicalocean) environments, equilibrium dynamics might be ad-equate to capture effects of changing ocean temperatureon plankton abundance. Fortunately, the models can alsobe tested in systems not at equilibrium (figs. 3, 4). De-veloping and testing model predictions for nonequilibriumdynamics is essential to understanding climate change im-pacts in natural systems. For example, seasonal planktonicsystems in temperate lakes and oceans likely never reachequilibrium and instead are governed by bloom dynamicsthat are characterized by a brief period of ideal growthconditions followed by resource limitation (Lopez-Urrutiaet al. 2006; Rose and Caron 2007).

Our analyses have shown that estimates of mortality,consumption, and so forth are not required for testingmodel predictions against data (table 2) as long as thetemperature dependence or independence of these param-eters is understood. Nonetheless, tests do require data onthe abundance of herbivores and their prey, any systematicbody size shifts, and concurrent changes in resource sup-ply, and this full set of data is rarely reported. Additionaldata sets should be collected with theoretical predictionsin mind. Testing the models in table 2 require data onabundance, temperature, changes in resource supply, andmodel specifications such as herbivore functional responseand whether mortality is density dependent.

Implications for Biogeographic Patterns and ClimateChange Responses

Analysis of temperature-dependent consumer-prey modelsproduced new insights about how temperature might af-


fect populations. Effects of tempreature on the demo-graphic and consumption rates of interacting species canlead to predictable changes in abundance. Our finding thatprimary producer abundance can be independent of tem-perature even when primary productivity is temperaturedependent contradicts previous models (Allen et al. 2002;Vasseur and McCann 2005). Temperature-dependent her-bivory has the greatest influence on primary production,causing it to be independent of temperature, in systemswhere herbivory is strong (herbivores are food limited;models 2 and 3) and can reduce plant abundance (e.g.,aquatic systems). In contrast, in systems where the impactof herbivory is controlled by predation or other factors,warming is likely to have a negative effect on the abun-dance of primary producers (fig. 1; models 4 and 5). Inthe absence of herbivory, warming causes a decline in plantabundance inversely proportional to the temperature de-pendence of primary productivity.

The result that temperature-dependent herbivory cancause temperature-independent primary producer abun-dance may have important implications for understandinglatitudinal gradients in terrestrial plant communities. Interrestrial systems, direct extensions of the metabolic tem-perature dependence models to whole system productivity(Kerkhoff et al. 2005) find that the simplest models arewrong. Biomass accumulation in terrestrial plants does notvary with temperature, despite instantaneous effects oftemperature on photosynthesis (Kerkhoff et al. 2005; En-quist et al. 2007). In fact, the observed relationship be-tween temperature and net primary productivity is con-sistent with our model of temperature-dependentherbivory (models 2 and 3; fig. 1), though so far thishypothesis has not been considered, despite evidence thatup to 30% of terrestrial primary production is consumedby herbivores annually in many systems (Cyr and Pace1993; Cebrian 1999). Thus our model predictions suggestthat temperature-dependent herbivory could explain pat-terns in nature.

Temperature-dependent herbivory is also relevant toecosystem models of global change impacts. Numerousassessments of global fisheries productivity have used sim-ple models to relate consumer biomass to environmentalconditions including temperature (Chassot et al. 2010;Cheung et al. 2010), and some have incorporated meta-bolic theory (Jennings et al. 2008). However, none haveincluded a temperature-dependent ratio of secondary toprimary productivity. Our models indicate that this dif-ference in rates can have large and unexpected outcomeson herbivore and plant abundances. For example, warmingof 3�C is projected in many regions with climate changein the coming century, and it could cause on the orderof a 10% decline in herbivore abundance due to meta-bolic scaling alone, which could imply a reduction in

abundance at higher trophic levels that would be of greatconcern in marine food webs (Arim et al. 2007). Such adecline in secondary producer abundance due to tem-perature-induced changes in trophic dynamics is not cur-rently considered in global models. Rather, these modelsscale consumer productivity directly to changes in primaryproductivity. Thus, our incorporation of metabolic theoryinto simple food webs identifies further hypotheses for theimpacts of temperature that need to be tested.

In summary and in conclusion, our results show thatincorporating temperature-dependent rates into trophicmodels alters predictions from direct effects of a temper-ature change on population abundance. Five commonconsumer-prey models that vary in their complexity andassumptions converge on a small set of predictions for theeffects of temperature on equilibrium abundance of con-sumers and primary producers. These models also predicteffects of changes in resource supply and short-term effectsof temperature, thus potentially relating diverse observa-tions of the effects of temperature change in differentplaces or times. This provides a mechanistic frameworkfor developing quantitative predictions of how globalchange affects species interactions and food web structure.The advantages of this approach include its basis in theorythat does not require detailed information on the speciesinvolved to generate predictions about the effects of tem-perature. Thoughtful application of general metabolictemperature-dependence models to more complex modelscan provide more informative tests of metabolic theoryand possibly yield new insights about the effects of tem-perature on ecological processes.

Acknowledgments

We are grateful to P. Abrams, J. Byrnes, J. Stegen, E. Wol-kovich, and five anonymous reviewers for comments thatimproved this manuscript.

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VOL. 166, NO. 2 THE AMERICAN NATURALIST AUGUST 2005 O

A Mechanistic Approach for Modeling Temperature-Dependent Consumer-Resource Dynamics

David A. Vasseurl,2,* and Kevin S. McCann2,t

1. Biology Department, McGill University, 1205 Avenue Docteur Penfield, Montreal, Quebec H3A 1B1, Canada; 2. Department of Zoology, University of Guelph, Guelph, Ontario N1G 2W1, Canada

Submitted September 8, 2004; Accepted April 13, 2005; Electronically published May 17, 2005

Online enhancement: appendix.

ABSTRACT: Paramount to our ability to manage and protect biological communities from impending changes in the environment is an understanding of how communities will respond. General mathematical models of community dynamics are often too simplistic to accurately describe this response, partly to retain mathematical tractability and partly for the lack of biologically pleasing functions representing the model/environment interface. We address these problems of tractability and plausibility in community/environment models by incorporating the Boltzmann factor (temperature dependence) in a bioenergetic consumer-resource framework. Our analysis leads to three predictions for the response of consumer-resource systems to increasing mean temperature (warming). First, mathematical extinctions do not occur with warming; however, stable systems may transition into an unstable (cycling) state. Second, there is a decrease in the biomass density of resources with warming. The biomass density of consumers may increase or decrease depending on their proximity to the feasibility (extinction) boundary. Third, consumer biomass density is more sensitive to warming than resource biomass density (with some exceptions). These predictions are in line with many current observations and experiments. The model presented and analyzed here provides an advancement in the testing framework for global change scenarios and hypotheses of latitudinal and elevational species distributions.

Keywords: predator-prey, allometry, global change, environmental variability, temperature, mathematical model.

Many of the characteristics that researchers use to describe

biological populations and communities, such as their

density, distribution, diversity, and dynamics, rely on environmental temperature. Recent climate projections suggest that unprecedented warming will occur in many of the earth's environments during the current century (Houghton et al. 2001) with uncertain impacts on bio-

logical populations and communities. Predictive models often consider that populations persist within a range of climatic conditions known as their climate envelope. Cur- rent climate projections indicate that envelopes and their inhabitant populations will move to higher latitudes in

response to changing conditions because of local speciation and extinction events at the range extrema or changes in migratory routes (Parmesan et al. 1999). Although evidence for such shifts in nature is accumulating (Parmesan et al. 1999; Humphries et al. 2002; Root et al. 2003), they may not occur as predicted by the population envelope approach since the envelopes of interacting species may not change symmetrically (Davis et al. 1998), the temporal associations of species may become disrupted (Harrington et al. 1999), and, for populations with fixed ranges, the

strength of the interactions themselves may vary with tem-

perature (Post et al. 1999; Jiang and Morin 2004). This

suggests we should invest in models treating communities rather than populations as the basic unit with which to assess the importance of environmental change (e.g., Ives 1995; Ripa et al. 1998; Ripa and Ives 2003).

Known physiological constraints and responses of or-

ganismal and within organism processes have been paramount in formulating predictions for population processes. Such approaches use a bioenergetic framework to estimate the flux in measurable individual and population parameters associated with changes in body size (e.g., Pe- ters 1983) and temperature (e.g., Brown et al. 2004). These

relationships have then been used to explain variability in metabolic rate (Gillooly et al. 2001), developmental rate

(Gillooly et al. 2002), population growth rate (Savage et al. 2004), and global trends in species density (Enquist and Niklas 2001); to predict temperature-induced changes in

population ranges (Humphries et al. 2002) and energy

* E-mail: [email protected].

t E-mail: [email protected].

Am. Nat. 2005. Vol. 166, pp. 184-198. ? 2005 by The University of Chicago. 0003-0147/2005/16602-40613$15.00. All rights reserved.

Temperature-Dependent Consumer-Resource Dynamics 185

usage (Ernest et al. 2003); and to describe gradients of

global biodiversity (Allen et al. 2002). The extension of

bioenergetic models to the community level has been limited to the analysis of body size in consumer-resource

dynamics (Yodzis and Innes 1992). Extending this bio-

energetic framework to include community-based tem-

perature dependence will arguably provide a useful tool for the description and prediction of communities in

changing environments. Although more realistic, community models require ad-

ditional parameter and function specification often com-

ing at the cost of generality, and when the interactions

among populations are themselves dependent on environmental conditions, scaling up models to the level of communities and ecosystems leads to an explosion in the number of required parameters. Researchers are left with a trade-off between model simplicity, which allows mathematical tractability but sacrifices model comprehensive- ness. We address this problem with a general but biologically plausible model for temperature dependence in consumer-resource systems. We combine the bioenergetic- allometric framework provided by Yodzis and Innes (1992) with a recent advancement in temperature scaling theory (Gillooly et al. 2001; Brown et al. 2004) to scale the per unit time parameters of a consumer-resource model. We show that the mathematical analysis of this system remains tractable while incorporating environmental dependence in a biologically pleasing manner. We make three main

predictions for the dynamics of consumer-resource systems undergoing long-term temperature change and show that this framework has great potential for future analyses of global change scenarios and ecological species gradients.

The Model

Yodzis and Innes (1992) provided the following framework for a system of consumers and resources based on the model first proposed by Rosenzweig and MacArthur (1963):

dR R JC R

-d C -M rR(- - (1) R

dt -

R + Ro

' (

where the state variables R and C describe the amount of

energy in the resource and consumer populations in units of biomass density (mass per unit area). In the absence of consumers (C = 0), resources increase according to the Verhulst equation, which is described by the production/ biomass ratio r and the population carrying capacity K.

Consumers ingest resources according to a Monod function defined by the maximum ingestion rate J and the resource density required to achieve half-saturation of this rate, R0 (Yodzis and Innes [1992] used a more general form of the functional response capable of producing a sigmoidal saturation function). The parameter 6 is the fraction of biomass lost during ingestion and digestion, and fe is the fraction of biomass removed from the resource population that is actually ingested by the consumer. The parameter M represents the amount of energy lost to consumer metabolism. This basic model structure can be easily iterated to include more diverse trophic structures and levels, although particular attention must be paid to the implementation of multispecies functional responses (Koen Alonso and Yodzis, forthcoming). All parameters used in the model are nonnegative.

Yodzis and Innes (1992) recognized the need to reduce the number of parameters in this model in order to obtain a general theory for the dynamics of consumer-resource systems. They suggested that the per unit time rates r could be scaled with resource body mass (mR) and I and M with consumer body mass (me) according to empirically derived power laws and assuming a scaling exponent of 0.75. The "true" value of such scaling exponents remains a con- tentious point, but Brown et al. (2000) present strong derivations for quarter-power scaling laws in biology. Stan- dardizing these relationships by body mass generates a mass-specific scaling exponent -0.25, which can then be incorporated in the energetic model framework using power functions.

Our argument for the inclusion of temperature as a parameter in consumer-resource models originates from its ability to explain variability in rates of growth, ingestion, and metabolism in the empirical literature; second to body mass, temperature explains the largest amount of residual variation in biological rates (Peters 1983). The wide range of temperature experienced by many species influences their rates of growth, foraging, reproduction, and metabolism (among others) via a direct influence on enzyme kinetics. This influence is often described using the empirically derived coefficient Q10 as the change in rate associated with a 100 change in temperature. This constant has been measured for a suite of biological and ecological rates across a broad taxonomic scale (e.g., Peters 1983). However, recent advances in metabolic theory have shown that scaling biological rates in this manner can lead to as much as 15% error over the range of biologically plausible temperatures from O0 to 400C since the Q,0 is itself dependent on temperature (Gillooly et al. 2001). Rather, it is more precise to scale rates according to the Boltzmann factor eE/kT, where T is temperature in Kelvin, E is the activation energy, and k is Boltzmann's constant (Gillooly et al. 2001). This factor originates from first principles;


Table 1: Empirically derived intercepts (ai) of the allometric relationships from Yodzis and Innes (1992) in kg (kg year)-l kg0.25

Parameter ai(To) Details Source

Metabolism aM (To): Vertebrate ectotherms 2.3a Average field metabolic rate for iguanid lizards and Brett and Glass 1973; Nagy 1982

active metabolic rate in salmon Invertebrates .51 (20) Average oxygen consumption for 77 species of marine Ikeda 1977

zooplankton Ingestion a1 (To):

Vertebrate ectotherms 6.4b Derived from maximal 02 consumption in lizards and Brett 1971; Bennett and Dawson in feeding experiments in salmon 1976

Invertebrates 9.7 (20) Average feeding rates of eight marine planktonic Ikeda 1977

copepods Production a, (To):

Unicells .386 (20) Average maximal division rate in 14 species of salt Williams 1964 marsh pennate diatoms

Note: We have added information on the temperatures at which the allometric intercepts were measured, T0. a Field metabolic rate for iguanid lizards was measured during the active season, which excludes hot, dry periods and cold periods (Nagy 1982). Brett and

Glass (1973) measured active metabolic rates at 50, 150, and 20TC. We take 200C as the intercept for this coefficient.

b Bennet and Dawson (1976) supplied a summary of Vo2max

during activity by reptiles at 300C. Brett (1971) measured food intake at 150C. Our corrected

coefficient for vertebrate ectotherm ingestion at 200C is 6.4 kg (kg year)-' kg0.25 (assuming E, = 0.7 eV).

higher kinetic energy leads to a larger fraction of molecular collisions with enough energy to activate a reaction. We write the biological rate functions including body mass and temperature scaling:

r = fa,(To)m-R0.25eEr(T-rT)/krT,

(1 - 6)J = fa(TO)m0.25eEj(T- To)kTTo,

(2)

M = am(To)m?0.25eE"(T-rT)/kTwT,

where the Ei

are the rate-specific activation energies. The

intercepts of the allometric relationships (a;(To)) are em-

pirically derived constants representing the maximum sus- tainable rates (physiological maxima) measured at temperature To, and the f are the fractions of those rates realized in nature. The intercepts (a,) are conservative within each of four metabolic classifications: unicellular poikilotherms, invertebrate poikilotherms, vertebrate ectotherms, and vertebrate endotherms (Robinson et al. 1983). However, the accuracy of these relationships is diminished when the average body masses (me, mR) represent a large, skewed, and/or platy- or leptokurtic distribution of body mass (Savage 2004).

Incorporating temperature dependence into a consumer-resource energetic model not only introduces mathematical complexity but also complicates the assumptions of the model; the methods by which certain metabolic classes cope with heat loss to a cooler ambient environment or heat gain from a warmer ambient environment become an important consideration. For poikilotherms, ambient temperature is closely tracked by body temperature, and thus the expressions in equations (2) should

well describe the dependence of community processes on ambient temperature. For ectotherms, the correlation between ambient and body temperature can be weaker because of behavioral thermoregulation; however, ambient temperature still largely determines body temperature for these organisms. For endotherms, maintenance of a constant body temperature invokes complicated rate sensitivities to temperature, requiring model extensions outside the limits of our general framework (e.g., Humphries et al. 2002, 2004).

In a survey of published literature, Yodzis and Innes (1992) provide a set of allometric intercepts for scaling the three biological rates r, 1, and M to consumer and resource

body mass. We incorporate their intercepts in the size and temperature scaling functions (eqq. [2]) by resolving the temperatures at which they were measured, To (table 1). In addition, we sought studies in the literature describing the effect of temperature on the rates r, J, and M. Gillooly et al. (2001) suggest that the range of activation energies for population rates ought to be within the range of ex-

perimentally derived activation energies for all chemical reactions (0.2-1.2 eV), and they provide activation ener-

gies for metabolic rates of a variety of functional groups. More commonly, temperature effects have been quantified using Q10 coefficients rather than activation energies. Pro- vided that the range of temperatures used to estimate the Q10 is known, an approximation of the activation energy (E) can be determined using the relationship

E = 0.1(kT2) In Q10, (3)

where To is the median of the range over which Q0o was


measured and k is Boltzmann's constant (Dixon and Webb 1964; Gillooly et al. 2001). It is important to consider that our model formulation precludes the need for estimates of M and I for populations of unicellular organisms since

they are herein always assigned to the resource level. Pop- ulations of heterotrophic organisms, which may under normal circumstances occupy a "consumer" role, can be

incorporated into the model as a "resource" given that their production per unit biomass (r) is some fraction (f) of their maximum capacity for ingestion less metabolic costs:

r = fr[(1 - )J - M] (4)

(from Yodzis and Innes 1992). As we show later in this article, choice of the function representing maximal production and the realized fraction of this amount has no effect on the qualitative behavior of the system.

We present a short survey of experimentally and em-

pirically derived values of the Q10 coefficients and corre-

sponding activation energies for each model parameter and metabolic classification in table 2. While data for me-

tabolism/temperature relationships abound, there has been

relatively little work describing the temperature depen-

dence of ingestion and production. We sought to include those studies reviewing a large range of taxonomy to provide "average" values for each metabolic functional group. In one of the larger summaries, Robinson et al. (1983) described the body size and temperature dependence of metabolic rate in 109 species of active fish and reptiles (vertebrate ectotherms) and 729 species of invertebrate poikilotherms, obtaining Q10 coefficients of 1.44 and 1.7 for these groups, respectively. These coefficients are smaller than those reported by many studies; however, Clarke and Johnston (1999) noted that Q10 coefficients for diverse taxonomic assemblages tended to be smaller than those of single-species groups. They found Q10 coefficients of 1.83 for 69 species of teleost fish, while within species, Q10,, coefficients averaged 2.40. This suggests that some form of functional compensation occurs in response to temperature in the diverse assemblage, highlighting the need for parameter specificity when formulating system-specific predictions. Hansen et al. (1997) provide Q10 coefficients for respiration and ingestion rates across a variety of zoo-

plankton functional groups, with coefficients averaging 2.51 and 2.97, respectively. The Q10 coefficients for the

ingestion rates of vertebrate ectotherms have been measured for juvenile cod using digestion velocity (3.41; Knut-

Table 2: Empirically derived Q10 temperature coefficients and their corresponding activation energies

Parameter Q1o Ei (eV) Details Source

Metabolism (E,): Vertebrate ectotherms .433 Fish Gillooly et al. 2001

.500 Amphibians Gillooly et al. 2001

.757 Reptiles Gillooly et al. 2001 1.44 .274 Standard metabolism of 109 species of active Robinson et al. 1983

(50-400C) fish and reptiles 1.83 .432 Standard metabolism of 69 species of teleost Clarke and Johnston 1999

(00-300C) fish Invertebrates .790 Multicellular invertebrates Gillooly et al. 2001

1.7 .393 Respiration rates of 729 species of Robinson et al. 1983

(00-400C) poikilotherms 2.51 ? .61 .652 ? .061 Respiration rates of seven functional groups Hansen et al. 1997

including ciliates, meroplankton larvae, and

copepods Ingestion (E,):

Vertebrate ectotherms 3.41 .671 Digestion velocity in juvenile cod (Gadus Knutsen and Salvanes 1999

(60-130C) morhua) 3.0 .748 Gastric evacuation rate in cod (G. morhua) Temming and Herrmann 2003

(1o-150C) Invertebrates 2.97 ? .16 .772 + .045 Maximal ingestion rates of 11 functional Hansen et al. 1997

groups including flagellates, ciliates, meroplankton larvae, and copepods

1.9 .462 Flow velocity through the burrow of the filter Julian et al. 2001

(100-220C) feeding Urechis caupo Production (E,):

Unicells 1.88 .467 Maximum expected growth rate for marine Eppley 1972 (00-400C) and freshwater photoautotrophic algae

2.8 .788 Net photosynthesis in lake cyanobacteria mats Wieland and Kuihl 2000 (200-300C)

Note: The Boltzmann constant k = 8.618 x 10-5 eV K-1.


sen and Salvanes 1999) and gut evacuation rate (3.0; Tem- ming and Herrmann 2003). Eppley (1972) summarized data for phytoplankton growth in marine and freshwater environments and found that growth rates fell between 0 and ft doublings per day, where loglo0t = 0.0275T- 0.070 and T is measured in degrees Celsius. This relationship gives a Q10 = 1.88 for the rate of maximal primary production in unicellular organisms. The inefficiency of C3 photosynthesis at high temperatures due to pho- torespiration may explain the relatively weaker dependence of primary production on temperature when compared with heterotrophic metabolism (Ricklefs and Miller 2000). Last, the assimilation efficiency (1 - 6), which is independent of both body size and temperature (Peters 1983), is related to the food type: 0.45 for herbivorous consumers and 0.85 for carnivorous consumers (see Yodzis and Innes 1992).

Model Analysis

In the analysis of differential equation models, it is useful to define both the qualitative and quantitative response of the model to changes in parameter values. Here we focus on the model's response to temperature. We refer to the changes in the stability of the equilibrium (stable/unstable) and the character of the equilibrium (node, focus, limit cycle) as qualitative changes. The response of the equilibrium densities and their resilience are herein described as quantitative changes. For simplicity, we describe our results only in response to increasing temperature (herein called warming) since the effect of decreasing temperature is easily inferred.

Qualitative Response to Temperature Change

For the purpose of determining the qualitative behavior of the model equilibrium, it is useful to define the nondimensionalized model (see app. A for derivation):

dR R xy RC dt

- - (1J 6)f, R+R0'

d- xC -1 + Yt-R (5)

where the units of time have been chosen such that r = 1. Correcting all allometric relationships such that the a define the rate at To = 200C (293 K), we can represent the new parameters x and y as

M aMm0.25 x e- (E,- EM)( T- To)/kTTo, (6) S

r farm-0.25

(1 - x)J fa e(E1-EM)(T-To)/kTTo (7) M aM

Parameter x describes the rate of consumer metabolism normalized to the production biomass ratio of the resource population, and parameter y is the consumer's realized rate of ingestion per unit metabolism (Yodzis and Innes 1992). The two parameters x and y contain the temperature dependence of the model, and these quantities are in turn governed by the activation energy differences E, - EM and E, - EM. The difference Er - EM represents the potential thermal efficiency (PTE) of the consumer- resource system. For positive values of PTE, the system has an increasing potential to retain energy with warming; increases in production at the resource level outpace increases in energy metabolism at the consumer level. This change in system energy is a potential change, since the amount of energy lost to trophic transfer can change disproportionately. The impact of the consumer on its resources is determined by the parameter y, whose response to temperature is determined by the difference E, - EM. For positive values, warming-induced increases in the maximum ingestion rate outpace metabolic demands, leading to a larger impact (per unit mass) on the resource population. We call this difference the consumer thermal impact (CTI).

Yodzis and Innes (1992) analyzed the qualitative changes in the equilibrium in response to changes in y and, in doing so, cataloged all possible outcomes for variation in the parameters influencing y. We reiterate their derivations in order to clearly describe how temperature (T) and the activation energies (El) influence the model inside this range of previously cataloged behavior.

The model has three possible equilibrium states, and we categorize them according to the existence or nonex- istence of each species:

Eq, : trivial, R,, C, = 0;

Eq2 : resource only, R, = K, Ce = 0; (8)

Eq3 : coexistence, Re

= -, Ce

=1 - )(1[( )fjRe

For plausible parameter combinations, Eq, is always unstable, while one of Eq2 or Eq3 can be stable depending on parameter values. To determine the response of the qualitative behavior of the model to changes in temperature, it is useful to employ a bifurcation analysis, which tracks equilibria and their inherent characteristics across a range of parameter space. Points in parameter space


where equilibria undergo qualitative changes in stability are called bifurcation points.

The exchange of stability between Eq2 to Eq, denotes a transcritical bifurcation, which we herein refer to as the "feasibility boundary" for the system. A feasible two- species equilibrium (Eq3) exists when 0 < Re < K, and therefore K(y - 1) > Ro defines the feasibility boundary (transcritical bifurcation) for the two-species system. In the feasible parameter space of Eq,, the equilibrium has two stable states: a stable node, whereby communities at nonequilibrium densities approach the equilibrium monotonically, and a stable focus, whereby the approach is characterized by decaying oscillations around the equilibrium point. The location of the focus/node boundary is dependent on both model parameters x and y, and its proximity to the feasibility boundary is controlled mainly by the body mass ratio mc/mR and PTE (for a full description, see Yodzis and Innes 1992). Also in the feasible parameter space, the equilibrium Eq3 can be an unstable focus. In this case, it is surrounded by a stable limit cycle, which is approached from outside (inside) by decaying (expanding) oscillations. The Hopf bifurcation denotes the change in stability of Eq, from a stable focus to an unstable focus and marks the emergence of a stable limit cycle. The state Eq3 is locally stable when (see app. A)

K(y - 1) < 1, (9)

Ro(y + 1)

and it is locally unstable, but surrounded by a limit cycle, when condition (9) is not satisfied.

From the above equations, it is apparent that the qualitative behavior of the model is completely determined by the parameters PR, K, and y. To further reduce the dimensionality of the analysis, Yodzis and Innes (1992) defined the ratio Ro/K as an inverse measure of resource abundance as perceived by the consumer population; as

R0 decreases (K increases), consumers perceive a higher density (or enriched) resource supply, resulting in a larger flux of biomass from the resource to the consumer population. We make the assumption that this "inverse enrichment ratio" is independent of temperature, and we discuss the full implications of this assumption later in this article.

We analyze changes in the loci of the feasibility boundary and Hopf bifurcation across a range of biologically plausible temperatures (00C < T< 400C) and across a range (? 1) in the CTI (E, - E,). This encompasses a satisfactory range in CTI given that measured activation energies of chemical reactions range from 0.2 to 1.2 eV (Gillooly et al. 2001). Since the value of the parameter y depends only on the consumer population, it is sufficient to perform two bifurcation analyses corresponding to the

two possible metabolic classifications for the consumer population considered here. Figure 1 shows the Hopf bifurcation surface for (a) an invertebrate poikilotherm consumer and (b) a vertebrate ectotherm consumer. When CTI > 0, the Hopf bifurcation locus increases with warming, reaching an asymptotic value of 1 in the Ro/K plane. This leads to a larger incidence of limit cycles in Ro/K parameter space since limit cycles occur below the Hopf bifurcation. Alternatively, where CTI < 0, the Hopf bifurcation locus decreases with warming, and the incidence of limit cycles in Ro/K parameter space lessens. When CTI = 0, the Hopf bifurcation is independent of tem-

a) Invertebrate Consumer

1.00

0.75

0.50,

'.

0.25

0.00

. b) Vertebrate Ectotherm Consumer

r. 1.00

0.75

0.50

0.25 "

40

30o * ' "

20 -1.0 -0.5

0.0 10

~CO 0 0

0.5 0 Consumer Ther

IPact (1.0eV Dmact leV

Figure 1: Hopf bifurcation surface across the independent parameters temperature and CTI for (a) an invertebrate consumer (al/aM = 19) and (b) a vertebrate ectotherm consumer (alaM = 2.8). Above the Hopf bifurcation, the equilibrium is stable, and below the Hopf bifurcation, the equilibrium is unstable. Along the two independent axes, the Hopf bifurcation surface approaches Ro/K = 1 according to a Monod function. The two axes of invariance occur at CTI = 0 eV, where temperature change has no effect on the Hopf bifurcation, and at T = 200C, where the intercepts of the temperature-dependent functions are defined.


perature. In both panels, the response of the Hopf bifurcation is similar in nature, but saturation of the curve to

Ro/K = 1 occurs much quicker for invertebrate consumers (a) because of the relative differences in the ratio of the intercepts al/a, (see table 1).

Similar results are observed for the feasibility boundary of invertebrate consumers and vertebrate ectotherm consumers (fig. 2), with the exception that the feasibility boundary is not a saturating function, but rather it grows/ decays exponentially with warming. When CTI > 0, the locus of the feasibility boundary grows exponentially with warming, and while CTI < 0, the locus of the feasibility boundary decays exponentially with warming. Below the feasibility boundary, the system is persistent, and where the curve crosses the Ro/K = 0 plane, the consumer cannot persist regardless of its capacity to ingest resources.

Empirical estimates of the activation energies influencing the bifurcation loci Ei (table 2) suggest that the CTI for invertebrate consumers falls in the range 0.1-0.38 and for vertebrate ectotherm consumers 0.24-0.47. Figure 3 shows the two-dimensional slices from figures 1 and 2 corresponding to empirical estimates of the CTI from table 2. In both examples, there is an increase in the parameter space occupied by unstable equilibria (limit cycles) with warming (although very slight for invertebrate consumers). However, the proportion of unstable parameter space within the domain of feasible solutions decreases with warming, since the feasibility boundary increases in

Ro/K. This leads to two predictions for the qualitative stability of consumer-resource systems in response to warming. First, warming may lead to qualitative instability; for any value of Ro/K< 1, a stable system may cross the Hopf bifurcation, resulting in an unstable (cycling) state. Sec- ond, warming does not lead to mathematical extinctions (where mathematical extinction corresponds to crossing the feasibility boundary) but rather may facilitate the persistence of consumer-resource systems because of the increase in feasible Ro/K parameter space.

Quantitative Response to Temperature

It is useful to determine the quantitative behavior of Eq3 in response to warming since the density of resource and consumer populations can be highly variable within any particular region of qualitatively similar parameter space. We determine the response of Re and C, to temperature using the derivates dRe/dT and dC,/dT and using a parameterized example.

The derivative of equilibrium resource density Re with respect to ambient temperature is a dampened exponential function whose sign is completely determined by the CTI:

a) Invertebrate Consumer

30

25/

20

C 15

O .

E

= b) Vertebrate Ectotherm Consumer

U 30

25

c 20

10, 40

5 30

." -1 .0 . oo`

-.05 10

Cns TherMal Pact (feV)

Figure 2: Locus of the feasibility boundary (transcritical bifurcation) across the independent parameters temperature and CTI for (a) an invertebrate consumer (a/a, = 19) and (b) a vertebrate ectotherm consumer (a/a, = 2.8). Above the feasibility boundary, the consumer cannot persist. Below the feasibility boundary, both the resource and consumer persist, and in this region, the system stability is determined by the Hopf bifurcation (fig. 1). In both a and b, the feasibility boundary varies exponentially along the two independent axes. The two axes of invariance occur at CTI = 0 eV, where temperature change has no effect on the feasibility boundary, and at T = 200C, where the intercepts of the temperature-dependent functions are defined.

dRe -Roy(E1 - EM) -_ (10) dT (y - 1)2kT2

This generates a rather simple relationship governing the directional response of equilibrium resource density to temperature change; where the CTI > 0, resource density decreases with warming. Alternatively, if the CTI < 0, resource density increases with warming. Where the CTI = 0, resource density is constant across temperature.


100 a) Invertebrate Consumer Non-Feasible Equilibrium

10 Stable Equilibrium

5' 1

0.1

0) 100 E b) Vertebrate Ectotherm Consumer

10 Non-Feasible Equilibrium

( 1. 1c Stable Equilibrium

0.1

0 10 20 30 40 Temperature (oC)

Figure 3: Two-dimensional slices of the bifurcation loci given the CTI values estimated from table 2. For invertebrate consumers (a), we estimated CTI from the coefficients E, = 0.77 and E, = 0.65 measured by Hansen et al. (1997). For vertebrate ectotherm consumers (b), we estimated CTI from the average values of E, = 0.71 and EM = 0.38 for fish (excluding reptiles and amphibians).

Empirical estimates in table 2 suggest that, for the majority of systems, CTI should be >0 and thus that dRe/dT< 0.

The consumer population displays a more complex response to temperature:

dCe (1 -

6)fe, (Er -

EM)(1 - Re/K)Re dRel 2Rei

dT x kT2 dT K

(11)

where the sign of dCe/dT relies on the PTE, the relative equilibrium resource density Re/K, and the response of equilibrium resource density to temperature (dRe/dT). With the potential for two real roots, the consumer density may reach local extrema in response to varying temperature; however, these local extrema can lie outside the range of biologically relevant conditions. The analysis of equation (11) proceeds more easily under the assumption that dRe/dT< 0, and the results below adhere to this assumption. Near the feasibility boundary, Re is only slightly less than K, and thus dCe/dT > 0. This is a rather obvious conclusion given that Ce = 0 at the feasibility boundary and increases to positive density with warming. When

PTE < 0, dCe/dT reaches a local maximum in the range K/2 < Re < K (recall that

Re is decreasing with warming)

and is always negative beyond Re K/2. Alternatively, when PTE > 0, dCedT is positive in the range K/2 < Re < K and reaches a local maximum when Re < K/2. It is important to consider that these relationships describe the quantitative behavior of equilibrium resource density in the range of stable parameter space; however, they do not provide any information about the response of equilibrium densities to temperature within unstable (cyclic) parameter space. In this region, it is more informative to perform numerical simulation to obtain the attributes of the limit cycle (see parameterized example below). We therefore proceed in our analysis of the quantitative behavior of the system using numerical simulation of an exemplary consumer-resource system.

Using the coefficients E, and E, derived from Hansen et al. (1997), E, derived from Eppley (1972), and the intercepts listed in table 1, we parameterize a model representing the interaction between a herbivorous invertebrate consumer and a unicellular resource (PTE = -0.19 and CTI = 0.12). Figure 4 shows the equilibrium response of this system to warming given three values of the enrichment


a) 1K

RolK= 13

Eo

.0 RK= 6

RolK = 0.9

0.01K

b)

o c

O co.0.01 K

...... ...

0.001K

0 10 20 30 40 Temperature (oC)

Figure 4: Equilibrium densities of resources (a) and consumers (b) across a gradient of temperature parameterized to represent the interaction between an invertebrate consumer and a unicellular resource. Resource biomass density is normalized by the carrying capacity K; consumer biomass is normalized by the resource carrying capacity K and by the body mass ratio (mc/mR)0'25. Three ratios of the inverse enrichment ratio Ro/K are shown to highlight three potential behaviors: Ro/K = 13 (dashed line) shows the equilibrium response near the feasibility boundary, RolK = 6 (solid line) shows the equilibrium response in the stable region, and Ro/K = 0.9 (dotted line) shows the equilibrium response as it crosses the Hopf bifurcation into unstable (cyclic) space. Coefficients ai are from table 1, E, = 0.467 (table 2; Eppley 1972), EM = 0.772 and 0.652, respectively (table 2; Hansen et al. 1997), f,,f1,f = 1, and (1 - 6) = 0.45.

ratio Ro/K: a low-enrichment community that crosses the

feasibility boundary (RIK = 13), a medium-enrichment community that remains in the stable state space (Ro/K = 6), and a high-enrichment community that crosses the Hopf bifurcation (RIK = 0.9). Resource density is a decreasing function of temperature for all values of the enrichment ratio within the range of stable state space (fig. 4). In the cyclic domain, the amplitude of cycles generally increases with warming, and the lower bound of the cycle drops to low densities. This occurs in concordance with the "paradox of enrichment," which suggests that consumer-resource systems become unstable and often nonpersistent because of large amplitude cycles after crossing the Hopf bifurcation (Rosenzweig 1971). The response of consumer density is more complicated because of the potential for a local maximum within the range of

biologically relevant temperatures. In the low-enrichment community, the consumer density increases with warming as it crosses the feasibility boundary and reaches a local maximum thereafter. The curves for medium and high

enrichment are decreasing functions for the range of temperatures shown, since Re < K/2 over the entire range. On the logarithmic scale of figure 4, it is evident that the equilibrium consumer density is more sensitive than the equilibrium resource density given their relative slopes at medium- and high-enrichment levels (RIK = 6, 0.9; ex-

cluding RoIK = 13 since it is proximate to the feasibility boundary). We have factored out the body mass ratio

(mc/mR)0-25 from figure 4b to show the characteristic re-

sponse of consumer biomass density. Given the coefficients listed in table 2, we expect CTI

to be >0 for the majority of systems. This leads to a robust prediction for the response of equilibrium resource biomass density: in the domain of stable solutions, equilibrium resource density declines with warming because of the increasing capacity for ingestion in the consumer population. Similarly, the median density of resources in the unstable domain decreases with warming, with a tendency for high-amplitude cycles at high temperatures. For the consumer population, the response of equilibrium density


to warming relies also on the PTE. In our example, PTE is <0, resulting in a decreasing equilibrium consumer density in response to warming when the system is sufficiently far from the feasibility boundary. Systems that are proximate to the feasibility boundary will initially increase with warming and reach a local maximum. For invertebrate consumers, the influence of the feasibility boundary is limited to a small range of the stable parameter space. However, for vertebrate ectotherm consumers whose feasibility boundary is potentially crossed for nearly all feasible values of Ro/IK, this effect will be more prominent (see fig. 3).

In addition to changes in the density, it is important to consider changes in the "attractiveness" or resilience of the system. Resilience of the system can be defined as the rate at which population density returns to equilibrium after a perturbation (Pimm 1991), and the negative reciprocal of the dominant eigenvalue of the Jacobian matrix provides a quantitative measure of the amount of time required for the system to reach e-' (or approximately 37%) of the initial perturbation displacement. This measure is an asymptotically unbiased estimate of the actual value; error in the estimate increases with the perturbation displacement. It is important to note that the eigenvalues determined in appendix A are those of the nondimensional system and require back transformation to properly estimate the return time.

Figure 5 shows the dependence of return time on temperature for each of the three low-, medium-, and high- enrichment communities from figure 4. Since the return time is estimated from the dominant eigenvalue of the Jacobian matrix, the effects of consumer and resource body

mass cannot be scaled out. We chose body sizes representative of the interaction between zooplankton and unicellular algae that fit the activation energies used in figure 4 (1 x 10-7 kg and 6 x 10-12 kg, respectively). For the low-enrichment community, the feasibility boundary pro- duces a vertical asymptote at low temperatures where the dominant eigenvalue passes through the origin. Similarly, for the high-enrichment community, there is a vertical asymptote at the Hopf bifurcation where the system becomes unstable (at both bifurcation points, the real portion of the dominant eigenvalue is equal to 0, and the return time is thus infinite). For each of the low- and medium-enrichment communities, return time decreases with warming since they are bounded well away from the Hopf bifurcation. The decrease in return time results from a larger throughput of energy at warmer temperatures, which allows the system to equilibrate more quickly following perturbation (see DeAngelis 1992). It is important to consider that larger body sizes of both resources and consumers increase the return time of the system because of their slower per unit mass rates of growth, ingestion, and metabolism but do not qualitatively affect the results.

Discussion

In response to an increase in mean temperature, three general predictions emerge from the analysis of our temperature-dependent model, given the empirical parameter estimates in table 1. First, mathematical extinctions do not occur with warming; however, stable systems may transition into an unstable (cyclic) state. Vertebrate ectotherm consumers are likelier than invertebrate consum-

S 10 ........ ............. RoK=0.9

S" RolK = 13 E S0.1

I

o...., RdK= 6 0.01

0.001 0 10 20 30 40

Temperature (oC)

Figure 5: Return times of the consumer-resource system parameterized to represent the interaction between an invertebrate consumer and a unicellular resource at the low-, medium-, and high-enrichment levels shown in figure 4. Return times are estimated as the reciprocal of the dominant eigenvalue of the Jacobian matrix; they represent the time required for the system to reach e- (or approximately 37%) of the initial perturbation displacement. The abrupt change in the low- and medium-enrichment curves is caused by the qualitative change in stability from stable node to stable focus.


ers to drive the system into an unstable state because of their relatively larger metabolic requirement per unit mass. Second, the biomass density of resources always decreases, and the biomass density of consumers will decrease with warming provided that their existence is not proximate to the feasibility boundary (e.g., consumers are not on the

verge of extinction because of an inability to acquire ad-

equate resources). Practical extinctions may occur with

warming, given that both resources and consumers can reach low densities. Third, given our exemplary parameters, consumer biomass density is more sensitive to warming than resource biomass density. This prediction depends on the proximity to the feasibility boundary and on the relative magnitudes of CTI and PTE. In the cyclic state, the median biomass density of consumers is more sensitive than that of resources. However, the change in

cyclic amplitude is larger for resource biomass density, and since the majority of the cycle period can be spent at low densities, the mean biomass density of resources may show increased sensitivity. This distinction may be important when considering the sensitivity of cyclic systems in nature.

Our predictions for the response of population biomass densities, sensitivities, and community stability and resilience rely on empirical estimates of the intercepts and parameters that govern the scaling functions. The intercepts for production and ingestion provided by Yodzis and Innes (1992; table 1) represent the physiological maxima that can be attained under ideal conditions. Realized rates of these maxima may be only small fractions when species are "ecologically limited" (f, f << 1) rather than "physiologically limited" (f, fj;:1 1). Our examples for invertebrate and vertebrate ectotherm consumers represent the behavior of the model at the physiologically limited extent. For ecologically limited consumers, the loci of the feasibility boundary and Hopf bifurcations are more sensitive to temperature (e.g., they show more curvature); for example, an ecologically limited invertebrate consumer may have bifurcation curves similar to those of a physiologically limited vertebrate ectotherm consumer. Additionally, the equilibrium densities depend on the extent to which consumers and resources are ecologically or physiologically limited. Despite these dependencies, the trends describing the response of equilibrium densities to warming are independent of the extent of ecological or physiological limitation; ecologically limited species are more prone to undergo the qualitative changes of the first prediction and more likely to behave as systems proximate to the feasibility boundary when at low temperatures for the second and third predictions.

Although our model does not suggest mathematical extinctions will occur at warmer temperatures (mathematical extinction corresponds to crossing the feasibility boundary), biomass densities of both consumers and resources

are predicted to decline with warming, increasing their susceptibility to extinction through demographic stochasticity, genetic bottlenecks, and Allee effects. In addition, we predict that systems may destabilize with warming, leading to limit cycles with relatively low minimum densities of both resources and consumers. Short of the present date, climate change has only been implicated in one species-level extinction (Pounds et al. 1999), although some studies predict high rates of extinction in the near future (Thomas et al. 2004). In a study of population densities of trees and terrestrial ectotherms (amphibians, reptiles, and invertebrates) the biomass density of both groups decreased at warmer temperatures (Allen et al. 2002). Petchey et al. (1999) found that 30%-40% of species of aquatic microbes in a microcosm were extinct after 7 weeks of a +20C week-1 change in temperature (approximately 0.10-0.2?C per generation). In their experiment, producer (resource) biomass increased with warming while consumer biomass decreased, and only consumers showed increased rates of extinction. Our model mimics the observed increase in resource biomass only when CTI < 0, suggesting that despite our empirical estimates for CTI (which are >0), there may be instances where the capacity for ingestion by consumers increases more slowly with warming than metabolism or where the capacity for ingestion decreases with warming. There is evidence supporting the existence of thermal optima for ingestion in a variety of species and similarly for critical thermal limits in production and metabolism, which could account for discrepancies between our model and empirical data. Like any scaling relationship based on diverse assemblages, our model is best suited to explain large-scale patterns since species-specific responses to temperature are obscured within the general scaling framework.

Voigt et al. (2003) compiled plant, herbivore, and car- nivore abundances from two grassland communities to determine whether the climate sensitivity of functional groups differed between trophic levels. Their analysis showed that the temporal variance in abundance, attributable to climatic variability, increased with trophic level. Similarly, Allen et al. (2002) show that the density of terrestrial ectotherms is more sensitive than the density of plants to temperature. Pianka (1981) suggested that differences in the metabolic requirements of carnivores, herbivores, and autotrophs could account for differences in their climatic sensitivity. However, the response of autotrophs additionally causes the resource availability to vary for herbivores and can lead to amplified sensitivity at higher trophic levels (Voigt et al. 2003). In our example system (fig. 4), both mechanisms account for the increased sensitivity of higher trophic levels: consumers ingest more energy per unit mass at higher temperatures, causing resource density to decline. Fewer resources combined with


an increased consumer ingestion rate lead to a relatively larger decline in consumer density. The generality of this property and mechanism for a broader class of consumer- resource systems remains to be determined.

Our amalgamation of the Boltzmann factor into the Yodzis and Innes (1992) consumer-resource model provides a general framework for temperature-dependent models of interacting populations. General theories for the inclusion of further environmental variables in allometric models may be limited, since body mass and temperature tend to be the only variables accounting for significant amounts of variability in broadscale regressions (e.g., Pe- ters 1983). The framework used to model consumer- resource dynamics in this study neglects to include the direct effects of consumer mortality in the model. The relationship between mortality, temperature, and body size follows the same relationship as metabolism (Savage et al. 2004), and evidence suggests that the two are governed by the same scaling parameters (Ei for fish mortality is 0.45 eV [Savage et al. 2004] and 0.43 eV for fish metabolism [table 2]). If, indeed, the scaling parameters are conservative, then directly including consumer mortality in the model would further limit any consumer from existing at its physiologically limited extent (see app. B in the online edition of the American Naturalist). There is still much to be learned about the influence of temperature on alternative model formulations, structures, and, with direct impact for our results, the potential temperature dependence of the per unit area parameters Ro and K.

The temperature dependence of carrying capacity K has received surprisingly little attention in the literature (Sav- age et al. 2004). In Verhulst population models, K defines the maximum attainable density of a population, and under steady state conditions, it is the equilibrium density. Verhulst growth is included in our model framework to define density-dependent growth of resources and assumes that factors such as nutrients and light are static. Popu- lation models that account for the metabolic costs offset- ting growth but neglect community interactions suggest that where resource supply is constant, K must decrease with temperature to balance the effects of increasing metabolic costs (Savage et al. 2004). Savage et al. (2004) argue that the findings of Allen et al. (2002; decreased ectotherm density with temperature) support a negative relationship between temperature and carrying capacity. However, our model framework similarly explains the decline in ectotherm density using a community framework, scaling only the per unit time elements of the model. Our model differs from that of Savage et al. (2004) in that resource density is not influenced by temperature in the absence of predators (since K is temperature invariant). Populations that exist truly in the absence of predators are rare, but tree biomass density, which is arguably limited by competition

rather than consumer grazing, provides a reasonable example for which data are available. Enquist and Niklas (2001) show that tree biomass density is constant across latitudes ranging from -40' to 600, which is at least suggestive that carrying capacity may be independent of temperature. Much work remains to determine the scaling of carrying capacity with temperature and, as importantly, to determine whether its implicit scaling in population models is analogous to the results produced by our community approach.

The half-saturation density of the functional response Ro, in unison with the maximum capacity for ingestion J, controls the realized rate at which resources are consumed. The effects of temperature on the half-saturation density itself are not well documented. However, there has been some research on the temperature dependence of the attack rate in the traditional Holling Type II functional response model (Holling 1965). This model defines the functional response as f(R) = caRCI(1 + acthR), where oa

is the attack rate, th is the amount of time required to handle a prey item, and R and C are resource and consumer densities. The parameters of our Monod model can be expressed as those of the Holling Type II, where the maximum capacity for ingestion - l/th and the half-saturation density Ro - 1/ath. In our study, we assume Ro is independent of temperature, and given that handling timescales as 1/J (where 1/J oc eEjlkT), this requires that the Holling attack rate (a) scales according to a oc e-E/kT. Holling (1965) considers attack rate to be a function of the reactive distance of the predator, speeds of movement of the predator and prey, and their capture success. Thompson (1978) showed that the attack coefficient of damselfly larvae increased with temperature according to a sigmoidal function over the range 50-27.5'C. However, inspection of Thompson's curve suggests that exponential growth well explains the changes in the attack rate below approximately 20TC. Marchand et al. (2002) observed a positive and nonlinear relationship between the attack rate of juvenile brook charr and temperature below their upper avoidance temperature of 22TC. The existence of an upper threshold for this relationship is not surprising, given that species-specific thermal tolerances are often well bounded within our range of "biologically plausible" temperatures. These results are at least suggestive of a positive exponential relationship among attack rate and temperature, and they thus indicate that temperature invariance of Ro may indeed be a reasonable suggestion. In practice, any scaling relationship that exists between R0 and temperature will most likely be influenced by environmental correlates of temperature that alter the efficiency of consumers. For example, an increase in the density of emergent macro- phytes in an aquatic system may reduce the effectiveness of sensory cues in zooplanktivorous fish.


Our results suggest that long term-changes in temperature can influence the equilibrium dynamics of species in predictable ways, given the dependence of their rates of growth, ingestion, and metabolism on temperature. Fur- ther work addressing short-term periodic variability, such as seasonal and El Nifio oscillations, and stochastic variability will provide additional insight into the influence of environmental conditions on short-term, nonequilibrium (equilibrium transient) dynamics. For those communities whose range is limited by the spatial extent of their habitat (e.g., lake communities), we expect that our model provides a testable and applicable framework for formulating predictions. For communities whose range is flexible, integrating this bioenergetic community approach into climate-envelope predictions will provide a stronger basis for the ecological consequences of global change scenarios.

Acknowledgments

We would like to thank M. Drever, M. Koen-Alonso, J. Rip, N. Rooney, J. Umbanhowar, C. Vasseur, and P. Yodzis for comments on an early draft of the manuscript and E. Novak for assistance with the data collection. Two anonymous reviewers provided indispensable feedback on the model and manuscript. Partial funding for this project was provided by a Natural Sciences and Engineering Research Council postgraduate scholarship to D.A.V.

APPENDIX A

Bifurcation and Sensitivity Analysis of the Model System

Starting with the model (eqq. [1]) from Yodzis and Innes (1992), we define the nondimensionalized model by selecting units of time such that r = 1. Normalizing the remaining rates in the model by r gives

dR RJC( R

dt r r R+R(

and given that x = M/r and y = (1 - 8)JM, the model reduces to

dR R xy RC_ - = RI-i dt (1R)fe R+Ro

dt - C R +

Ro

Solving for dR/dt = dCldt = 0, we obtain the nontrivial equilibrium conditions:

c= -I Re[(l

- 6)fe

Ce-=

)[R(1

-xWe. Re,

R0 Re - 0- (A3) y-1

Since all model parameters are nonnegative and Ce > 0 for all 0 < Re < K, we derive Ro/IK< (y - 1) as the upper limit for feasibility (transcritical bifurcation). Since RoIK is always positive, the ratio (1 - 6)JIM must be >1 for a two- species equilibrium to exist. This provides a derivation of the energetic constraints of the model; energy ingestion must be greater than energy metabolism in order to sustain consumers in the model.

To determine the stability of the equilibrium densities (eqq. [A3]), we define the Jacobian matrix at the nontrivial equilibrium point Eq3,

[R aR 3R aC

Jac -

Eq3 acac OR a CEq3

Ky- Roy - K - R -x y(y - 1)K (1 - 16fe

(A4) fe(1 - 6)(Ky - K- Ro)

yK

and the solution of its eigenvalues,

aR/aR ? (aR/OiR)2 - 4(-aR/aC x aC/aR) X1,2 2 (A5)

The model equilibrium (A3) is globally stable when both eigenvalues have negative real parts, and since aR/aC x aC/aR < 0 for all Ro/IK< y - 1, the discriminant in equation (A5) will always be less than aR/8R. Therefore, we must satisfy only the condition 3R/IR < 0. This condition is satisfied when

R0 y- 1l > . (A6) K y+1

The condition (A6) defines the Hopf bifurcation locus in the RoIK plane. Below this stability threshold, the equilibrium becomes locally unstable but is surrounded by a stable limit cycle. Within the realm of locally stable equilibria, the approach to equilibrium can be monotonic


(node) or damped oscillations (focus). The limit between nodes and foci occurs when X1,2 transition from real to complex numbers (for a full description, see Yodzis and Innes 1992).

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Associate Editor: Peter J. Morin Editor: Jonathan B. Losos

LETTER Phylogenetic community ecology and the role of social

dominance in sponge-dwelling shrimp

Kristin M. Hultgren,1* and

J. Emmett Duffy2

1National Museum of Natural

History, Smithsonian Institution,

MRC 163, PO Box 37012,

Washington, DC, 20013-7012, USA2Virginia Institute of Marine Sci-

ence, PO Box 1346, Gloucester Pt.,

VA, 23062-1346, USA

*Correspondence:

E-mail: [email protected]

AbstractWhen functional traits are evolutionarily conserved, phylogenetic relatedness can serve as a proxy for eco-

logical similarity to examine whether functional differences among species mediate community assembly.

Using phylogenetic- and trait-based analyses, we demonstrate that sponge-dwelling shrimp (Synalpheus)

assemblages are structured by size-based habitat filtering, interacting with competitive exclusion mediated

by social system. Most shrimp communities were more closely related and/or more similar in size than ran-

domized communities, consistent with habitat filtering facilitated by phylogenetically conserved body size.

Those sponges with greater space heterogeneity hosted shrimp communities with greater size diversity, cor-

roborating the importance of size in niche use. However, communities containing eusocial shrimp – which

cooperatively defend territories – were less phylogenetically related and less similar in size, suggesting that

eusociality enhances competitive ability and drives competitive exclusion. Our analyses demonstrate that

community assembly in this diverse system occurs via traits mediating niche use and differential competi-

tive ability.

KeywordsCompetition, coral reefs, eusociality, habitat filtering, phylogenetic community ecology, snapping shrimp,

spatial scale, Synalpheus.

Ecology Letters (2012) 15: 704–713

INTRODUCTION

A long tradition in ecology has sought to explain assembly of eco-

logical communities by linking coexistence to the ecological and tax-

onomic differences among species (Elton 1946; Diamond 1975).

Modern studies have built on this tradition by using phylogenetic

relatedness as a proxy for overall ecological similarity in attempts to

better quantify the importance of niche differences in community

assembly (Webb et al. 2002; reviewed in Cavender Bares et al. 2009;

Vamosi et al. 2009). The fundamental premises of the phylogenetic

approach to community assembly are that phenotypic traits deter-

mine habitat use and competitive ability, and that these traits are

generally conserved among related species, such that phylogenetic

relatedness provides a proxy for functional similarity, which influ-

ences whether species can coexist (Webb et al. 2002; reviewed in

Cavender Bares et al. 2009; Vamosi et al. 2009). Under these

assumptions, the processes of assembly can be inferred from a

community’s phylogenetic structure, that is, relatedness among spe-

cies in the observed community relative to that of a random draw

of species from the regional pool. Phylogenetic community ecology

initially proposed two alternative predictions. First, if co-occurring

species are more phylogenetically related than random communities

(phylogenetic clustering), the community is interpreted as being

structured by habitat filtering, which results in closely related species

with similar habitat tolerances co-occurring (Webb 2000; Webb et al.

2002; Mouillot et al. 2005; Horner-Devine & Bohannan 2006; Va-

mosi & Vamosi 2007). Conversely, phylogenetic overdispersion of

communities is interpreted as evidence that competition prohibits

co-occurrence of closely related, ecologically similar species (Lovette

& Hochachka 2006; Slingsby & Verboom 2006). Communities that

are randomly assembled with respect to phylogeny have a more

ambiguous interpretation and can reflect either neutral processes

such as dispersal (Hardy 2008; Kembel 2009), or multiple processes

acting simultaneously to obscure any overall phylogenetic signal

(Helmus et al. 2007).

However, recent developments emphasize that inferring the pro-

cesses of community assembly from phylogenetic structure is more

complicated than initially assumed. First, this framework rests on

the key assumption that ecological traits are strongly conserved

(Kraft et al. 2007; Kembel 2009), yet growing evidence shows that

many traits are only moderately phylogenetically conserved (Ingram

& Shurin 2009; Kraft & Ackerly 2010). Moreover, the degree of

trait conservatism can vary within a lineage; for example, traits that

are conserved at broader taxonomic scales can be convergent

among more closely related species (Cavender-Bares et al. 2006).

Coming full circle, these developments have refocused attention on

individual traits thought to mediate community assembly processes.

One powerful approach is to integrate data on both trait distribu-

tion and phylogenetic relatedness among species. For example,

Ingram & Shurin (2009) showed in rockfish assemblages that traits

relating to local resource use tended to be more evenly spaced

within communities (because of competitive exclusion), whereas

traits related to environmental gradients tended to be clustered

(habitat filtering).

A second complication is that the pattern of phylogenetic related-

ness expected under competitive exclusion differs for niche-based

traits (e.g. traits involved in habitat matching) versus traits influenc-

ing general competitive ability (Mayfield & Levine 2010). Coexis-

tence or exclusion is then predicted to depend on the relative

magnitude of differences in these two types of traits. Specifically,

coexistence is predicted to occur when differences in traits related

to niche partitioning are larger than differences in competitive abil-

ity (Chesson 2000; Mayfield & Levine 2010). Crucially, this is

thought to produce either of two patterns: (1) when modest (phylo-

© 2012 Blackwell Publishing Ltd/CNRS


genetically conserved) niche differences exceed small differences in

competitive ability, communities will consist of phylogenetically

related species, whereas (2) when strong niche differences over-

whelm large differences in competitive ability, communities will

consist of phylogenetically unrelated species (Mayfield & Levine

2010). In this study, we examine how community variation in two

traits – one related primarily to niche partitioning and another

linked to competitive ability – interact to affect community phyloge-

netic relatedness of marine invertebrate communities.

Previous studies of phylogenetic community ecology have been

conducted primarily in terrestrial communities, on well-studied

groups such as plants or vertebrates (reviewed in Vamosi et al.

2009), with relatively few studies in aquatic or marine systems

(Horner-Devine & Bohannan 2006; Helmus et al. 2007; Ingram &

Shurin 2009). Yet, the phylogenetic approach to community assem-

bly seems especially promising for exploring assembly of hyperdi-

verse communities such as those of coral reefs. We used

phylogenetic- and trait-based analyses to examine community assem-

bly in sponge-dwelling shrimp in the Synalpheus gambarelloides species

group (hereafter Synalpheus) – a diverse, monophyletic group of > 40

species that live exclusively in the interior canals of sponges on

West Atlantic reefs (Morrison et al. 2004; Rios & Duffy 2007).

Synalpheus shrimps often dominate the faunal assemblages inhabiting

sponge hosts in this region (Duffy 1992; Macdonald et al. 2006),

and many closely related species co-occur on in a given reef, and

even within individual sponges. Sponges are a limiting resource: the

vast majority of individual sponges are occupied (Macdonald et al.

2006), and shrimp are fiercely territorial (Duffy et al. 2002; Toth &

Duffy 2005). Although up to five different species of Synalpheus can

co-occur in an individual sponge, coexistence of multiple species is

less common than expected by chance (Macdonald et al. 2006).

These observations suggest that competition among Synalpheus

species is strong.

Shrimp body size is a key trait mediating host use and is strongly

positively correlated with the size of the sponge’s internal canals,

even after controlling for shrimp phylogenetic relatedness (Hultgren

& Duffy 2010). As in most animals, body size also influences com-

petitive ability in alpheid shrimp (Shein 1977; Hughes 1996), confer-

ring a competitive advantage to large species, all else being equal.

However, all else is not equal; in particular, Synalpheus species vary

in social structure, a trait also likely to influence competitive ability.

Although most species of Synalpheus worldwide live in monogamous

pairs, several species are eusocial, living in large cooperative colo-

nies of 10s to 100s of individuals with reproduction limited to one

or a few females. Eusociality has evolved independently at least

three times in this group (Duffy et al. 2000), and experimental and

field studies provide strong indirect evidence that eusocial species

tend to be superior competitors over pair-forming species. First,

eusocial shrimp cooperate to drive out intruders from their host

sponges (Toth & Duffy 2005) and are particularly aggressive

towards heterospecifics (Duffy et al. 2002). Second, compared with

pair-living species, eusocial Synalpheus use more sponge host species,

are more abundant, occupy a greater proportion of sponges and

tend to co-occur with fewer congeners in sponges (Macdonald et al.

2006; Duffy & Macdonald 2010).

Synalpheus biology thus provides evidence for two important traits

hypothesized to mediate community assembly. First, body size

adapts shrimp to the architecture of spaces within their sponge

hosts and is thus likely to be important in niche partitioning.

Second, social organization is likely to be important in interspecific

competition for space in sponges. In this study, we examine com-

munity assembly in sponge-dwelling Synalpheus using both trait- and

phylogeny-based analyses. We first examined phylogenetic conserva-

tism of these two traits – body size and eusociality – thought to be

important in mediating sponge habitat use and competitive interac-

tions. Next, we examined phylogenetic and trait similarity of Synal-

pheus communities across six Caribbean regions. We found that

phylogenetic relatedness of Synalpheus communities is moulded by an

interaction between traits that help define the habitat niche (body

size matching to structure of sponge spaces) and traits that foster

competitive ability – namely cooperative defense of sponges by

eusocial Synalpheus colonies.

METHODS

Community sampling

We analysed shrimp community data from six regions across the

Caribbean, collected during 26 field trips occurring over 21 years; in

most cases, host use was documented in previous monographs

(Fig. 1). Sampling regions included Carrie Boy Cay, Belize

(Macdonald et al. 2006; Rios & Duffy 2007); Bocas del Toro, Pan-

ama (Kristin Hultgren, Emmett Duffy, and Ruben Rios unpublished

data); San Blas, Panama (Duffy 1992); Discovery Bay, Jamaica (Mac-

donald et al. 2009); Curacao (Hultgren et al. 2010) and Barbados

(Hultgren et al. 2011). Sponge sampling protocol was similar over all

collections, and data from the most extensively sampled region

(Belize: 1990–2009) indicate that Synalpheus-sponge associations are

very consistent over time (Macdonald et al. 2006; Rios & Duffy

2007). Sampling protocol has been extensively described elsewhere

(e.g. Macdonald et al. 2006); briefly, whole individual sponges were

collected from coral reefs and seagrass beds from 1 to 30 m depths

using SCUBA or snorkelling. As Synalpheus do not voluntarily leave

their host sponges, live Synalpheus were individually removed, identi-

fied and preserved. For most sponges collected from 2007 to 2009

(mean n = 17 individuals/species), we measured sponge volume by

displacement and measured mean diameter of 10–20 randomly

selected sponge internal canals (depending on sponge size) using

methods described previously (Hultgren & Duffy 2010). We quanti-

fied canal size heterogeneity using the coefficient of variation (here-

after sponge CV) of 10 randomly selected canals (we were unable to

measure the sponge Hymeniacidon amphilecta). Although sponge vol-

ume, and hence shrimp abundance, varied among and within sponge

hosts, Synalpheus community species richness did not differ signifi-

cantly among the nine sponge hosts we compared (mean rich-

ness = 2.04–2.43: Wilcoxon test P = 0.398). Sponges were identified

with the help of taxonomic experts (primarily Dr. Klaus Ruetzler,

Smithsonian Institution). In each region, sampling adequacy was esti-

mated by fitting Michaelis–Menten and Chao2 functions to plots of

cumulative Synalpheus species richness as a function of number of

individual sponges sampled. These analyses suggest that we sampled

on average 89% of the true Synalpheus species richness in each region

(Macdonald et al. 2006, 2009; Hultgren et al. 2010, 2011).

Phylogeny of sponge-dwelling shrimp

We constructed a phylogenetic tree using data from three molecular

loci and 33 morphological characters, collected from 38 species of


Letter Community phylogenetics of coral reef shrimp 705

(a) (b)

Figure 1 (a) Sampling regions in the Caribbean. Community indicates number of individual sponges collected; species pool indicates Synalpheus richness; in references,

1 = Rios & Duffy 2007; 2 = Macdonald et al. 2006; 3 = Kristin Hultgren and Emmett Duffy, unpublished data; 4 = Duffy 1992; 5 = Macdonald et al. 2009;

6 = Hultgren et al. 2010; 7 = Hultgren et al. 2011. (b) Phylogenetic tree of sponge-dwelling Synalpheus used in the study, shown as a Bayesian consensus tree (node

numbers indicate Bayesian posterior probability values). Eusocial species are underlined and bolded; species in quotation marks are undescribed. Boxes indicate size

category of each shrimp species; names on the right indicate species complexes. Alpheus estuariensis and Synalpheus obtusifrons are the outgroups.


706 K. M. Hultgren and J. E. Duffy Letter

Synalpheus in a previous study (Hultgren & Duffy 2011). Molecular

loci included partial sequences from the mitochondrial cytochrome

oxidase I gene (COI), a mitochondrial ribosomal gene (16S) and the

nuclear gene elongation factor 2 (EF2) (~1800 basepairs total). Cod-

ing of morphological characters and DNA extraction, amplification,

sequencing, alignment and calculation of nucleotide substitution

models are described in detail in Hultgren & Duffy (2011). As indi-

viduals of a species from different locations formed monophyletic

clades, we used character data from one exemplar individual per spe-

cies (Appendix S1 in Supporting Information). We included six taxa

that lacked EF2 sequences because simulations suggest that inclusion

of taxa with � 50% missing characters in an analysis increases tree

accuracy (Wiens 2006). We included two outgroups (Alpheus estuariensis

and Synalpheus obtusifrons) from outside the gambarelloides group, and

used Bayesian methods (MrBayes v3.12) to construct the tree using a

partitioned Bayesian analysis (Ronquist & Huelsenbeck 2003); for

more details, see Hultgren & Duffy (2011). We ran a Markov Chain

Monte Carlo search with two runs and four chains for 108 genera-

tions, at which point runs had converged to a stationary distribution

(standard deviation of split frequencies < 0.004). We sampled the

chain every 100 generations, discarded the first 25% of the samples

as burn-in and estimated nodal support using Bayesian posterior

probabilities (bpp). Branch lengths were estimated in MrBayes and

were used in all community and trait analyses.

Shrimp trait data

We quantified body size of each shrimp species using carapace

length (CL), measured as the distance in mm from the rostrum to

the posterior edge of the carapace. Shrimp CL scales directly with

body width and correlates strongly to sponge host canal size

(Hultgren & Duffy 2010), indicating that body size is a key func-

tional trait mediating habitat use in these animals. Degree of soci-

ality was calculated using a modified version of the eusociality (E)

index (Keller & Perrin 1995); see Duffy et al. 2000 for more

details). When available, we used E and CL species means from a

previous study (Duffy & Macdonald 2010); for others, we esti-

mated mean CL using at least 6 ovigerous and 10 non-ovigerous

individuals, excepting three species in which only male and female

types were available (Appendix S1 in Supporting Information). As

it is possible for processes such as dispersal to drive patterns of

clustering if species show phylogenetically conserved differences in

relative abundance (Hardy 2008; Kembel 2009), we also tested

whether Synalpheus abundance (estimated using the full data set)

was a phylogenetically conserved trait. We quantified the phyloge-

netic signal of each trait using the K statistic (Blomberg et al.

2003) calculated using the Picante package (Kembel et al. 2010)

implemented in the R programming language (R Development

Core Team 2011). A K value of 1.0 indicates that trait similarity

across a lineage is proportional to the shared evolutionary history

expected under a Brownian motion model of neutral divergence;

K < 1 indicates greater trait convergence than expected under

Brownian motion, while K > 1 indicates a stronger trait conserva-

tism than expected (Blomberg et al. 2003). We assessed whether

traits were significantly conserved by comparing observed K to a

distribution of K values calculated by randomizing trait values 999

times across the tips of the tree; a P < 0.05 indicates greater

phylogenetic signal than expected (Kembel et al. 2010; Kraft &

Ackerly 2010).

Phylogenetic- and trait-based community analyses

We used the Picante package (Kembel et al. 2010) implemented in

R to calculate the phylogenetic relatedness of Synalpheus communi-

ties living in individual sponges, relative to the relatedness of ran-

domly assembled communities. We first calculated (1) mean

pairwise phylogenetic distance (MPD) between species in a commu-

nity, which generally has more power to detect patterns attributable

to habitat filtering, and (2) mean nearest phylogenetic taxon distance

(MNTD) between the focal taxon and its most closely related

neighbour in the community, which has more power to detect

trends because of competition (Webb et al. 2002; Kraft et al. 2007).

We then calculated the standardized value of MPD and MNTD val-

ues, which are comparable (respectively) to the net relatedness index

(NRI) and nearest taxon index (NTI) in Phylocom (Webb et al.

2002):

NRI ¼ �1� ðMPDobserved �MPDrandomÞ=ðsdMPDrandomÞ

NTI ¼ �1� ðMNTDobserved �MNTDrandomÞ=ðsdMNTDrandomÞwhere sdMPDrandom and sdMNTDrandom represent the standard

deviation of the MPD and MNTD values, respectively, for the ran-

domly assembled communities. We focused all subsequent compari-

sons on NRI and NTI, which represent the standardized effect size

of phylogenetic relatedness, and allowed us to compare sponge

communities in different sponge hosts while controlling for poten-

tial differences in overall shrimp richness (Webb et al. 2002). Posi-

tive values of NRI and NTI indicate that communities are more

phylogenetically related than randomized communities (often con-

sidered evidence for habitat filtering, given conserved traits),

whereas negative values indicate that communities are less related

than randomized communities (evidence for competitive exclusion).

As differences in species abundance can affect estimates of phylo-

genetic structure (Hardy 2008), we used species abundances (rather

than presence–absence data) and compared each community to 999

random communities using the independent swap method (Gotelli

& Entsminger 2003); this method maintains species richness and

occurrence totals within individual sponges, has lower Type I error

rates and can be more appropriate when there is phylogenetic signal

in species abundance (Kembel 2009). Although both NTI and NRI

were similar in magnitude and direction, we focus on NTI values as

this index is less sensitive to errors in higher level phylogenetic

structure (Webb 2000); NRI values are reported in Appendix S2 in

Supporting Information. We trimmed the species tree (Fig. 1) to

produce customized species pool phylogenies for each region. The

Jamaica species pool phylogeny contained one polytomy, so we

used phylogenies with all three resolutions of the polytomy for

Jamaica analyses, averaging NRI/NTI values from all three trees.

Picante utilizes a phylogenetic distance matrix to calculate MPD

and MNTD, making it simple to substitute in a trait distance

matrix to examine trait distributions in individual communities.

We focused our trait analyses on body size, the trait with the

strongest phylogenetic signal and the clearest mechanistic links to

habitat use (Hultgren & Duffy 2010), and calculated trait diversity

measures (NTIsize and NRIsize) for individual communities by

substituting a body size distance matrix into Picante. In this case,

positive values of NTIsize indicate that species in a community

are more similar in size than in randomized communities (evi-

dence for size-based habitat filtering), and negative values indicate



that species are less similar in size than in random communities

(evidence for competitive exclusion based on size). We tested

whether phylogeny-based (NTI) or trait-based (NTIsize) community

diversity indices deviated from a null expectation (NRI or

NTI = 0) using nonparametric two-tailed Wilcoxon tests, as data

were non-normal and variances were heterogeneous. To avoid

excessive statistical comparisons, we pooled NTI values for all

sponge species across regions, and used a Bonferroni-corrected

a-value of 0.0055.

Effects of eusociality and sponge host dimensions on phylogenetic

structure

We tested whether the presence of competitively dominant eusocial

shrimp species affected similarity by comparing the mean size

(NTIsize) and phylogenetic (NTI) diversity indices from shrimp

communities with versus without one of the six eusocial species

(i.e. quantifying eusociality as a categorical trait), using a paired two-

tailed Wilcoxon test. We then examined how sponge space dimen-

Figure 2 (a) Phylogenetic similarity (NTI) and (b) size similarity (NTIsize), for Synalpheus communities in different sponges and different regions. Sponge hosts are listed

across the top; values in parentheses indicate number of individual sponges assessed per region. (c) Mean phylogenetic and size similarity for communities in different

sponge hosts, pooled across regions. For all, positive values of NTI and NTIsize indicate that communities are more phylogenetically related or similar in size than

random communities, while negative values indicate communities are more phylogenetically unrelated or dissimilar in size. Bars indicate standard error; asterisks indicate

significant deviations from zero for a sponge species, pooled across regions (signed-rank test, two-tailed P-values: *P < 0.05, **P < 0.005, ***P < 0.0001).



sions and eusociality interacted to affect similarity using a linear

mixed model, implemented using the lme4 package (Bates & Sarkar

2007) in R (R Development Core Team 2011). This allowed us to

compare models with different combinations of fixed (eusociality,

sponge canal variability) and random (sponge host species) effects,

using the small sample version of Akaike Information Criterion

(AICc; Burnham & Anderson 2004). As sampling of different

sponge hosts was highly uneven across regions, we could not

include region as a factor. For these analyses, we coded eusociality

as a continuous variable (Keller & Perrin 1995) by calculating mean

eusociality of all individual shrimp in a sponge (hereafter mean E)

for each shrimp community. We quantified sponge canal variability

using mean sponge CV for each sponge species, as CV values were

not available for individual sponges. We did not include shrimp spe-

cies richness as a factor, as NTI and NRI represent standardized

effect sizes of phylogenetic relatedness based on randomized com-

munities with the same species richness and thus inherently control

for variation in richness.

Community variation in habitat heterogeneity and trait

distributions

We examined how distributions of our two primary traits (body size

and eusociality) varied among shrimp communities in different

sponge hosts. First, we examined how variability in shrimp body

size among sponges was related to sponge canal space heterogene-

ity, by regressing pooled NTIsize and NRIsize means for different

sponge hosts against sponge canal CV. Second, we examined

whether community variation in body size (NTIsize) was correlated

with variation in eusociality (NTIeusociality, calculated using a distance

matrix of E values; values for individual sponge hosts are presented

in Appendix S2 in Supporting Information).

RESULTS

Phylogenetic signal (K) of shrimp body size was estimated at 0.49,

indicating less signal than expected under Brownian evolution, but a

significantly stronger signal than expected under randomized trait dis-

tributions (P = 0.031) and similar to estimates of phylogenetic signal

for morphological traits in other species (Blomberg et al. 2003). Low

phylogenetic signal may be due in part to heterogeneity of size conser-

vatism across the tree; for example, species in the longicarpus species

complex tended to vary more in size than species in the brooksi species

complex (Fig. 1). Phylogenetic signal of eusociality (K = 0.18,

P = 0.722) and species abundance (K = 0.12, P = 0.862) did not dif-

fer significantly from randomized trait distributions.

Patterns of body size and phylogenetic similarity among co-occur-

ring sponge-dwelling shrimp provided strong evidence of the

Figure 3 Mean values of (a) phylogenetic similarity (NTI) and (b) trait (size) similarity (NTIsize) for Synalpheus communities with or without eusocial species present,

across different sponge species (sponge species pooled across regions). P-value indicates significant differences between communities with or without eusocial species

(Wilcoxon test, two-tailed P-value).



importance of shrimp body size and competition in community

assembly (Figs. 2 and 3; see Appendix S2 in Supporting Informa-

tion for NRI values). In three of nine host sponge species

(Agelas clathrodes, A. dispar and Calyx podatypa), shrimp communities

were both more phylogenetically related (NTI P < 0.005) and more

similar in size (NTIsize P < 0.005) than randomized communities,

indicating strong support for size-based habitat filtering. Shrimp

communities in Xestospongia proxima showed a similar though non-

significant pattern, probably because of small sample size (n = 3

communities). In two sponge species (Lissodendoryx colombiensis and

Hymeniacidon amphilecta), shrimp communities were phylogenetically

clumped (NTI P < 0.005), but showed more disparity in body size

than randomized communities (NTIsize P < 0.05), suggesting com-

petitive exclusion acting to reduce size similarity, and possibly habi-

tat filtering on another unknown, phylogenetically conserved trait.

The role of niche differentiation by size in these cases is further

supported by the high diversity of canal sizes available in

L. colombiensis (Fig. 4b); no quantitative canal size data are available

for H. amphilecta, though our field observations suggest it has com-

parably variable canal sizes. In the sponges Hyattella intestinalis and

Hymeniacidon caerulea, shrimp communities were more similar in body

size (NTIsize P < 0.0001), indicating habitat filtering by body size.

However, communities in H. intestinalis were also phylogeneti-

cally overdispersed relative to randomized communities (NTI

P < 0.0001), possibly suggesting competitive exclusion acting on

another phylogenetically conserved trait. Finally, shrimp communi-

ties in Xestospongia rosariensis were less phylogenetically similar (NTI

P < 0.0001) and less similar in size (NTIsize P < 0.0001) than ran-

domized communities, indicative of a strong imprint of size-based

competitive exclusion.

Communities from individual sponges that contained eusocial

species were generally less phylogenetically related (NTI P = 0.0117,

Wilcoxon signed-rank test) and less similar in size (NTIsize

P = 0.0195) than communities from sponges without eusocial

species (Fig. 3). Across the entire data set, the linear mixed model

that best explained variation in phylogenetic relatedness included

eusociality (E), sponge host and an E*sponge host interaction

(AICc Weight = 0.68, Table 1). A similar model that included

sponge CV also received some support [AICc Weight = 0.24; see

Burnham & Anderson (2004) for inclusion criteria]. There was

strong support for E in these models, as the parameter estimate for

E exceeded two standard errors (SE) of E (Gelman & Hill 2007).

The model that best explained community variation in size included

E*sponge CV and E*sponge interaction terms (AICc

Weight = 0.70, Table 1), and other models including sponge CV

also received substantial support (AICc Weight = 0.27). Sponge CV

and sponge CV* E interactions received strong support in these

models (parameter estimates > 2 SE), whereas the main effect of E

had far less explanatory power in predicting size similarity (parame-

ter estimate of E � 2 SE).

Across sponge species, variation in eusociality within a commu-

nity (NTIeusociality) tended to increase with variation in body size

(NTIsize, though not quite significantly (F1,7 = 3.971, P = 0.0880,

Fig. 4a). Sponges that were dominated by eusocial shrimp (Xestospon-

gia proxima and X. rosariensis, dark circles in Fig. 4) showed strong

community variation in social organization (high NTIeusociality),

reflecting that two eusocial species never coexisted, presumably

because of competitive exclusion. Variation in body size among co-

occurring shrimp species (NTIsize) was strongly correlated with het-

erogeneity in sponge space sizes (sponge CV; F1,6 = 14.664,

P = 0.0087, Fig. 4b). Results of analyses were similar when the NRI

index was used (Appendix S3 in Supporting Information).

DISCUSSION

This study supports strong roles for both size-based habitat filter-

ing, and competitive exclusion mediated by social cooperative

defense, in assembly of sponge-dwelling shrimp communities. Most

communities contained shrimp species that were more phylogeneti-

cally related, and/or more similar in body size, than randomized

communities, indicating a strong role for habitat filtering based on

body size or other phylogenetically conserved traits. The importance

of size matching is also supported by the finding that in the two

sponges with the most variable canal size dimensions, shrimp body

sizes were much more variable than in randomized communities.

Superimposed on these niche-based patterns, communities with

Figure 4 (a) Community variation in shrimp sociality within a sponge host

(NTIeusociality) as it relates to shrimp body size–based niche differences (NTIsize).

(b) NTIsize of shrimp communities in different sponge hosts, as a function of

sponge canal size heterogeneity. For (a) and (b), initials next to each point

indicate sponge species and genus; icon colour indicates mean pooled

proportional abundance of eusocial species in each sponge host.



competitively dominant, eusocial Synalpheus species generally showed

lower phylogenetic relatedness and lower similarity in body size than

those without eusocial species, consistent with a strong imprint of

competitive exclusion driven by more effective territory defense by

social species. Thus, a small number of competitively dominant

community members appear to have a disproportionate influence

on phylogenetic structuring of communities, by increasing the mag-

nitude of competitive processes driving phylogenetic overdispersion.

Phylogenetic overdispersion of shrimp communities occurred

almost exclusively in sponges containing eusocial species, primarily

because eusocial species never co-occurred in the same individual

sponges. Although eusociality has evolved independently at least

three times in Caribbean sponge-dwelling Synalpheus (Duffy et al.

2000; Morrison et al. 2004) and we found no significant phyloge-

netic conservatism in sociality, four of the six eusocial species in

this study (and 48% of total recorded shrimp abundance) were from

the monophyletic rathbunae species complex (Fig. 1). If competition

prohibits more than one eusocial species from co-occurring, coexis-

tence will be seen only with more distantly related species of sub-

stantially different size capable of occupying sponge canals either

too large or too small for eusocial species to defend effectively.

This could result in the patterns of phylogenetic overdispersion

observed in these communities.

We hypothesize from several lines of evidence that this strong pat-

tern of phylogenetic overdispersion in communities with eusocial

species is driven by competition. First, eusocial species of Synalpheus

recognize and defend their nest against both non-nestmate conspe-

cifics and heterospecifics (Duffy et al. 2002). Although the relative

effectiveness of defense by eusocial versus pair-living species has not

been explicitly tested, eusocial shrimps display coordinated defensive

activity (Toth & Duffy 2005) suggesting that their defenses are espe-

cially effective. Second, whereas most pair-living Synalpheus species

have swimming larvae, eusocial shrimp queens produce crawling

juveniles that tend to stay in the natal sponge (Duffy & Macdonald

2010). Thus, eusocial colonies typically contain individuals spanning

the entire spectrum of the species’ size range, and thus may domi-

nate a wider size range of available canal space than pair-living spe-

cies. These characteristics may explain why in areas where they have

Table 1 Assessment of different models explaining variation in community phylogenetic (NTI and NRI) or size (NTIsize and NRIsize) similarity, using the Akaike Infor-

mation Criterion

Response

variable Model AICc Delta AICc

Model

likelihood AICc weight E

Strength of Support

Sponge CV E* sponge CV

NTI E, sponge*E 559.52 0.00 1.00 0.68 1.22

E + sponge CV, sponge*E 561.64 2.12 0.35 0.24 1.22 0.06

E*sponge CV, sponge*E 563.79 4.26 0.12 0.08 0.29 0.05 0.00

E*sponge CV, sponge 584.66 25.14 0.00 0.00 0.81 0.11 1.38

E, sponge 588.01 28.49 0.00 0.00 2.11

E + sponge CV, sponge 590.01 30.48 0.00 0.00 2.11 0.15

Sponge 603.13 43.60 0.00 0.00

Sponge CV, sponge 605.01 45.49 0.00 0.00 0.22

NRI E, sponge*E 563.34 0.00 1.00 0.68 1.22


E*sponge CV, sponge*E 567.59 4.26 0.12 0.08 0.23 0.01 0.06


E, sponge 598.06 34.73 0.00 0.00 2.27


Sponge 615.66 52.32 0.00 0.00

Sponge CV, sponge 617.56 54.22 0.00 0.00 0.21

NRIsize E*sponge CV, sponge*E 419.71 0.00 1.00 0.70 1.10 2.37 1.18


E, sponge*E 427.45 7.74 0.02 0.01 0.10


Sponge CV, sponge 434.32 14.61 0.00 0.00 2.30


Sponge 442.44 22.74 0.00 0.00

E, sponge 444.46 24.76 0.00 0.00 0.11

NTIsize E*sponge CV, sponge*E 421.19 0.00 1.00 0.69 1.08 2.26 1.18



E, sponge*E 428.37 7.18 0.03 0.02 0.18

Sponge CV, sponge 433.44 12.25 0.00 0.00 2.20


Sponge 441.11 19.92 0.00 0.00

E, sponge 442.91 21.73 0.00 0.00 0.26

E is mean eusociality score; models with interaction terms include component main effects. AICc = small-sample unbiased AIC value, Delta AICc = difference between

the models AICc and the lowest AICc. Values in the Strength of Support column (equivalent to |parameter estimate| for each variable, divided by 2*SE) indicate support

for each variable in the model; values > 1.0 (in bold) indicate that the 95% confidence interval of the parameter estimate does not include zero (support for the estimate

in the model), while values < 1.0 indicate no support for the estimate (Gelman & Hill 2007).



been extensively surveyed, eusocial species are, on average, 17 times

more abundant than pair-living species, inhabit a greater range of

sponge hosts and tend to be less likely to co-occur with their cong-

eners than pair-living species, suggesting some means of ecological

dominance (Macdonald et al. 2006; Duffy & Macdonald 2010). The

propensity of eusocial species to form large colonies (tens to hun-

dreds of individuals) also could make it more difficult for two colo-

nies to co-occur within the space limitations of a sponge, although

abundance of some non-eusocial species can also be similarly high,

for example, hundreds of individuals inside an individual sponge

(Macdonald et al. 2006; Rios & Duffy 2007). Nevertheless, presence

of eusocial species cannot explain all of the variation in community

phylogenetic relatedness, as phylogenetically overdispersed shrimp

communities occurred in some regions (Curacao) where eusocial spe-

cies were never recorded (Hultgren et al. 2010).

Despite the tendency towards competitive exclusion by eusocial

species, the most common phylogenetic patterns we observed – in

five of the nine host sponge species, and > 60% of individual com-

munities – were co-occurrence of closely related species of Synal-

pheus in individual sponges. Shrimp communities in three of these

sponge species also showed significant similarity in body size – a

pattern that provides some evidence for size-based habitat filtering.

Body size is only one of several traits likely to be important in

adaptations to the sponge niche, however, and it is important to

point out that phylogenetic relatedness can serve as a more general

proxy for ecological similarity as multiple, phylogenetically con-

served traits are often important in determining habitat use (Blom-

berg et al. 2003; Helmus et al. 2007; Ingram & Shurin 2009; Kraft &

Ackerly 2010). Most of the sponges inhabited by Synalpheus contain

chemical compounds deterrent to fish (Pawlik et al. 1995), suggest-

ing that adaptations to sponge chemistry could also act as a strong

habitat filter for Synalpheus. For example, members of the Synalpheus

paraneptunus complex are typically limited to living in sponges in the

genus Xestospongia (91% of total abundance). Strong habitat filtering

based on traits such as sponge chemistry could help explain how

competitively diverse communities can coexist in X. proxima, despite

relatively small differences in body size (e.g. Fig. 4a). Similarly, sev-

eral sponge hosts showed contrasting patterns of size and phyloge-

netic similarity. These contrasting patterns are likely driven by both

habitat constraints (sponge habitat heterogeneity) and variation in

traits related to competitive ability (eusociality).

In summary, assembly of Caribbean sponge-dwelling shrimp com-

munities appears to be strongly influenced by both traits that deter-

mine use of the habitat niche (body size) and traits that foster

competitive dominance (eusociality). If eusociality can serve as a rea-

sonable proxy for competitive ability within a shrimp community,

then our results are also compatible with a model proposed by May-

field & Levine (2010), in which differences among species in com-

petitive ability (eusociality, in our case) and in traits influencing niche

use (body size matching of habitat spaces) interact to facilitate two

different modes of coexistence. First, communities of shrimp species

that were similar in body size also tended to consist of non-social

species, consistent with the prediction that species with only modest

differences in niche-based traits can coexist as long as differences in

competitive ability are even weaker (Mayfield & Levine 2010; Fig. 2,

position A). This scenario describes coexistence of similarly sized,

pair-living shrimp species in our study (Fig. 4a, lower left quadrant).

Second, co-occurring shrimp species that differ strongly in social

structure, and thus competitive ability, tended also to differ in body

size and to live in sponges with more heterogeneous canals, consis-

tent with the prediction that asymmetric competitors can coexist

only where the species have large niche differences (Mayfield &

Levine 2010; Fig. 2, position B). This describes cases where highly

competitive eusocial species coexist with species of substantially dif-

ferent body size (Fig. 4a, upper right quadrant). These coexistence

scenarios are also supported within individual sponge species, where

data show that communities with eusocial shrimp tend to show

stronger dissimilarity in body size among species (Fig. 3b). Thus, we

have shown that both competition and niche differentiation are

important and interact to mediate assembly of highly diverse symbi-

otic reef shrimp communities. Although it is important to stress that

multiple traits likely affect assembly – and that it is difficult to quan-

tify competitive ability differences and niche differences with single

traits – it is noteworthy that body size and social organization

together explain a substantial part of the variation among sponge

species in shrimp community structure. Integrating multiple sources

of phylogenetic and trait data sheds important light on the often

complex set of processes affecting community assembly.

ACKNOWLEDGEMENTS

Funding for this work was provided by the National Geographic

Society (Research and Exploration Grant no. 8312-07), the Smith-

sonian Marine Science Network to KMH and NSF IOS-1121716 to

JED. Tripp Macdonald, Narissa Bax, Deyvis Gonzalez, Chris Free-

man and other individuals provided invaluable assistance in the

field; Klaus Ruetzler and Janie Wulff kindly assisted with sponge

identifications; Ming Wen-An and Jon Lefchek helped with statisti-

cal analyses in R. This study benefited from conversations with

Brian Enquist and Nate Swenson; earlier versions of the manuscript

were greatly improved by the comments of Randall Hughes, Jeremy

Davis and three anonymous referees.

STATEMENT OF AUTHORSHIP

JED and KMH collected trait and community data. KMH con-

structed phylogenetic tree, conducted trait and community analyses,

and wrote the first draft of the manuscript; JED made substantial

revisions to the manuscript.

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Proc. Nat. Acad. Sci. USAVol. 69, No. 5, pp. 1109-1113, May 1972

Niche Overlap as a Function of Environmental Variability(food size/birds/ecology/exclusion/model)

ROBERT M. MAY* AND ROBERT H. MAC ARTHUR

Institute for Advanced Study, Princeton, New Jersey, and Department of Biology, Princeton University, Princeton, N.J. 08540

Contributed by Robert H. Mac Arthur, February 16, 1972

ABSTRACT The relationship between environmentalvariability and niche overlap is studied for a class of modelbiological communities in which several species competeon a one-dimensional continuum of resources, e.g., foodsize. In a strictly unvarying (deterministic) environment,there is in general no limit to the degree of overlap, shortof complete congruence. However, in a fluctuating (sto-chastic) environment, the average food sizes for speciesadjacent on the resource spectrum must differ by anamount roughly equal to the standard deviation in thefood size taken by either individual species. This mathe-matical result emerges in a nonobvious yet robust wayfor environmental fluctuations whose variance relative totheir mean ranges from around 0.01% to around 30%. Inshort, there is an effective limit to niche overlap in the realworld, and this limit is insensitive to the degree of en-vironmental fluctuation, unless it be very severe. Recentfield work, particularly on bird guilds, seems in harmonywith the model's conclusion.

One of the central concepts in ecology is the competitiveexclusion principle, which forbids the coexistence of two ormore species making their livings in identical ways. Recently,an increasing amount of attention has been paid to the ques-tions: How similar can competing species be if they are toremain in an equilibrium community? How identical is"identical"? How close can species be packed in a naturalenvironment?An answer to these questions may begin by noticing that in

laboratory experiments, where the environment can be care-fully kept unvarying, species whose ecology is well-nigh identi-cal have coexisted for long periods (1). A conjecture (2, 3)is that in the real world, environmental fluctuations will put alimit to the closeness of species packing compatible with anenduring community, and that species will be packed closeror wider as the environmental variations are smaller or larger.Motivated by these ideas, we consider a one-dimensional

resource spectrum, sustaining a series of species, each of whichhas a preferred position in the spectrum, and a characteristicvariance about this mean position, as given by some "utiliza-tion function" (see Fig. 1). For example, the resource spec-trum may be food size, and the consumers may be birdspecies each having a utilization function that describes theirmean food size and its variance. The dynamics of this situa-tion may be plausibly modeled by a system of first-order dif-ferential equations, with competition coefficients that dependon how closely species are packed; that is, on the degree ofniche overlap (on the ratio of d to w in Fig. 1).

In the stability analysis of such models, two qualitativelydifferent circumstances need be distinguished. In the un-

realistic case when all the environmental parameters arestrictly constant (deterministic), then in general the systemremains stable even if an arbitrarily large number of speciesare packed in, arbitrarily close. On the other hand, when therelevant environmental parameters fluctuate (stochasticenvironment), there is a limit to the niche overlap consistentwith long-term stability.However, this limit to species packing depends on the en-

vironmental variance in a far-from-obvious and extremelyinteresting way (Fig. 3). If the fluctuations in the resourcespectrum are severe, having variances comparable in mag-nitude with their mean values, the species packing is indeedroughly proportional to the environmental variance, as onewould expect intuitively. But for fluctuations ranging frommoderate to exceedingly small, the species packing attainsan effective limiting value roughly equal to the width of theutilization functions. Thus, as the ratio between the varianceand mean value in the resource spectrum, or other pertinentenvironmental parameter, falls from 0.3 to 0.0001, the closestspecies packing consistent with stability falls only from 2 to 1times the utilization function variance. Moreover, our generalresult is a robust one, being rather insensitive to the detailsof the mathematical model.

Collecting these statements, we observe that the speciespacking parameter d indeed goes to zero when the environ-mental variance becomes strictly zero, but that for any finiteenvironmental variance, d remains roughly equal to theutilization function width, w. This result, which at first glanceseems odd, reflects the technical fact that the mathematicscontains an essential singularity around d = 0 (Eq. [6] andFig. 2), so that there is a qualitative difference between anenvironmental variance that is small but finite, and one thatis zero.

Following Hutchinson's (4) initial observations, Mac Arthur(3) has recently reviewed a body of semiquantitative work

FIG. 1. The curve labeled K represents some resource con-tinuum, say amount of food as a function of food size, that sus-tains various species whose utilization functions (characterizedby a standard deviation w and a separation d) are as shown.

1109

* On leave from the University of Sydney, Sydney, Australia.

Zoology: May and Mac Arthur,

Xmin

d/wFIG. 2. The minimum eigenvalue of the stability matrix

(Eq. [4]) as a function of niche overlap, diw, for an n-speciesguild, where n = 2,3,4 and n >> 1.

bearing on species packing and character displacement amongcompeting species. These empirical data, which are discussedmore fully in section IV, match the conclusions drawn fromour model.Two corollaries are worth mentioning.First, most of the ideas advanced to account for the gradient

in species diversity as one goes from the tropics to the polesmay be summarized under three headings (1, 5): (i) as a mat-ter of history, there has been more time for speciation in thetropics than most other places; (ii) total niche "volume" isgreater in the tropics, which tend to be more productive, lessseasonal, and more floristically complex, both in stratificationand diversity; (iii) more niche overlap is permitted in thetropics by the unvarying environment. The potential numberof species is the total volume [i.e., (ii) ] divided by the effectiveniche volume per species [i.e., (iii)], and this potential will berealized if enough time is available [i.e., (i) ]. The intuitivebasis for the argument (iii) was set out in the second para-graph of this introduction, but the quantitative conclusionthat niche overlap is only weakly dependent on the degree ofenvironmental fluctuation (unless very severe) suggests that(iii) is a relatively unimportant factor in explaining thespecies diversity gradient, at least until one gets to extremelatitudes. It should be emphasized that our conclusion thatspecies packing, d, is roughly proportional to utilization func-tion width, w, implies only that niche overlap is largely inde-pendent of the environmental variance, 0.2. It remains truethat the total number of species packed into an interval onthe resource spectrum is greater if they are specialists (smallw) than if they are generalists (large w); the question as towhat ultimately determines w remains open.

Second, in this model, which explicitly treats only onetrophic level, it is obvious that greater complexity (in the formof more species, more closely packed) makes for lesser sta-bility. In a perfectly stable deterministic environment, arbi-trarily close packing and rich speciation is possible, and to acertain limited extent the greater the environmental steadi-ness, the closer the packing, and the richer the consequentassembly of species. Insofar as this example adds a piece tothe complexity-stability jigsaw puzzle, it is that complexityis a fragile thing, permitted in this instance by environmentalsteadiness: this is quite the opposite of the conventional"complexity begets stability" wisdom (6).

Proc. Nat. Acad. Si. USA 69 (1972)

The details of the model are outlined in section 1, and theresults derived in section II. Section III contains a shortaccount of work bearing on the insensitivity of the main re-sults to the details of the model.

I. THE MODEL DEFINED

Suppose one has a one-dimensional continuum of resources,such as food size, or vertical habitat, or horizontal habitat,that may be schematically depicted as in Fig. 1, where thecurve labeled K shows amount of food as a function of foodsize, or amount of habitat as a function of height, and, ingeneral, amount of resource as a function of x. Supposefurther that this resource sustains various species, each ofwhich has a utilization function f(x) as depicted in Fig. 1,which characterizes the species' use of the resource spectrum.In particular, we note the mean position and the standarddeviation, w, about this mean for the various species; i.e., themean and the variance of the food size, or of the habitatheight, etc. The separation, d, between the mean positions ofspecies that are adjacent on the resource continuum willclearly be a measure of how densely the species are packed.Mac Arthur (3, 7) has established a criterion that ensures

that the actual community utilization of the resource willprovide the best least-squares fit to the available resourcespectrum. This requires the populations of the n species,Ni(t) [labeled sequentially i = 1, 2, ., n], to obey

dN'(t) = Ni(t) _k_-E aijNi(t)] [1]

where the ki are integrals with respect to x over the productof the resource spectrum and the utilization function of theith species, and the competition coefficients atj are convolu-tion integrals between the utilization functions of the ith andjth species. With this, we are assured both that the equilib-rium populations (obtained by setting all d/dt = 0) minimizethe squared difference between available and actual "pro-duction," and also that nonequilibrium initial populationswill move in time towards this minimum configuration.Eq. [1 ] is, of course, the Lotka-Volterra competition equa-

tion, but tied to the underlying model illustrated by Fig. 1,so that we have explicit recipes for the ki and aij in terms ofdirect biological assumptions. Specifically, if we assume thatall the species' utilization functions are the usual bell-shapedgaussian curves, with common width w, and that they are

uniformly spaced along the resource continuum (commond), the competition coefficients are

atj = (w2)-1/2 dxexp -2 (X- (i-j)d)2

-[a]('1e, [2]

where we have for notational convenience defined

a = exp (-d2/4w2). [3]

Quite apart from the teleology implicit in the assumption thatcommunities minimize anything, a choice of fit other thanleast-squares will lead to equations superficially differentfrom [1]: however, their competition matrix characterizingsmall displacements from equilibrium will end up similar tothat given below. As Lotka (8), and others since, have em-

phasized, Eq. [1] represents the first term in a Taylor ex-

pansion of a much wider class of equations, and thus shouldbe useful in discussing the stability of potential equilibria.

1110

Niche Overlap and Environmental Variability 1111

In the stability analysis of equations such as [1], we firstfind the equilibrium populations, N,*, and then study small-amplitude perturbations by linearizing about this equilib-rium. As a further simplification in our model, we rather arbi-trarily choose the resource spectrum to be such that thecommunity best-fit to it (i.e., the equilibrium community)has equal populations for all species; for a large number ofspecies, n >> 1; this means a flat resource spectrum. The con-ventional analysis then shows the stability of the systemto be given simply by the eigenvalues of the n X n competi-tion matrix A, which from [2 ] has the form

1 a a4 a9 a

a 1 a a4.

A = a4 a 1 a .

a9 a4 a 1

[a'.iian.. . . . 1 ~~_j

b

[4]

In short, in this section we have made several particularassumptions, which have given a specific form for the com-petition matrix, namely [4]. Indeed, this is a form that canbe plausibly justified from quite ad hoc considerations. Ingeneral, the system stability, and hence the permissible degreeof niche overlap, hinges upon some such competition matrix.Other assumptions could give other (but similar) matrices,and the extent to which our conclusions are or are not tiedup with the specific model outlined here is discussed insection III.

II. THE MODEL ANALYZEDDeterministic environment

As just described, all the parameters in our model system areunvarying constants. Consequently the equilibrium con-figuration is stable, with perturbations damping out, so longas all the eigenvalues, X, of A are positive (notice that a minussign was absorbed in the definition of the competition matrix).But A is a positive definite form for all 0 < a < 1 (i.e., for alld, see Eq. [3]), with the consequence that stability sets nolimit to the species packing in a strictly deterministic en-vironment. Moreover, in general the more species packed in,the better the least-squares fit to the resource spectrum.

Nevertheless it is interesting to see how the smallest eigen-value of A, which sets the stability character, varies withniche overlap, as measured by d/w. For n >> 1, we have (seeAppendix)

Xmin = 1 - 2ca + 2a4- 2a9 + 2a6 .... [5]

This series may be summed, by an elegant method, to get anapproximation that is very accurate unless d >> w (see Ap-pendix):

Xmin = 4Tr1/2(w/d) exp [-Tr2W2/d2]. [6]

This is a remarkable result. For substantial niche overlap,i.e,. d/w small, Xmin tends to zero faster than any finite powerof d/w: there is an essential singularity at diw = 0. Thus, al-though Xmin is indeed necessarily positive even for small d/w,it becomes exceedingly tiny, corresponding to extremely longdamping times. This result foreshadows the results below.

Fig. 2 illustrates Eq. [6], along with numerical results forn = 2, 3, 4. Notice that for practical purposes, n = 4 ishard to distinguish from an = co

FIG. 3. The closest niche overlap, diw, consistent with com-munity stability in a randomly varying environment, whosefluctuations are characterized by a variance (relative to the mean)of 2/k. The variance is plotted on a logarithmic scale to em-phasize that, over a wide range, it has little influence on thespecies packing distance for n > 2.

Stochastic environment

More realistically, there will be random environmentalfluctuations, so that the resource continuum will be noisy.This means the quantities ki in Eq. [1 ] will not be constants,but rather will be random variables. We assume

ki = ki + 'y(t) [7]

where k, is the constant mean value (having the common valuek for large n), and ey(t) is gaussian "white noise", with vari-ance measured by 2.In this stochastic problem, we may no longer talk of the

species populations, but only of their joint probability distri-bution. To a good approximation, this is a multivariate normaldistribution in the fluctuations about the means, and theprobability of any species becoming extinct will be small(corresponding to the mechanical "stability" of the determi-nistic case) if the smallest eigenvalue of the competitionmatrix A roughly obeys

Xmin > 0r2/k [8]

This result (9) is commonsensical. In a randomly fluctuatingenvironment, it is not enough that all the eigenvalues bepositive, but rather they should be bounded away from zeroby an amount roughly proportional to the environmentalnoise level.Combining the qualitative equation, [8], with Fig. 2, we

arrive at an estimate of the closest species packing, diw, con-sistent with stability for a given environmental noise level,a2/k. These results, illustrated in Fig. 3, are as discussed inthe Introduction.In particular, we see explicitly from Eq. [6] that for large

n this closest degree of niche overlap depends on the environ-mental fluctuations only as -/lun 2, a very weak dependence.The results for n = 3, 4, although allowing a slightly closerlimiting packing distance, display a similar insensitivity tothe degree of random fluctuation, so long as it is not severe.

Proc. Nat. Acad. Sci. USA 69 (1972)

1112 Zoology: May and Mac Arthur

III. HOW ROBUST ARE THESE RESULTS?

The question arises, to what extent are these results peculiarto our particular model? We catalogue some answers.

(i) We chose gaussian utilization functions. Alternativef(x) ranging from the opposite extremes of rectangles throughto back-to-back exponentials or Lorentz lineshapes lead to Amatrices different from [4], but the plot of Amin as a functionof diw retains the essential features of Fig. 2 in all cases.

(ii) We chose the width and separation -of the utilizationfunctions to be constant. If the width w changes in some

systematic way along the resource continuum, our results are

preserved, as long as the separation d changes in the same

proportion, keeping d/w roughly constant.(iii) The resource spectrum of Fig. 1 was assumed to be

such that, at equilibrium, all populations are equal. Extensiveinvestigation of various resource spectrum shapes for n =

2, 3, and 4 suggests that our results are not dependent on thisfeature, so long as all species are present in significant numbersin the equilibrium community.

(iv) The implications of use of Eq. [1] were discussed insection I.

(v) The stochasticity of the environment was taken to begaussian "white noise," i.e., no correlation between thefluctuations at successive instants. In practice, this means onlythat fluctuations be correlated over times short comparedto all other relevant time scales in the system (9).

(vi) Our model is for competition in one resource dimen-sion. Cody's (10) classification of partitioning in the three-resource dimensions of horizontal habitat, vertical habitat,and food for 10 grassland bird communities around the worldshows eight of them to be organized largely in one dimension(food selection), so that our model is not wholly unreasonable.Moreover, the model is directly relevant to niche overlapin two or more orthogonal resource dimensions, and may even

be useful as a metaphor for more complicated circumstances.

IV. COMPARISON WITH REAL ECOSYSTEMS

In a classic paper, Hutchinson (4) observed that in variouscircumstances, including both vertebrate and invertebrateforms, character displacement among sympatric species leadsto sequences in which each species is roughly twice as massiveas the next; i.e., linear dimensions as measured by bills or

mandibles in the ratio 1*2-1-4. Mac Arthur's more recentand quantitative reviews (3) of such data point to there beinga limiting value to niche overlap in the natural world, corre-

sponding to diw in the range 1-2. Also pertinent is Simpson's(11) review of the factors making for latitudinal and alti-tudinal species diversity gradients among North Americanmammals; it concludes that degree of niche overlap is notan important contributing factor.The work that seems to come closest to our one-dimensional

model is that of Terborgh, Diamond, and Beaver on variousguilds of birds in an assortment of habitats that have variousdegrees of environmental stability. Even so, such compari-sons with the theory are necessarily approximate, partly be-cause our a (Eq. [3]) comes from utilization functions thatare not just percentage of time or of diet, but rather haveweighting terms for resource renewal (3, 7): all available in-formation from nature contains unweighted utilizations.

Terborgh (12) has shown five species of tropical antbird,segregating by foraging height, have mean heights separated

by one standard deviation; i.e., diw 1. Mac Arthur's analy-sis (3) of Storer's data (13) on the food weight distributionfor three congeneric species of hawks also leads to d/w - 1.Diamond's (14) extensive data on weights of tropical birdcongeners that sort out largely (but not wholly, so that d/wshould be smaller than our one-dimensional theory predicts)by size differences leads to weight ratios around 1-6-2-3;when Hespenheide's analysis (15) of the relation betweenweight ratio and a is used, Diamond's results become aO*8-0-9, i.e., d/w 0*6-1 *0. In the Sierra Nevada, Beaver(personal communication) has shown that species packing ina brushland bird community appears equal to that in a forestfoliage gleaning guild, although the microenvironment isthought to be significantly more unvarying in the forest.In brief, the basic conclusion that emerges in a nonobvious

but robust way from our mathematical model, namely thatthere is a limit to niche overlap in the natural world and thatthis limit is not significantly dependent on the degree of en-vironmental fluctuation (unless it be severe, as in the arctic),seems to be in harmony with such facts as are known aboutreal ecosystems.

APPENDIX

For large n, where "end effects" at the extremes of the resourcespectrum are unimportant, we may pretend that the resourcecontinuum is cyclic (so that the species labeled 1 adjoins thatlabeled n), whereupon the competition matrix A of Eq. [4] isslightly modified to become related to a class of matrices discussedby Berlin and Kac (16). Using their approach, one can obtainEq. [5]. That this trick of imposing artificial cyclic boundaryconditions does not alter the eigenvalues for n >> 1 is a point madeclear in the literature on the physicists' Ising model, from whichcomes Berlin and Kac's paper.The series in Eq. [6] is identically equal to the contour integral

1 exp(zIlna)dz2i sin (rz)

Here the contour C encloses all poles of the integrand up toz = in, where the series has n terms. An n P, C is the circleat infinity in the complex plane. Using the standard Jordancontour, and ignoring correction terms of relative order exp(-4rwh21/d2), which are thoroughly negligible for d/w < 3 or so,we arrive neatly at Eq. [6].At the other extreme, for n = 2 the eigenvalues of A are easily

found directly. For other finite values, such as n = 3, 4, we takea meat axe and display Xli. as a numerical function of diw.

This research was sponsored in part by the National ScienceFoundation, Grant GP-16147 A 1.

1. Miller, R. S. (1967) in Advances in Ecological Research(Academic Press, New York), Vol. 4, pp. 1-74 (see pp. 35-46).

2. Miller, R. S. (1967) in Advances in Ecological Research(Academic Press, New York), p. 67.

3. Mac Arthur, R. H. (1971) in Avian Biology (Academic Press,New York), Vol. I, pp. 189-221; (1972) GeographicalEcology (Harper and Row, New York), in press.

4. Hutchinson, G. E. (1959) Amer. Natur. 93, 145-159.5. Klopfer, P. H. (1962) in Behavioral Aspects of Ecology

(Prentice-Hall, Englewood Cliffs), chap. 3; Pianka, E. R.(1966) Amer. Natur. 100, 33-46; Mac Arthur, R. H. (1969)Biol. J. Linn. Soc. 1, 19-30; (1969) Diversity and Stabilityin Ecological Systems; Brookhaven Symposium in BiologyNo. 22 (Nat. Bur. Standards, Springfield, Va.).

6. May, R. M. (1971) Math. Biosci. 12, 59-79.



7. Mac Arthur, R. H. (1969) Proc. Nat. Acad. Sci. USA 64,1369-1371; (1970) Theor. Pop. Biol. 1, 1-11.

8. Lotka, A. J. (1925) Elements of Physical Biology (Williamsand Wilkins, Baltimore), p. 62.

9. May, R. M. (1971) Proc. Ecol. Soc. Aust., in press; Astrom,K. J. (1970) Introduction to Stochastic Control Theory(Academic Press, New York); Sykes, Z. M. (1969) J. Amer.Stat. Ass. 64, 111-130.

10. Cody, M. (1968) Amer. Natur. 102, 107-148.11.- Simpson, G. G. (1964) Syst. Zool. 13, 57-73.

Niche Overlap and Environumental Variability 1113

12. Terborgh, J. (1972), quoted in Mac Arthur, R. H. (1972)Geographical Ecology (Harper and Row, New York), Figure6-4.

13. Storer, R. W. (1966) Auk 83, 423-436.14. Diamond, J. M. (1962) The Avifauna of the Eastern High-

lands of New Guinea (Publ. Nuttall Ornithol. Club, Cam-bridge, Mass.), in press.

15. Hespenheide, H. A. (1971) Ibis 113, 59-72.16. Berlin, T. H. and Kac, M. (1952) Phys. Rev. 86, 821-835.

R E V I E W A N DS Y N T H E S I S The merging of community ecology and phylogenetic

biology

Jeannine Cavender-Bares,1*

Kenneth H. Kozak,2 Paul V. A.

Fine3 and Steven W. Kembel3†

1Department of Ecology,

Evolution and Behavior,

University of Minnesota, St.

Paul, MN 55108, USA2Bell Museum of Natural

History, and Department of

Fisheries, Wildlife, and

Conservation Biology, University

of Minnesota, St. Paul, MN,

55108, USA3Department of Integrative

Biology, University of California,

Berkeley, CA 94720, USA†Present address: Center for

Ecology and Evolutionary

Biology, University of Oregon,

Eugene, OR 97403, USA.

*Correspondence: E-mail:

[email protected]

Abstract

The increasing availability of phylogenetic data, computing power and informatics tools

has facilitated a rapid expansion of studies that apply phylogenetic data and methods to

community ecology. Several key areas are reviewed in which phylogenetic information

helps to resolve long-standing controversies in community ecology, challenges previous

assumptions, and opens new areas of investigation. In particular, studies in phylogenetic

community ecology have helped to reveal the multitude of processes driving community

assembly and have demonstrated the importance of evolution in the assembly process.

Phylogenetic approaches have also increased understanding of the consequences of

community interactions for speciation, adaptation and extinction. Finally, phylogenetic

community structure and composition holds promise for predicting ecosystem processes

and impacts of global change. Major challenges to advancing these areas remain. In

particular, determining the extent to which ecologically relevant traits are phylogeneti-

cally conserved or convergent, and over what temporal scale, is critical to understanding

the causes of community phylogenetic structure and its evolutionary and ecosystem

consequences. Harnessing phylogenetic information to understand and forecast changes

in diversity and dynamics of communities is a critical step in managing and restoring the

Earth�s biota in a time of rapid global change.

Keywords

Community assembly, deterministic vs. neutral processes, ecosystem processes,

experimental approaches, functional traits, phylogenetic community ecology, phylo-

genetic diversity, spatial and phylogenetic scale.

Ecology Letters (2009) 12: 693–715

I N T R O D U C T I O N

Community ecology investigates the nature of organismal

interactions, their origins, and their ecological and evolu-

tionary consequences. Community dynamics form the link

between uniquely evolved species and ecosystem functions

that affect global processes. In the face of habitat

destruction worldwide, understanding how communities

assemble and the forces that influence their dynamics,

diversity and ecosystem function will prove critical to

managing and restoring the Earth�s biota. Consequently, the

study of communities is of paramount importance in the

21st century.

Recently, there has been a rapidly increasing effort to

bring information about the evolutionary history and

genealogical relationships of species to bear on questions

of community assembly and diversity (e.g. Webb et al. 2002;

Ackerly 2004; Cavender-Bares et al. 2004a; Gillespie 2004;

Fine et al. 2006; Strauss et al. 2006; Davies et al. 2007;

Vamosi et al. 2008). Such approaches now allow community

ecologists to link short-term local processes to continental

and global processes that occur over deep evolutionary time

scales (Losos 1996; Ackerly 2003; Ricklefs 2004; Pennington

et al. 2006; Mittelbach et al. 2007; Swenson et al. 2007;

Donoghue 2008; Emerson & Gillespie 2008; Graham &

Fine 2008). This effort has been facilitated by the rapid rise

in phylogenetic information, computing power and compu-

tational tools. Our goal here is to review how phylogenetic

information contributes to community ecology in terms of

the long-standing questions it helps answer, the assumptions

it challenges and the new questions it invites. In particular,

we focus on the insights gained from applying phylogenetic

approaches to explore the ecological and evolutionary

factors that underlie the assembly of communities, and

how the interactions among species within them ultimately

influence evolutionary and ecosystem processes.



There are three perspectives on the dominant factors

that influence community assembly, composition and

diversity. First is the classic perspective that communities

assemble according to niche-related processes, following

fundamental �rules� dictated by local environmental

filters and the principle of competitive exclusion (e.g.

Diamond 1975; Tilman 1982; Bazzaz 1991; Weiher &

Keddy 1999). An alternative perspective is that commu-

nity assembly is largely a neutral process in which species

are ecologically equivalent (e.g. Hubbell 2001). A third

perspective emphasizes the role of historical factors in

dictating how communities assemble (Ricklefs 1987;

Ricklefs & Schluter 1993). In the latter view, the starting

conditions and historical patterns of speciation and

dispersal matter more than local processes. The relative

influence of niche-related, neutral and historical processes

is at the core of current debates on the assembly of

communities and the coexistence of species (Hubbell

2001; Chase & Leibold 2003; Fargione et al. 2004;

Ricklefs 2004; Tilman 2004). This debate falls within

the larger historic controversy about the nature of

communities and the extent to which they represent

associations of tightly interconnected species shaped over

long periods of interaction or are the result of chance co-

occurrences of individually dispersed and distributed

organisms (Clements 1916; Gleason 1926; Davis 1981;

Brooks & McLennan 1991; Callaway 1997; DiMichele

et al. 2004; Ricklefs 2008).

Here we review how the merging of community

ecology and phylogenetic biology advances these debates

and allows new areas of enquiry to be addressed. First,

phylogenetics helps to resolve the long-standing contro-

versy about the relative roles of neutral vs. niche-related

processes in community assembly and facilitates identifi-

cation of the kinds of processes that underlie community

assembly. Second, insights from phylogenetic approaches

present strong challenges to the classical idea that the

species pool (and the traits of species within it) is static

on the time scale over which communities are assembled.

These approaches are also beginning to demonstrate that

community interactions might strongly influence how the

pool itself evolves and changes across space and time.

Finally, phylogenetic diversity and composition is relevant

to predicting ecosystem properties that impact global

processes.

We argue that ongoing efforts to integrate knowledge

of phylogenetic relationships of organisms with their

functional attributes will enhance understanding of the

distribution and function of the Earth�s biota at multiple

scales, increasing our ability to predict outcomes of

species interactions as well as the consequences of these

outcomes for ecosystem and evolutionary processes.

Progress towards this end will require consideration of

both phylogenetic and spatial scale in the interpretation of

ecological and evolutionary patterns (Box 1, Figs 1 and 2)

and cognizance of the multiplicity of processes that

underlie patterns. Observational, experimental and theo-

retical studies aimed at deciphering the mechanisms

involved in community assembly and how they shift with

scale are paving the way for phylogenetic approaches to

large-scale prediction of ecosystem dynamics in response

to global change.

We first discuss the historical origins of the classic

debates in community ecology that phylogenetics helps to

address. We then turn to specific examples in the general

areas highlighted above and review contributions made

possible by integrating community ecology and phyloge-

netic biology. In doing so, we discuss the challenges

involved in further progress. We close with a summary of

the major advances, challenges and prospects for the

emerging field of phylogenetic community ecology. We

include illustrative examples from animals, plants and

other organisms in discussing the contributions of

phylogenetic information to understanding community

assembly and the feedbacks to evolutionary processes.

However, we focus largely on the plant literature in

discussing the ecosystem and global consequences of

community assembly, reflecting the plant orientation of

much of the relevant literature.

H I S T O R I C A L O V E R V I E W

Niche-related processes and assembly rules

Early ecologists, including Darwin, recognized that specific

attributes of species could influence their interactions with

other species and with the environment in predictable ways.

In particular, Darwin noted a paradox inherent in

phenotypic similarity of species with shared ancestry. On

the one hand, if closely related species are ecologically

similar, they should share similar environmental

requirements and may thus be expected to co-occur. On

the other hand, closely related species should experience

strong competitive interactions due to their ecological

similarity, thereby limiting coexistence and thus driving

selection for divergent traits.

The idea that similar phenotypes should share habitat

affinities was championed by the Danish plant ecologist,

Eugenius Warming (1895), who emphasized differences in

the physiological abilities of plants to adjust to some

environments but not others. The core idea was that similar

physiological attributes would be selected for by similar

environments in different regions and that plant pheno-

types should match their environments in predictable ways

(Collins et al. 1986). These ideas were important in the

development of niche theory (e.g. Grinnell 1924; Elton

694 J. Cavender-Bares et al. Review and Synthesis


Box 1 Scale dependency of phylogenetic community structure

Spatial and temporal scale

The processes that influence species diversity shift with spatial scale (e.g. Davies et al. 2005; Silvertown et al. 2006; Diez et al.

2008) and phylogenetic patterns of species assemblages are likely to reflect those shifts. We might expect at the

neighbourhood scale that density-dependent interactions will be strongest giving way to environmental filtering at the

habitat scale, mediated by organismal dispersal, and finally to biogeographical processes (Ricklefs 2004; Wiens & Donoghue

2004) at larger spatial scales (Fig. 1). Similarly, viewed over longer temporal scales, biogeographical processes also dominate

as drivers of species distributions. Empirically, phylogenetic clustering has been shown to increase with spatial scale in plant

communities (Cavender-Bares et al. 2006; Swenson et al. 2006, 2007; reviewed in Vamosi et al. 2008). The proposed

explanation is that as the spatial extent of the analysis increases, greater environmental heterogeneity is encompassed, and

groups of closely related species with shared environmental requirements sort across contrasting environments. At larger

spatial scales, phylogenetic clustering may continue to increase, depending on the vagility of clades, as the signature of

biogeographical processes comes into focus (Box 1, Fig. 2b).

Phylogenetic scale

Several studies have demonstrated that community phylogenetic structure also depends on the taxonomic or phylogenetic

scale in terrestrial plant (Cavender-Bares et al. 2006; Swenson et al. 2006, 2007) and aquatic microbial communities (Newton

et al. 2007). One hypothesis is that competition and other density-dependent interactions are most predictably intense

among close relatives. Hence if competition drives ecological character displacement or competitive exclusion, the

consequences for phylogenetic structure should be observable within clades but become more diffuse in community

assemblies that span diverse taxa. At the same time, as a greater diversity of taxa are included in the analysis, the range of

possible trait values and niches is likely to expand. Whereas traits may be labile within a clade, at larger taxonomic scales, the

ranges of possible trait values for the clade may often be limited relative to a more phylogenetically diverse group of species

(Box 1, Fig. 2). Hence, patterns reflective of processes within narrowly defined communities are likely to be missed in

analyses that include broad taxonomic diversity.

Biogeographic processes: Speciation, extinction

Time

Space

------------- Dispersal ----------------

Environmental filtering

Density dependent interactions

A

Figure 1 The processes that drive the organization of species in a focal area operate over varying temporal scales and depend fundamentally

on the spatial scale of analysis. At the broadest spatial scale, species distributions are determined largely by biogeographical processes that

involve speciation, extinction and dispersal. These processes occur over long temporal scales. Dispersal varies with the mobility of the

organism and can alter patterns of species distributions established through ecological sorting processes (Vamosi et al. 2008). At decreasing

spatial scales, the environment filters out species lacking the physiological tolerances that permit persistence, given the climate or local

environmental conditions. The environment can include both abiotic factors (temperature, soil moisture, light availability, pH) or biotic

factors (symbionts, pollinators, hosts, prey). Density-dependent processes are likely to operate most intensively at neighbourhood scales.

These processes may include competition, disease, herbivory, interspecific gene flow, facilitation, mutualism, and may interact with the

abiotic environment to reinforce or diminish habitat filtering. At a given spatial scale (e.g., A), species distributions depend on multiple

factors, which may be difficult to tease apart. Methods that can partition the variance among causal factors driving community assembly

facilitate understanding of mechanism. This figure was adapted from figures in Weiher & Keddy (1999) and Swenson et al. (2007).

Review and Synthesis Phylogenetic community ecology 695


Box 1 continued

Ph

ylo

gen

etic

clu

ster

ing

of

spec

ies

Spatial scale

More inclusive(large clades)

Phylogenetic scale

(a) (b)

(c)

Ph

ylo

gen

etic

co

nse

rvat

ism

in t

rait

s

Less inclusive(small clades)

Trait A

Trait B

Figure 2 Hypothesized variation in phylogenetic clustering and trait conservatism with phylogenetic scale (a) Phylogenetic conservatism of traits and

phylogenetic clustering of species in communities varies as more of the tree of life is encompassed in an analysis. Ecologically relevant

traits may be labile towards the tips of the phylogeny (less inclusive phylogenetic scale) because close relatives often have divergent or

labile traits as a result of character displacement and ⁄ or adaptive radiation or due to drift and ⁄ or divergent selection following allopatric

speciation. At increasing phylogenetic scales (as more of the tree of life is encompassed), we expect traits (dashed line) to show increasing

conservatism because traits within clades are less variable than traits among clades. However, conservatism of traits deeper in the

phylogeny may diminish due to homoplasy, particularly if lineages in different geographical regions have converged towards similar trait

values as a result of similar selective regimes, for example. (b) Phylogenetic clustering (solid line), or the spatial aggregation of related

species, also tends to increase with phylogenetic scale (data not shown) and with spatial extent. Competition and other density-dependent

mechanisms are predicted to be strongest at small spatial scales and may prevent close relatives from co-occurring. Once the spatial scale

at which species interactions are strongest is surpassed, the similar habitat affinities of more recently diverged species will cause spatial

clustering. Phylogenetic clustering continues to increase with increasing phylogenetic scale due to biogeographical history (i.e. most species

from a clade tend to be concentrated in the region in which the clade originated). The strength of this trend should depend on dispersal

ability. Highly mobile species (dotted line) are less likely to show a signature of their biogeographical history, whereas clades that contain

species with more limited vagility (solid line) are likely to be clustered spatially at the largest spatial extent. (c) Organisms often show trait

trade-offs or correlations as a result of selection for specialization or due to biochemical, architectural or other constraints (e.g. Reich et al.

2003; Wright et al. 2004) that can be represented in two dimensional �trait space�. Often, trait variation represented by members of an

individual clade may be limited due to common ancestry, as shown here. Thus, while traits can be labile within clades (shown by random

arrangement in trait space of tips descended from a common ancestor), the range of variation represented by an individual clade is likely to

be limited (indicated by the dotted circle) at some phylogenetic scale relative to the global trait space occupied by organisms drawn from



1927; Hutchinson 1959) in which similarities and differences

among species in their resource and habitat requirements as

well as their impacts on the environment were understood

to be important in determining the outcomes of species

interactions (reviewed in Chase & Leibold 2003).

While early naturalists seamlessly integrated ecological

and evolutionary thinking, theoretical developments starting

in the 1920s (reviewed in Ricklefs 1987; Schluter & Ricklefs

1993), and critical experiments by Gause led to the adoption

of the �competitive exclusion principle� and the notion of

limiting similarity (Hutchinson 1959; MacArthur & Levins

1967) which posited that species that are too similar

ecologically could not coexist. This became one of the

central paradigms of community ecology and led to a

growing separation between ecology and evolutionary

biology, reinforcing the convenient assumption that evolu-

tionary processes were not relevant at the time scales of

ecological processes. The competitive exclusion paradigm

precipitated the view within ecology that new species could

not join a community without the compensating disappear-

ance of others, and that there are �assembly rules� guiding

the assembly of communities (Diamond 1975; Weiher &

Keddy 1999). The importance of evolutionary process in

ecology was still recognized by ecologists, however; empir-

ical studies and theoretical models indicated the presence of

evolved trade-offs that prevent all species from occurring in

all environments, thus permitting coexistence (Tilman 1982;

Bazzaz 1996; Chesson 2000; Reich et al. 2003). Darwin�sparadox led to the conclusion that shared ancestry should

result in non-random ecological associations of taxa with

respect to relatedness, resulting in contrasting patterns of

species coexistence depending on the relative importance of

competition or physiological tolerances in driving species

distributions (Elton 1946; Williams 1947; Simberloff 1970;

Webb et al. 2002). More recently, patterns of phylogenetic

relatedness of species within and across communities, or

�phylogenetic community structure�, have been used to

explore the processes underlying them and the scale at

which they operate (Webb et al. 2002; Cavender-Bares et al.

2006; Swenson et al. 2006; Emerson & Gillespie 2008;

Vamosi et al. 2008).

Neutral processes

The roles of dispersal, disturbance and stochastic processes

in community assembly, which played a central role in the

theory of island biogeography (MacArthur & Wilson 1967),

were clearly recognized by early ecologists (e.g. Braun 1928)

and paleobiologists (Davis 1981). These processes were

given new prominence by Hubbell (2001) in his Unified

Neutral Theory of biodiversity. Hubbell challenged the

perspective that deterministic niche processes influence

community assembly asserting that ecological communities

are open, continuously changing, non-equilibrial assem-

blages of species whose presence, absence and relative

abundance are governed by random speciation and extinc-

tion, dispersal limitation and ecological drift. According to

this view, species differences do not predict outcomes of

competition, species do not specialize for specific habitats,

and interactions between species and with the environment

are not relevant to community assembly. Tests of phylo-

genetic community structure have attempted to quantify

the relative importance of species-neutral forces vs. those

driven by species differences (Kembel & Hubbell 2006;

Kelly et al. 2008; Jabot & Chave 2009), and this an area of

increasing interest for the application of phylogenetic tools

(Box 2).

Historical processes

Ricklefs (1987) brought to the ecological debate a focus on

the importance of historical processes in influencing local

diversity, inviting incorporation of �historical, systematic

and biogeographical information into the phenomenology

of community ecology�. He reminded ecologists that the

equilibrium theory of island biogeography (MacArthur &

Wilson 1967) was based on a balance of regional processes

(those that increase colonization) and local processes

(those that cause local extinction). He argued that limiting

similarity was in most cases a weaker force than regional

processes in community assembly, and specifically, that

local diversity, rather than being determined solely by local

environmental factors and limiting similarity, was consis-

tently dependent on regional species diversity. According

to this view, which gained support from empirical studies

(e.g. Cornell & Washburn 1979; Sax et al. 2002), commu-

nities were rarely saturated because local species respond

to larger species pools by reducing their niche breadths

through increased specialization. The historical perspective

thus re-opened the door to bring an evolutionary

perspective into community ecology, and emphasized the

shifting nature of the species pool and the ecological and

Box 1 continued

across the tree of life (small grey circles). This highlights the possibility that the range of clade-wide values for a given trait can be reasonably

predicted from a small number of individuals within the clade. At broad phylogenetic scales, convergence of traits between distantly related

clades (shown by close proximity in trait space of tips from two unrelated clades within the dashed circle) may occur due to similar selective

pressures on different continents or islands, for example. This explains the decrease in trait conservatism (dashed line) in (a).



Box 2 Quantifying phylogenetic community structure

In addition to the difficulties in ascribing phylogenetic signal in communities to any one process or cause in the absence of

detailed information on the interactions and traits of species, a further barrier to the synthesis of existing studies of

community phylogenetic structure has been the wide variety of methods employed. While many studies have used the same

terminology of phylogenetic overdispersion and clustering to describe patterns of relatedness relative to some null model, it

is important to note that the underlying methods used to measure phylogenetic community structure have varied a great

deal. Vamosi et al. (2008) provide a recent review of some of the most commonly used phylogenetic diversity metrics and

software.

Most measures of community phylogenetic structure can be divided into two broad categories: those that measure the

relatedness of species occurring together in a community or sample, and those that measure the concordance of

phylogenetic and ecological dissimilarities among species. To date there has been little quantitative evaluation of the relative

strengths and weaknesses of these different approaches (but see Hardy 2008).

Measures of phylogenetic relatedness within communities are in many ways similar to earlier measures of taxonomic

similarity within communities (Elton 1946). Faith (1992) proposed perhaps the first quantitative measure of phylogenetic

diversity (PD) based on the evolutionary branch length spanned by a given set of species, and this metric has been widely

applied in ecology and conservation biology (Redding et al. 2008). The net relatedness index and nearest taxon index (Webb

2000) measure average branch lengths separating taxa within communities, allowing comparison with the patterns expected

under some null model of community assembly. Other measures based on tree balance (Heard & Cox 2007; Redding et al.

2008) use the shape of phylogenetic trees rather than relatedness per se to understand phylogenetic diversity. Several

measures of phylogenetic diversity within communities can take species abundances and evenness into account (Chave et al.

2007; Helmus 2007a), and methods to partition variation in phylogenetic diversity into components attributable to spatial

and environmental variation (Helmus 2007b) or to measure relationships between trait and phylogenetic diversity (Prinzing

et al. 2008) are increasingly common. Phylogenetic beta diversity measures (Graham & Fine 2008) such as UniFrac

(Lozupone & Knight 2008), PD dissimilarity (Ferrier et al. 2007) and the phylogenetic Sørenson index (Bryant et al. 2008)

measure the total branch lengths separating taxa within individual communities relative to the shared or total tree length for

taxa in multiple communities. Other measures of phylogenetic beta diversity such as the phylogenetic depth of species

turnover between communities could provide a means of quantifying the phylogenetic nature of changes in community

structure in space and time.

Measures of the concordance between phylogenetic and ecological dissimilarities of species are also widely used. These

methods compare pairwise phylogenetic distances (or phylogenetic covariances) among species to some measure of the

ecological similarity of those species. Concordance among these dissimilarities has been measured in several ways including

Mantel tests (Cavender-Bares et al. 2004a; Kozak et al. 2005) and logistic regression approaches (Helmus 2007b) based on

linear correlations (Cavender-Bares et al. 2004a; Kozak et al. 2005) or quantile regression (Slingsby & Verboom 2006).

To determine whether communities are phylogenetically clustered or overdispersed, observed results from all of

these approaches are compared to the patterns expected under some null model of phylogenetic relatedness or

community assembly. Many of these null models are based on a conceptual model of randomization of species labels

across the tips of the phylogeny, or of community assembly from some larger pool of species that might potentially

colonize each local community (Gotelli & Graves 1996). The choice of species pool and null model can strongly

influence the outcome of the results, highlighting the importance of choosing methods and defining the species pool in

a way that is appropriate to the hypothesis being tested (Kembel & Hubbell 2006; Hardy 2008). Kraft et al. (2007) used

simulation studies to demonstrate that the size of local communities and the regional species pool from which

communities are assembled both influence the ability of different methods to detect a phylogenetic signal in

community structure. The effects of regional pool size on phylogenetic community structure varied depending on the

assembly process that was operating. Swenson et al. (2006) compared the phylogenetic structure of local assemblages to

species pools drawn from increasingly larger geographical scales and found an increasing signal of local phylogenetic

clustering, which they attributed to environmental filtering.

Our understanding of the relative strengths and weakness of these different methods is poorly developed. Quantitative

comparisons of these different measures and null models when applied to studies of community phylogenetic structure are

only beginning to be conducted, with mixed results. Recent studies have found that different null models differ in their Type

I error rates (Kembel & Hubbell 2006; Hardy 2008) and that measures of similarity within communities differ in their ability

to detect different community assembly processes (Kraft et al. 2007). More generally, there is a need for model-based



evolutionary forces at play at different temporal and spatial

scales (Box 1, Fig. 2).

The nature of communities

Relevant to the importance of historical processes in

community assembly are the roles of speciation and

adaptation in community assembly. This issue is connected

to one of the earliest debates in community ecology, which

focused on the nature of communities. Frederick Clements

(1916) viewed a community as a group of interdependent

and inextricably linked species, or as a �superorganism�, in

contrast to Henry Gleason (1926), who defined communi-

ties as chance assemblages of individually distributed

species. Clements� Lamarkian views not with standing,

these perspectives can be viewed as opposite ends of the

spectrum of the kinds of real communities that exist in

nature. Consider at one extreme, assemblages of species that

evolved together over long time periods and developed

tightly woven interdependencies, and at the other extreme,

assemblages of recently colonizing species drawn from

disparate sources following major disturbances (such as

temperate regions that were heavily impacted by glacial

cycles). While the individualistic perspective has largely been

adopted by ecologists (but see Callaway 1997), evolutionary

studies have continued to demonstrate the importance of

evolutionary dynamics between interacting species (Ehrlich

& Raven 1964; Thompson 2005; Bascompte & Jordano

2007; Jablonski 2008; Ricklefs 2008; Roderick & Percy

2008).

An integrated perspective on the nature of communities

emerged with the introduction of historical ecology (Brooks

& McLennan 1991). Brooks and McLennan argued that

community development involves both evolutionary pro-

cesses, including speciation and adaptation, as well as

dispersal and colonization, resulting in both recent and

historical elements in most communities. They emphasized

a conservative homeostatic element that is composed of

species that evolved in situ through the persistence of

ancestral associations, a perspective supported by fossil

evidence (DiMichele et al. 2004). Reminiscent of the

Clementsian view, they argued that this portion of any

community is �characterized by a stable relationship across

evolutionary time� and may thus �act as a stabilizing selective

force on other members of the community by resisting the

colonization of competing species�. They also saw a strong

role for adaptive processes in which either old residents or

new arrivals adapt to changing interactions or novel

conditions. This contrasted other contemporary views that

communities assemble by �ecological fitting� in which new

members that evolved elsewhere fit themselves into existing

communities without adaptive shifts, like �asymmetrical pegs

in square holes� (Janzen 1985). An important advance

represented by phylogenetic community ecology is to

incorporate data and methods to examine the role of

evolution in community assembly, and in turn, to examine

the influence of community interactions on processes of

speciation and adaptation (Fig. 3).

These historical debates in community ecology encom-

pass fundamental questions about the relative importance

of deterministic, neutral and historical processes in

community assembly, as well as the relative roles of

speciation, adaptation, extinction and dispersal. Several

recent advances have enabled ecologists to re-examine

these debates from a phylogenetic perspective, including

(1) the availability of comprehensive phylogenetic infor-

mation for many lineages, (2) the availability of abundance

and geographical occurrence data and associated environ-

mental data, (3) computing power for null model analysis

and (4) the rapid rise of new statistical and informatics

tools for statistical testing. In the next sections, we review

how phylogenetics has been applied to discern the

processes driving community assembly (e.g. Webb et al.

2002), to examine the role of in situ evolution relative to

simulations and tests of the ability of these methods to detect the signature of different ecological and evolutionary

processes that may give rise to phylogenetic signal in community structure, and recent studies have begun to address this

need (Jabot & Chave 2009). Quantitative comparisons of metrics of co-occurrence (Gotelli 2000) and trait similarity within

communities (Collwell & Winkler 1984) were instrumental in providing a sounder theoretical framework to support research

in these areas, and will be required as studies of community phylogenetic structure continue to increase in popularity.

We note that a variety of underlying processes might cause closely related species to be more ecologically similar than

distantly related species. For example, both random (e.g. drift through ecological space, also know as Brownian motion) and

deterministic evolutionary processes (e.g. stabilizing selection) can result in a positive relationship between phylogenetic

divergence and ecological divergence (Blomberg et al. 2001; Losos 2008; Revell et al. 2008; Wiens 2008). Nevertheless, so

long as close relatives exhibit greater ecological similarity than distant relatives, phylogeny can have important consequences

for community assembly. Therefore, we imply no specific causal process when using the term �trait conservatism�throughout this review, although we acknowledge that developing metrics to quantify the degree of trait conservatism and

rate of trait change relative to various models of evolution is an important area for future research.

Box 2 continued



dispersal in community assembly (e.g. Losos 1996;

Gillespie 2005) and to investigate the macroevolutionary

responses of organisms to interspecific interactions (e.g.

Jablonski 2008; Phillmore & Price 2008; Roderick & Percy

2008). We then turn to the ecosystem consequences of

community phylogenetic structure and the potential for

phylogenetics to facilitate a more predictive framework for

understanding the links between traits, species composition

and ecosystem or even global processes (Chave et al. 2006;

Edwards et al. 2007; Cadotte et al. 2008).

P H Y L O G E N E T I C C O M M U N I T Y S T R U C T U R E ,

N E U T R A L P R O C E S S E S A N D A S S E M B L Y R U L E S

Weiher & Keddy (1999) clarify that an important goal of

community ecology is to determine the rules that govern the

assembly process in order to predict the composition of

ecological communities from species pools. One contribu-

tion of phylogenetic community ecology relates to whether

communities are largely shaped by niche-based assembly

rules or by neutral processes (Webb et al. 2002). A central

distinction between the two perspectives is that the neutral

theory assumes that species differences do not matter, while

the niche assembly theory assumes that they do. Under the

niche assembly theory, the phylogenetic distance between

species can serve as a proxy for the evolved ecological

differences between them, assuming close relatives are

ecologically more similar to each other than more distantly

related species. This relatively simple measure can then be

diagnostic, if the assumption holds.

There is a burgeoning literature that takes advantage of

phylogenetic distances between species (or phylogenetic

community structure) to test whether differences among

species are important in community assembly. Phylogenetic

community structure is the pattern of phylogenetic related-

ness of species distributions within and among communi-

ties. It is subjected to statistical tests by examining the extent

to which species are more closely related (phylogenetically

clustered) or less closely related (phylogenetically overdi-

spersed or �even�) than expected in relation to null models in

which species distributions are randomized (see Box 2 on

Quantifying phylogenetic community structure). Patterns of phylo-

genetic community structure (including diversity and dis-

persion patterns) are not meaningful in their own right, but

they serve as a means to infer processes and shifts in

processes with scale, in concert with other evidence, and to

eliminate competing hypotheses. They also have conse-

quences for ecosystem function (Cadotte et al. 2008) and

conservation (Faith 1992), which we discuss in the last

section.

Webb et al. (2002) laid out a heuristic framework

for using community phylogenetic structure to uncover

deterministic processes, or assembly rules, in community

assembly. This framework made the simplifying assumption

that ecological sorting processes due to trait-environment

matching (environmental filtering) and interspecific com-

petition are the two dominant forces structuring commu-

nities and that they cause non-random species assemblages

with respect to phylogenetic relatedness. Specifically, Webb

et al. (2002) suggested that when close relatives occur

together more than expected (phylogenetic clustering), the

underlying cause was environmental filtering on shared

physiological tolerances (trait conservatism). In contrast,

when species in communities are less related than expected

(phylogenetic overdispersion), Webb et al. (2002) suggested

that this could result either from competition causing

overdispersion of conserved traits or environmental filtering

on ecologically important convergent traits. This simple

framework is consistent with the niche-assembly perspective

of community ecology, which posits that ecological com-

munities are limited membership assemblages of species that

coexist due to partitioning of limiting resources (Chase &

Leibold 2003).

This framework has stimulated much research demon-

strating significant non-random phylogenetic structure in

communities at multiple spatial and taxonomic scales

across diverse taxa (e.g. Losos et al. 2003; Cavender-Bares

et al. 2004a; Kozak et al. 2005; Horner-Devine & Bohan-

nan 2006; Kembel & Hubbell 2006; Lovette &

Hochachka 2006; Slingsby & Verboom 2006; Swenson

Figure 3 Traits arise as innovations along the tree of life, often

reflecting their biogeographical origins, and tend to be shared by

species that have common ancestry (phylogenetic history). Traits,

in turn, play a central role in ecological processes that influence the

distribution of organisms and the organization of communities.

For plants, in particular, physiological traits and the organization of

species with different traits in communities influence processes and

emergent properties of ecosystems. Hence, plant functional traits

are an important mechanistic link by which phylogenetic history

influences ecological processes. Interactions within communities

also influence traits and evolutionary processes, causing a feedback

loop between ecological and evolutionary processes.



et al. 2006; Davies et al. 2007; Hardy & Senterre 2007;

Helmus 2007b; Verdu & Pausas 2007), including recent

reviews focused on insular communities (Emerson &

Gillespie 2008) and emerging patterns across spatial scales

(Vamosi et al. 2008). In particular, community phylo-

genetic structure has been used as a means to quantify

the relative importance of species-neutral processes vs.

deterministic processes (e.g. Kembel & Hubbell 2006;

Hardy & Senterre 2007; Kelly et al. 2008). Using the lack

of phylogenetic community structure to provide support

for neutral processes, however, has proved challenging

because of the difficulty in ruling out contrasting niche-

based processes that operate at different spatial, temporal

or phylogenetic scales (Box 1). Uncertainty of appropriate

null models for such tests and how to circumscribe the

species pool are further challenges (Box 2). A related but

alternative approach has been proposed using phyloge-

netic beta diversity – a measure of the geographical

turnover in phylogenetic diversity – in relation to

geographical distance and environmental gradients to

tease apart neutral processes, such as dispersal limitation,

from niche-based processes, such as environmental

filtering (Graham & Fine 2008). This provides the

possibility of identifying the scale and conditions under

which neutral vs. niche-based processes predominate.

Environmental filtering

Studies of phylogenetic community structure have been

successful in providing evidence for and revealing the

mechanisms underlying deterministic processes. At local

spatial scales, the co-occurrence of closely related species

(phylogenetic clustering) is often interpreted as evidence for

environmental filtering (or habitat filtering) on phylogenet-

ically conserved traits (Webb 2000; Cavender-Bares et al.

2006; Kembel & Hubbell 2006; Lovette & Hochachka 2006;

Swenson et al. 2007). Shared physiological tolerances and

habitat affinities within lineages are widespread, such as the

hygrophilic habit of willows (Salix) and the xerophylic habit

of cacti (Cactaceae). Hence, ecological similarity of closely

related species, in the absence of strong biotic interactions,

should cause closely related species to occupy similar

environments, and hence to cluster spatially (Wiens &

Graham 2005). However, ecological similarity of closely

related species cannot be assumed without specifically

testing for it (Losos 2008) because ecological niches and

their underlying traits can be labile (Losos et al. 2003;

Cavender-Bares et al. 2004a; Pearman et al. 2008).

Examining the conservatism in ecologically relevant

functional traits in relation to the spatial distribution of

traits or their distributions across environmental gradients

can help decipher the processes that cause phylogenetic

structure in communities (Cavender-Bares & Wilczek 2003).

For example, in Mediterranean woody plant communities,

frequent fire disturbance drives the phylogenetic clustering

of species in communities because fire protection of seeds is

highly conserved (Verdu & Pausas 2007). At the same time,

environmental filtering can also cause phylogenetic overdi-

spersion if traits important for habitat specialization are

labile and close relatives specialize for different niches

(Losos et al. 2003; Cavender-Bares et al. 2004a; Fine et al.

2005; Ackerly et al. 2006). Gradients in water availability and

fire frequency thus drive phylogenetic overdispersion in

Florida oak communities because traits related to fire and

drought resistance are convergent (Cavender-Bares et al.

2004a,b). Ecological divergence of close relatives, or

character displacement, may be the expected outcome of

natural selection (Schluter 2000).

Competitive interactions

Darwin�s hypothesis that similarity in resource use due to

shared ancestry would cause closely related species to

compete more strongly than distantly related species

inspired an examination of the frequency of co-occurring

congeneric species (Elton 1946; Williams 1947), species-to-

genus ratios (e.g. Simberloff 1970), and more recently, of

phylogenetic diversity, (Webb 2000; Webb et al. 2002) in

natural communities. Several studies have implicated com-

petition as the likely causal mechanism for phylogenetic

overdispersion in communities, including the fynbos shrub

communities in South Africa (Slingsby & Verboom 2006),

sunfish communities in Wisconsin (Helmus 2007b), mam-

malian carnivores (Davies et al. 2007), monkey, squirrel and

possum assemblages (Cooper et al. 2008), eastern North

American salamanders (Kozak et al. 2005), warblers (Lovette

& Hochachka 2006) and bacteria (Horner-Devine &

Bohannan 2006) (Table 1). However, we note that compet-

itive interactions and character displacement might also

cause trait divergence between close relatives (Schluter 2000;

Grant & Grant 2006) that permits their coexistence,

resulting in phylogenetic clustering of species within a

community (e.g. a benthic stickleback is more closely related

to a limnetic stickleback from the same lake, than it is to

benthic stickleback from a different lake).

Direct evidence for an increase in competitive interac-

tions with phylogenetic relatedness comes from experiments

with plants in controlled environments (Cahill et al. 2008).

In a meta-analysis of plant competition experiments, Cahill

et al. (2008) compared the relative competitive ability of 50

vascular plant species competing against 92 competitor

species measured in five multi-species experiments. Within

the eudicots, competition was more intense among closer

relatives. Within the monocots, however, relatedness was

not predictive of interaction strength.



Table 1 Causes and consequences of phylogenetic community structure

A. Processes inferred to cause phylogenetic community structure

Ecological mechanisms Dispersion Representative studies

Density dependent mechanisms:

Competition ⁄ limiting similarity + Slingsby & Vrboom 2005, Kozak et al. 2005,

Horner-Devine & Bohannen 2006, Davies et al. 2007,

Helmus et al. 2007, Cahill et al. 2008

Herbivore ⁄ Pathogen specificity + Webb et al. 2006, Gilbert & Webb 2007

Herbivore facilitated ecological sorting + ) Fine et al. 2004, 2006, Fig. 4

Facilitation of nurse plants + Valiente-Banuet & Verdu 2007

Pollinator-plant interactions + ) Sargent & Ackerly 2008

Temporal niche dynamics + ) Cavender-Bares et al. 2004a, Kelly et al. 2008;

Environmental filtering + ) Webb 2000, Ackerly et al. 2004, Cavender-Bares et al. 2004a,b,

Cavender-Bares et al. 2006, Verdu & Pausas 2007,

Kraft et al. 2007

Facilitation by mutualists ) Sargent & Ackerly 2008

Plant-pollinator interactions + ) Sargent & Ackerly 2008

Neutral processes x Hubbel 2001, Kembel & Hubbel 2006

Combinations of processes x Lovette & Hochachka 2006, Cavender-Bares et al. 2006

Dispersal ? ? x Vamosi et al. 2008

Evolutionary ⁄ genetic mechanisms

Biogeographic history Ricklefs 2004, Wiens & Donoghue 2004, Vamosi et al. 2008

Allopatric speciation (depends on scale) + Johnson & Stinchcombe 2007

Sympatric speciation ) Johnson & Stinchcombe 2007

Character displacement ) Schluter 2000, Grant & Grant 2006

Convergent evolution + Cavender-Bares et al. 2004a, Kraft et al. 2007

Mimicry ) Brower 1996

Gene flow and local hybridization + Dobzhansky 1937, Mayr 1942, Losos 1990, Levin 2006,

Grant & Grant 2008, Fig. 5

B. Consequences of phylogenetic community structure and composition

Feedbacks to evolutionary processes Representative studies

Density dependent diversification rates Gillespie 2004, Ruber & Zardoy 2005, Kozak et al. 2006,

Phillmore & Price 2008, Rabosky & Lovette 2008,

Williams & Duda 2008

Evolution of increased host specialization Roderick & Percy 2008

Co-evolutionary arms races Ehrlich & Raven 1964, Farell 1998, Thompson 2005,

Hoberg & Brooks 2008

Ecosystem properties and processes

Productivity Maherali & Klironomos 2007, Partel et al. 2007,

Cadotte et al. 2008

Capacity to respond to environmental change Knapp et al. 2008

Invasion resistance Strauss et al. 2006, Diez et al. 2008

Decomposition, nutrient cycling Kerkhoff et al. 2006, Swenson et al. 2007, Weedon et al. 2009

Temperature sensitivity ⁄ Response to global change Edwards et al. 2007, Edwards & Still 2008, Willis et al. 2008

Conservation value Faith 1992, Gerhold et al. 2008

Phylogenetic community structure has been used to infer ecological and evolutionary processes that influence community assembly, in

concert with other evidence, and to predict consequences for ecosystems and evolutionary processes. (A) Processes that have been shown or

hypothesized to influence community phylogenetic structure including both ecological and evolutionary mechanisms (a plus (+) indicates that

the process increases a tendency towards phylogenetic overdispersion ⁄ evenness; a minus ()) indicates that it decreases phylogenetic

dispersion towards clustering; an x indicates that the process(es) is (are) predicted to generate random patterns; and a ? indicates that the

directionality cannot be predicted. (B) Hypothesized and empirically determined consequences of phylogenetic community structure, in terms

of diversity and composition. For brevity, only representative studies are listed; patterns of phylogenetic comunity structure are reviewed

elsewhere (Vamosi et al. 2008, Emerson & Gillespie 2008). Studies that propose hypotheses versus those that test them empirically are not

distinguished.



Determining the generality of increased competitiveness

among close relatives has important consequences for using

niche-based assembly rules to understand and predict the

outcomes of community interactions. For example, the

hypothesis that the strength of species interference increases

with phylogenetic similarity has been used to predict the

invasiveness of exotics in California grasslands. Strauss et al.

(2006) showed that highly invasive grass species are, on

average, significantly less related to native grasses than are

introduced but noninvasive grasses. They reasoned that

matches between characteristics of the exotic and those of

members of the existing native community limited invasion

success. In a related study of plant communities in the

Auckland region of New Zealand, Diez et al. (2008) found

that the relationship between exotic invasion and presence

of congeneric natives depended on the spatial scale. Within

habitats, there was correlative evidence that native species

limited invasion of closely related exotics. At larger spatial

scales, a positive association between congeneric and native

abundances suggested that congeneric native and exotic

species respond similarly to broad-scale environmental

variation.

The extent to which phylogenetic relatedness can

predict invasion success across a range of systems

remains to be explored. An experimental approach that

introduces species into model communities with a range

of phylogenetic distances from resident species would test

whether phylogenetically similar species are less likely to

become established. Ideally, such experiments would be

established at nested spatial scales given the dependency

of invasion processes on scale (Davies et al. 2005; Diez

et al. 2008) and in contexts that do not introduce exotic

species to a region. Positive results at the neighbourhood

scale would provide strong support for a scale-dependent

link between species interference and species relatedness

(Strauss et al. 2006). Experiments with well-characterized

micro-organisms (e.g. Dictyostelid cellular slime moulds;

Schaap et al. 2006) are likely to be informative. The

(a) (b)

(c) (d)

Figure 4 If most herbivores are generalists, and only a subset of the plant species pool can defend or tolerate the dominant enemies, then

plant species composition will shift to become dominated by those species that share these defence and tolerance traits. In this figure, green

squares, red stars and orange circles represent different defence traits that confer tolerance of herbivory in plants within a community, and

thin lines indicate a species has been eliminated from a community by the herbivore. If defence traits are conserved (a), heavy herbivore

pressure will drive phylogenetic clustering within the community. For example, large mammalian herbivores consume a wide variety of plants,

yet grasses are able to tolerate high herbivory pressure and in the presence of these large herbivores, quickly dominate communities. If

herbivores are excluded, plant composition changes, and trees or forbs can take over (McNaughton 1985, Pringle et al. 2007). However, if

such traits that confer tolerance or defence are convergent, generalist enemies will drive the phylogenetic community structure towards

overdispersion (b). If specialists exert a large proportion effect on plant fitness within a community, this will result in strong patterns of

density dependence (Janzen 1970, Connell 1971). This should increase local diversity by favouring rare species which can escape their natural

enemies more often than more abundant species. Furthermore, if related plants have qualitatively similar defence strategies (trait

conservatism) (c), strong Janzen–Connell regulation in a community could limit the co-occurrence of closely related species and promote the

co-occurrence of distantly related species at neighbourhood scales, causing community phylogenetic overdispersion (Webb et al. 2006). In this

figure, �specialist enemies� can eat only plants from the pool that have similar defence traits, similar to Becerra (1997). (d) If plants� defence

traits are convergent, however, Janzen–Connell regulation by specialist enemies will promote random patterns in plant community

phylogenetic structure.



breadth of species distributions across environmental

gradients may also be important to consider in interpret-

ing relationships between phylogenetic relatedness and

invasion success, given the theoretical and counterintuitive

relationship between species coexistence and niche

breadth (Scheffer & van Nes 2006).

While competition is one possible mechanism for

phylogenetic overdispersion, again, it cannot be assumed.

In addition to environmental filtering on convergent traits,

other density-dependent interactions such as host–pathogen

interactions or plant–insect interactions (Fig. 4) (Webb et al.

2006), and facilitation during succession (Valiente-Banuet &

Verdu 2007; see below), have also been shown or

hypothesized to cause phylogenetic overdispersion. We also

suggest that a lack of reproductive isolation between closely

related and ecologically similar species could prevent their

long-term coexistence and cause phylogenetic overdisper-

sion (Fig. 5) through mechanisms difficult to distinguish

from competitive exclusion (Losos 1990; Levin 2006) (see

Section Gene flow and lack of reproductive isolation). The

multiplicity of processes that can cause the same pattern

(Table 1) highlights the importance of understanding the

functional biology of species and the nature of their

interactions.

M O V I N G B E Y O N D T H E E N V I R O N M E N T A L

F I L T E R I N G – C O M P E T I T I V E E X C L U S I O N

P A R A D I G M

Janzen–Connell mechanisms, natural enemies and trophicinteractions

In observational studies of the spatial association of species

(e.g. Uriarte et al. 2004) competitive effects between close

relatives may be difficult to distinguish from other density-

dependent effects without experimental tests. Closely

related species are likely to share pests and pathogens

(Gilbert & Webb 2007). Adult harbouring of pathogens

and pests may reduce recruitment and competitive ability

of species in proximity to close relatives, promoting phylo-

genetic overdispersion (Webb et al. 2006). Here we focus

on plant–herbivore and plant–pathogen communities to

illustrate how trophic interactions may influence phylo-

genetic community structure. There are three variables that

together interact to determine the directionality of trophic

interactions on phylogenetic community structure and

whether this will lead to overdispersion, clustering or

random patterns (Fig. 4). These are: (1) the strength of

the interactions, (2) the degree of specialization of the

interactions and (3) the amount of trait conservatism or

(a) (b) (c)

Figure 5 In clades where the degree of reproductive isolation between species is associated with their time since divergence, interspecific

gene flow may have consequences for community assembly and resulting patterns of phylogenetic community structure. Shown here is an

example in which closely related lineages that are ecologically similar merge into a single gene pool where they come into contact locally. As

only lineages that are reproductively isolated can coexist without merging, local communities tend to be comprised of taxa that are more

distantly related (and ecologically divergent) than expected by chance. An expected outcome of this process is the assembly of communities

that exhibit phylogenetic overdispersion. (a) Phylogenetic relationships of species in the regional pool. These species maintain their genetic

integrity in other portions of their geographical ranges where they do not come into contact. (b) Closely related and ecologically similar

lineages that lack reproductive isolating mechanisms merge into a single gene pool where they come into contact, thereby preventing their

long-term coexistence in local communities. (c) Close relatives thus occur less than expected in communities relative to the regional species

pool (phylogenetic overdispersion). These influences are likely to be important only in communities dominated by a single clade (e.g. oaks) in

which hybridization occurs among close relatives.



convergence found in prey or host defences against higher

trophic levels.

Some plant communities experience much greater her-

bivory, disease and predation than others; for example, many

authors have proposed that there is a latitudinal gradient

in the strength of enemy attack (Coley & Barone 1996;

Mittelbach et al. 2007). Communities that have a low degree

of trophic complexity may be more likely to be governed by

environmental filtering or plant–plant competition than by

trophic interactions. Yet, most plant communities support

abundant and diverse communities of natural enemies, and

many studies have documented that natural enemies are

often the most dominant factors influencing plant commu-

nity dynamics; indeed they are often much stronger forces

than environmental factors or plant–plant competition

(McNaughton 1985; Carson & Root 2000).

In addition, attack from natural enemies can result in

selection for plant traits that are an advantage in one habitat

type but are a disadvantage in other habitats. This

interaction of herbivory with abiotic gradients can amplify

the effect of environmental filtering, because plant strategies

for each habitat include trait trade-offs that become more

divergent with more herbivore pressure, resulting in

stronger patterns of habitat specialization, influencing

community assembly within a region. Two examples are

the trade-off between competitive ability and defence

investment across resource gradients such as white-sand

and clay forest (Fine et al. 2004, 2006) and shaded

understorey and light gaps (Coley et al. 1985).

Whether enemies are mostly specialists or generalists within

a community of hosts causes large effects in the phylogenetic

structure of host communities, with phylogenetic clustering

becoming less likely with increasing specialization (Fig. 4).

Herbivores and pathogens are not always specialists in the

sense of a one-host-one-plant relationship, but in many

communities the dominant herbivores tend to display a strong

phylogenetic signal in their diet (Agrawal & Fishbein 2006).

Yet, in some communities, like grasslands, the most important

herbivores are large ungulates that eat a wide variety of plants

(McNaughton 1985). The implication of the degree of

specialization by natural enemies for plant community

structure, in turn, depends on whether the plants� defence

traits are phylogenetically conserved or convergent (Fig. 4).

There is strong circumstantial evidence that at least some

of the defensive compounds in plants are conserved

(Fig. 4a,c). Detailed analyses of insects and fungal pathogens

feeding on their host plants in tropical and temperate forest

communities reveal that many enemies feed only within

narrow subsets of the angiosperm phylogeny (generally

within families or genera) (Berenbaum 1990; Coley et al.

2005; Novotny & Basset 2005; Weiblen et al. 2006; Dyer

et al. 2007). In the few cases that defence chemistry has been

measured in multiple plant species within a lineage, there is

evidence for trait conservatism in the qualitative type of

defence, with patterns of trait convergence in the quanti-

tative amount of defence investment and ⁄ or specific

chemical structure within a broad category of defence type

(i.e. terpenes) (Berenbaum 1990; Becerra 1997; Coley et al.

2005; Fine et al. 2006).

In general, while trophic interactions influence commu-

nity structure in complex ways, there is a predictable

framework in which to investigate the directionality of these

effects on community structure, and phylogenetic informa-

tion plays an important role. Interpreting patterns of

phylogenetic community structure and evaluating the role

of trophic interactions in producing these patterns will be

facilitated by paying attention to the strength and specificity

of these interactions, as well as to the amount of

convergence and conservatism in defence traits.

Mutualism and facilitation

While negative interactions, such as competition and

Janzen–Connell mechanisms, are often emphasized in

structuring communities, facilitation and mutualisms tend

to be underemphasized despite their known importance (e.g.

Stachowicz 2001; Callaway et al. 2002; Bascompte &

Jordano 2007; Maherali & Klironomos 2007). Mutualisms

can influence phylogenetic community structure in either

direction (clustering or overdispersion), depending on the

nature of the interactions (Sargent & Ackerly 2008). Plant–

pollinator interactions have been hypothesized to increase

phylogenetic clustering due to the benefits accrued to

congeners through shared pollinators (Moeller 2005; Sargent

& Ackerly 2008). It stands to reason that mutualisms and

other positive interactions should promote phylogenetic

clustering any time that mutualists are spatially aggregated

and specialized enough that they enhance the survival of

phylogenetically similar species. While positive interactions

may promote phylogenetic clustering when they enhance

fitness of phylogenetically similar species, they may promote

high phylogenetic diversity (overdispersion) if they increase

the co-occurrence of distantly related species. For example,

early residents in Mexican plant communities facilitated

establishment of a diverse assemblage of species by creating

protected microhabitats for regeneration (Valiente-Banuet &

Verdu 2007). Positive interactions tended to occur between

these early �nurse plants� and distantly related benefactors.

Hence, in this case, facilitation caused overdispersion of

communities.

Gene flow and lack of reproductive isolation

A lack of reproductive isolation might also have conse-

quences for community assembly and phylogenetic com-

munity structure, particularly in communities dominated by



a single clade. For example, in clades where the evolution of

reproductive isolation is positively associated with both

divergence time and the extent of ecological divergence

between species (Funk et al. 2006), gene exchange may

preclude the long-term coexistence of closely related

lineages in local communities (Losos 1990; Levin 2006)

causing phylogenetic overdispersion (Fig. 5). This can occur

if gene pools of two lineages merge within local commu-

nities even though they may maintain their genetic integrity

in other parts of their geographical ranges. Alternatively,

sympatry of close relatives may be limited by hybridization

and production of hybrid offspring with reduced fitness. In

such �tension zones� the lack of reproductive isolation

between taxa, coupled with selection against hybrid indi-

viduals, prevents both the merger of the hybridizing lineages

and their establishment within each other�s ranges (Burke &

Arnold 2001). Under both of these models, coexistence

would be limited for close relatives, but not for distantly

related ones causing a tendency towards phylogenetic

overdispersion (assuming that the degree of reproductive

isolation increases with time since divergence). Gene

exchange can also increase genetic variation and evolution-

ary change in populations, potentially promoting divergence

(Arnold 1992; Grant & Grant 2008). Adaptive divergence

enabled by low-level gene exchange between lineages could

enhance a tendency for close relatives to occur in

contrasting habitats causing phylogenetic overdispersion.

The challenge of linking pattern to process

Ecologists learned in past decades that attempts to infer

community assembly rules from community patterns (e.g.

Diamond 1975) could not replace experimental and other

classical methods for determining ecological processes (e.g.

Connell 1980; Strong & Simberloff 1981). The difficulty of

interpreting process from pattern again confronts us now

that data and tools for phylogenetic analysis are widely

available, presenting a challenge to phylogenetic commu-

nity ecology. We argue that novel insights arise when

patterns of phylogenetic relatedness are used in conjunc-

tion with an understanding of the functional biology of

organisms in the context of their ecological interactions

and evolutionary history, bearing in mind the importance

of scale (Box 1). In particular, it is important to

understand the nature and strength of interactions between

organisms and their environment, the strength and

specificity of biotic interactions, as well as the amount of

convergence and conservatism in traits that influence these

interactions. Finally, we argue that controlled experiments

that make use of phylogenies in their design (e.g. Agrawal

& Fishbein 2008) can play an important role in determin-

ing the strength and specificity of these kinds of

interactions.

T H E E V O L U T I O N A R Y C O M P O N E N T O F

C O M M U N I T Y A S S E M B L Y

An expanding area of phylogenetic community ecology

challenges the classical assumption in ecology that the

species pool is static at time scales relevant to ecological

processes. Ecologists have often agreed explicitly (e.g.

Weiher & Keddy 1999) or implicitly to leave to evolutionary

biologists and paleobiologists the roles of speciation,

extinction and biogeographical dispersal in generating the

species pool. However, the availability of time-calibrated

phylogenies and their application to studies of community

assembly have revealed the dynamic nature of the species

pool and demonstrated that generation of the pool, as well

as evolution of species traits within the pool, must be

considered part of the assembly process (Fig. 3) (e.g. Brooks

& McLennan 1991; Losos et al. 1998a; Ackerly 2004;

Gillespie 2004; Pennington et al. 2006; Givnish et al. 2008).

As we discuss below, interspecific interactions within

communities can feed back to evolutionary processes

(Haloin & Strauss 2008) causing, for example, in situ

speciation and adaptive radiation (e.g. Schluter 2000) that

add species to the regional pool. Such feedbacks are likely to

operate differently on islands where many species are

descended from a small number of ancestors compared to

continental settings where there is a pool of species from

surrounding areas (Losos 1996). Investigations of this kind

shed light on early controversies about the nature of

communities and provide insight into the biogeographical

and evolutionary processes that influence community

assembly, answering Ricklefs (1987) plea from two decades

ago.

Community assembly through dispersal vs. in situevolution

By providing a temporal dimension to community ecology,

phylogenetic information allows community ecologists to

assess when and where traits of ecological significance

originated, and consequently, whether communities are

primarily assembled through in situ evolution or through

dispersal and habitat tracking (e.g. Brooks & McLennan

1991; Spironello & Brooks 2003; Ackerly et al. 2006). The

assembly process has thus been characterized as a race

between adaptation and colonization (Urban et al. 2008).

Evidence that ecologically relevant traits are phylogenetically

conserved has lent support to the hypothesis that it is easier

for organisms to move than to evolve (Donoghue 2008).

Chaparral communities in Mediterranean California provide

an important example of using phylogenies to determine the

relative roles of in situ evolution and migration in commu-

nity assembly. Plant species with sclerophyllous leaves and

low specific leaf area were long thought to have acquired



these traits through convergent evolution in response to

Mediterranean climates (Cody & Mooney 1978). However,

Ackerly (2004) found that these traits evolved prior to the

Mediterranean climate in most lineages, providing evidence

that these species tracked the climates to which they were

previously adapted. Far from being an example of in situ

convergent evolution, Mediterranean chaparral communities

were shown to represent an example of dispersal and

ecological sorting on phylogenetically conserved traits that

evolved elsewhere. Nevertheless, other studies demonstrate

a strong role for convergent evolution in community

assembly. For example, Anolis lizard communities on

different islands and iguanian lizard communities on

different continents were assembled through in situ

convergence of ecomorphs (Losos et al. 1998a; Melville

et al. 2006).

The shifting role of evolution in community assemblythrough time

Phylogenetic approaches have also revealed that communi-

ties assembled through dispersal vs. those assembled

through in situ evolution represent two extremes of a

continuum. Evidence suggests that available ecological

space is filled either by adaptation of early occupants or

by dispersal of conserved ecological types, depending on

which occurs first (Stoks & McPeek 2006). Hawaiian

Tetragnatha spiders provide a striking example of this pattern

where communities on different islands have formed by

both in situ evolution of adaptive phenotypes as well as by

colonization of pre-adapted phenotypes (Gillespie 2004). In

particular, some species colonized new islands without

changing their ecological niche and conserving their

ecomorph. For the spiders that arrived on islands where

their old niche was already filled, these species then

diversified after colonizing a new island, switching ecologi-

cal niches and thus changing ecomorphs. Prinzing et al.

(2008) found a similar pattern in the Dutch flora. They

showed that vascular plant communities are either com-

prised of many lineages that are nested within different

clades with low functional trait diversity or few lineages that

evolved with high functional trait diversity, where functional

trait diversity is determined by the variance in traits found to

be important in defining ecological niches. They interpreted

this as evidence that there are suites of available niches that

can be filled either by in situ evolution in which one lineage

radiates generating high functional diversity, or through

colonization by many different lineages such that species

from diverse lineages generate similar functional diversity

within communities.

Phylogenetic studies of the assembly process in island

adaptive radiations reveal that the extent to which a

community acquires its species through dispersal and

in situ evolution changes as it is assembled (Emerson &

Gillespie 2008). Phylogenetic community ecology has thus

raised a key question at the intersection of ecology and

evolutionary biology: When does dispersal or in situ

evolution predominate in the assembly process? Relative

rates of dispersal and diversification are likely to be critical.

In island studies where dispersal is slower than speciation,

early species that are pre-adapted to existing ecological

conditions arrive via dispersal, but in situ speciation and

adaptive divergence subsequently take over as the predom-

inant process by which species assemble in the community

(Emerson & Gillespie 2008).

F E E D B A C K S T O E V O L U T I O N A R Y P R O C E S S E S

Community-level interactions feed back to influence evolu-

tionary process of speciation and adaptation (Fig. 3)

(Antonovics 1992; Bascompte & Jordano 2007; Johnson

& Stinchcombe 2007; Haloin & Strauss 2008; Hoberg &

Brooks 2008; Jablonski 2008). Classical community ecolo-

gists have generally focused on the interactions among

members of communities and have been reluctant to

consider how they might impact the evolutionary processes

that generate the regional species pool from which

communities are assembled (Fig. 3). An important area in

which phylogenetic community ecology can advance clas-

sical community ecology is the investigation of how

interactions among species within communities feed back

to influence the evolutionary processes that impact species

ecological roles and ultimately the diversity of traits and

species in the regional pool.

Plant–insect interactions provide well-known examples of

how evolutionary innovations that emerge at one trophic

level can influence evolutionary processes at higher trophic

levels as a result of co-evolutionary arms races (Ehrlich &

Raven 1964; Farrell 1998). Insects feeding on host plants

drive divergent selection for new defences which, in turn,

drive selection in insects to evolve strategies to circumvent

these novel defences (Kawecki 1998). These novel strategies

can have the effect of increasing the amount of specializa-

tion in the herbivore (especially if they incur a cost) –

further strengthening selection in the plant for more defence

investment (and ⁄ or novelty).

The ecological roles of insect herbivores and selection

pressures on host plants can change over time and space,

altering species interactions and selection patterns (Thomp-

son 2005). For example, isolated islands often have limited

subsets of both mainland plants and their specialist

enemies, especially soon after colonization. Planthoppers

from the genus Nesosydne (Hemiptera: Delpacidae) are

recent colonists to the Hawaiian islands (Roderick & Percy

2008). On the mainland, this genus is generally always

associated with monocot lineages like grasses and sedges.



In contrast, on Hawaii this lineage has expanded its host

breadth to cover more than 25 plant families, mostly

eudicot lineages. This ecological release is probably due to

both selection for increased host breadth in the insects due

to less competition from other herbivores and selection in

the plant lineages for lower levels of defences due to their

own escape from their specialist enemies after arriving in

Hawaii. Yet within these newly arrived planthopper

lineages, Nesosydne species are already beginning to

re-specialize on the Hawaiian lineages, with 77% of the

species monophagous, feeding on only a single plant

species (Roderick & Percy 2008). This illustrates how

changing phylogenetic community structure influences

evolution of herbivore-host specialization.

Evolutionary feedbacks have important consequences for

the temporal dynamics and diversity of the species pool. In

general, phylogenetic studies of species with a deep history

of coexistence indicate that rates of ecological and mor-

phological diversification tend to be greatest during the early

phases of a clade�s radiation (when ecological opportunity is

abundant) and then decline as niches are filled and

ecological interactions among co-occurring species constrain

further opportunities for diversification (Kozak et al. 2005;

Harmon et al. 2008; Wellborn & Broughton 2008). Several

recent studies on birds, fishes and salamanders suggest that

as lineages spread through a geographical area to form

communities, the rate at which new species accumulate in

the regional pool declines as geographical space is filled and

as ecological niches are filled with competing species (Ruber

& Zardoya 2005; Kozak et al. 2006; Phillmore & Price 2008;

Rabosky & Lovette 2008; Williams & Duda 2008).

Although the potential links between community ecology

and macroevolution are exciting, a variety of challenges

must be overcome to fully understand the extent to which

community interactions shape long-term evolutionary pro-

cesses (Johnson & Stinchcombe 2007). Perhaps the biggest

hurdle is reconciling mismatches of evolutionary and

ecological patterns that emerge at different spatial and

temporal scales (Jablonski 2008). Focused comparative

studies using well-resolved phylogenies between interacting

species on islands of different ages hold promise for

disentangling the relative strengths of historical contingency,

deterministic ecological interactions, speciation and dis-

persal (Losos et al. 1998b; Emerson & Gillespie 2008).

C O N S E Q U E N C E S O F P H Y L O G E N E T I C C O M M U N I T Y

S T R U C T U R E A N D T R A I T C O N S E R V A T I S M F O R

C O M M U N I T Y D Y N A M I C S A N D E C O S Y S T E M

P R O C E S S E S

While considerable effort has been placed on using

phylogenetic community structure to infer causal

processes in community assembly, much less work has

focused on the consequences of phylogenetic history and

phylogenetic community structure for ecosystems and their

responses to global change (Table 1). As outlined in Fig. 3,

phylogenetic history influences both traits of species, as well

as the organization of communities, both of which influence

ecosystem properties. Here we focus on the plant literature,

reflecting the general orientation of ecosystem-level

research. We know that important functional attributes of

plants, such as leaf traits (Ackerly & Reich 1999) wood

density (Chave et al. 2006; Swenson & Enquist 2007),

allocation patterns (McCarthy et al. 2007) and element

concentrations and their stoichiometric ratios (Kerkhoff

et al. 2006), show evidence of trait conservatism as inferred

from phylogenetic or taxonomically based variance parti-

tioning. These and related studies highlight the possibility of

predicting clade-level ranges of trait values from a subset of

individuals within a clade (Box 1, Fig. 2). Such traits can

have important consequences for ecosystem functions,

including decomposition rates, nutrient cycling and carbon

sequestration (Vitousek 2004; Weedon et al. 2009). It

follows that both phylogenetic community structure and

composition may influence ecosystem-level processes and

that phylogenetic information can thus help predict ecosys-

tem properties and responses to changing environments. An

important emerging area of investigation focuses on using

phylogenetics to understand and predict long-term commu-

nity dynamics (Willis et al. 2008), ecosystem processes

(Cadotte et al. 2008) and responses of ecosystems to global

change (Edwards et al. 2007).

Predicting ecosystem function from communityphylogenetic diversity

The phylogenetic structure of communities shows promise

for predicting ecosystem processes. Two recent studies of

links between phylogenetic diversity and ecosystem function

in plants (Cadotte et al. 2008) and plant-mycorrhizal

communities (Maherali & Klironomos 2007) have demon-

strated that phylogenetic diversity can predict community

productivity better than species richness or functional group

diversity. While biodiversity experiments, such as those

analysed by Cadotte et al. (2008) may not be truly

representative of natural communities because they are

often artificially assembled and weeded, they provide

support for the hypothesis that phylogenetically diverse

communities can maximize resource partitioning and hence

use greater total resources. This is based on the evidence

that the more differentiated species are the greater

their resource exploitation (Finke & Snyder 2008). If

phylogenetic relatedness predicts ecological similarity,

phylogenetic diversity should enhance complementarity

and increase ecosystem productivity by maximizing total

resource uptake. By the same logic, high phylogenetic



diversity may be predicted to increase ecosystem stability by

ensuring that sufficient ecological strategies are represented

in an assemblage to ensure persistence of the ecosystem in

the face of changing conditions. Knapp et al. (2008) found

an uncoupling between species richness and phylogenetic or

functional diversity in urban areas in Germany. They

hypothesized that despite high species richness in these

areas, low phylogenetic and functional diversity in urban

ecosystems should limit their capacity to respond to

environmental changes. Similarly, phylogenetic diversity

may be linked to nutrient cycling, resistance to invasion,

soil carbon accumulation and other ecosystem processes,

goods and services. Such links, if they continue to be

substantiated, lend support to the argument that phylo-

genetic diversity has higher utility than species richness as a

conservation criterion for management decisions (Faith

1992; Gerhold et al. 2008).

Deterministic models of community dynamics usingecologically important traits – is there a role forphylogeny?

Theoretical approaches to understanding communities have

been successful in accurately predicting the transient

dynamics and outcome of species interactions based on

fundamental ecological properties of organisms in low

diversity systems (Dybzinski & Tilman 2007; Purves et al.

2008). In a test of the resource ratio hypothesis (Tilman

1982), Dybzinski & Tilman (2007) accurately predicted the

outcome of species competition from minimum resource

concentrations in monocultures (R*). Purves et al. (2008)

used a mathematical model that relies on a small number of

species-level parameters, including canopy join heights (Z *,

a measure of shade tolerance) as well as understory and

overstory mortality rates to predict long-term community

dynamics in forests of the Upper Midwestern United States.

Extending such models to predict the future of vegetative

communities globally faces many challenges, including

encapsulation of the extreme diversity in tropical forests.

Phylogenetics may allow species to be parameterized by

lineage, reducing the number of parameters in the model

and the data required, and by linking phylogenetically similar

species in a predictive framework. A recent study demon-

strates that phylogenetic conservatism in the ability of

species to adjust their flowering time phenology to climatic

warming in New England underlies a phylogenetically

biased pattern of local extinction and is thus predictive of

long-term community dynamics (Willis et al. 2008).

Perhaps the biggest challenge facing this emerging area of

phylogenetic community ecology is to determine whether

ecological traits that are most predictive in ecological and

dynamic global vegetation models are evolutionarily labile,

and are therefore not well predicted by phylogeny.

Theoretical studies have indicated, for example, that

alternative designs of equal fitness in the same environment

are likely to evolve (Marks & Lechowicz 2006), and

empirical studies have shown evidence for many-to-one

mapping of critical ecological traits, such that the same

ecological function can evolve through more than one

pathway (Wainwright et al. 2005). As a result, close relatives

may not necessarily be more ecologically similar than distant

relatives. Nevertheless, there is increasing evidence that

ecologically relevant traits are likely to show as much

phylogenetic conservatism as reproductive and other taxo-

nomically relevant traits (Prinzing et al. 2001; Donoghue

2008). This presents us with the challenge to understand the

extent and phylogenetic scale of conservatism in ecological

traits – a challenge that will require both experimental

manipulations and analytical surveys within and across a

broad range of taxa.

Phylogenetic vs. functional group approaches in dynamicglobal vegetation models

Dynamic global vegetation models are increasingly using a

functional trait-based approach to predict responses of

biomes to climate change (e.g. Bonan et al. 2003).

Edwards et al. (2007) argue that phylogenetic information

provides a powerful means to scale from organism

physiology to global processes. They reason that physi-

ological traits used to scale between individuals and

ecosystems vary among different groups of organisms,

and these differences originated as evolutionary innova-

tions along the branches of the tree of life. For example,

C3 and C4 grasses are commonly used functional groups

in ecological experiments and in global vegetation models

(e.g. Bonan et al. 2003). However, variations of the C4

photosynthetic pathway have evolved multiple times, and

it turns out that the response of species to temperature

depends more on the phylogenetic lineage than on the

qualitative delineation of the photosynthetic apparatus as

C3 or C4 (Edwards and Still, 2008). Thus phylogenetic

information may be more useful than functional group

classification schemes in dynamic global vegetation mod-

els that predict responses of the Earth�s biota to climate

change (Edwards et al. 2007).

We hypothesize that the power of phylogeny to predict

ecologically relevant traits is likely to increase with the

phylogenetic scale of the analysis up to a point (Box 1,

Fig. 2). However, at the largest phylogenetic scales, the

probability of trait convergence may be high due to the

presence of similar selective regimes in geographically

disjunct regions of the globe. Phylogenetically based

functional groups may thus be most useful at intermediate

phylogenetic scales, and are likely to be most useful in cases

where trait data are incomplete and diversity is high.



C O N C L U S I O N

The merging of community ecology and phylogenetic

biology now allows community ecologists to consider

phenomena occurring over broader temporal and spatial

scales than was previously possible. The rapidly expanding

field of phylogenetic community ecology is thus poised to

resolve long-standing controversies in classical community

ecology and to open new areas of enquiry. Studies in this

emerging field have addressed fundamental questions about

the role of niche-based vs. neutral processes in community

assembly, challenged the assumption that evolutionary

processes are not relevant to community assembly, revealed

influences of community interactions on evolutionary

processes, and begun to provide predictive information

about the responses of communities and ecosystems to

global change.

A large number of studies have analysed the phylo-

genetic structure of communities to examine the evidence

for neutral or niche-based processes in community

assembly. The most convincing of these are studies that

examine the functional ecology of organisms and test for

conservatism in traits and niches. These have revealed

many different processes that cause non-random phylo-

genetic community structure (Table 1). Two challenges

facing this area of study are determining the extent and

scale of phylogenetic conservatism in ecologically impor-

tant traits, rather than assuming it, and drawing on

functional biological information to interpret phylogenetic

patterns in communities. The merging of phylogenetics

and community ecology will continue to advance the

debate about the roles of neutral vs. niche-related

processes by working at multiple spatial scales and

investigating turnover in phylogenetic diversity of organ-

isms across environments over distances greater than

dispersal distances. Such studies can provide evidence for

or against ecological sorting and evolution of habitat

specialization, not predicted under neutral theory. In

general, we argue that there is a need for greater emphasis

on experimental and modelling approaches (cf. Kraft et al.

2007) in a phylogenetic context that examine the

conditions under which specific processes are important

in community assembly. Such approaches would be

useful, for example, to determine whether close relatives

are generally expected to show stronger competitive

interactions than distant relatives and at what temporal

and spatial scale such interactions are likely to influence

community assembly.

One of the most important contributions phylogenetic

community ecology has made is a greater appreciation for

the role of evolution in community assembly. Ecologists are

now challenged to consider broader temporal and spatial

scales in explaining coexistence, diversity and community

composition. In particular, phylogenetic community ecology

offers insight into the conditions under which it has been

easier to move than to evolve. Time-calibrated phylogenies

allow the possibility to test not only the extent to which

communities assemble through dispersal vs. in situ evolution,

but also the relative timing of the arrival of species and the

evolution of functional traits, providing insight into the

conditions under which evolution is favoured over dispersal.

An important area of investigation is the influence of

community interactions on processes of speciation, adapta-

tion and extinction. A challenge in this area is reconciling

macroevolutionary trends with results from microevolution-

ary studies (Jablonski 2008), but it is one that can be

overcome with focused studies integrating well-resolved

phylogenies, functional traits and interactions among

species.

Finally, the application of phylogenetic information to

predicting community dynamics, ecosystem function and

responses to global change shows increasing promise. An

important challenge involves the comprehensive examina-

tion of the extent to which ecologically important traits

useful in predictive models are phylogenetically conserved.

To the extent that they are, phylogenetic biology will offer

increased predictive power in ecology.

The questions that phylogenetic community ecology

addresses are fundamental to understanding the nature of

biological communities. With the increasing rate of global

change – including land use change, habitat loss, species

invasions, alterations in element cycling and global climate

change – basic understanding of the causes and conse-

quences of community structure has never been more

important. Protecting our biological resources requires

continued commitment to understanding how communities

assemble and how they respond to forces of change.

A C K N O W L E D G E M E N T S

This work was supported by funding from the National

Center for Ecological Analysis and Synthesis (NCEAS), the

Long-Term Ecological Research (LTER) Network Office

and the National Science Foundation (NSF) DEB-0620652

(JCB); NSF DEB-0824599 (KHK); NSF DEB-0743800

(PVAF), and a postdoctoral fellowship from the Natural

Sciences and Engineering Research Council of Canada

(NSERC) to S.W.K. For discussions and other assistance,

the authors wish to thank participants of the LTER-NCEAS

working group �Linking phylogenetic history, plant traits,

and environmental gradients at multiple scales� as well as

Jonathan Losos, Jeremy Lichstein, Ray Dybzinski, Michael

Donoghue, David Ackerly, Margaret Metz, Peter and

Rosemary Grant, Richard Ree, Mark Ritchie, Mathew

Leibold, Robert Holt, Clarence Lehman, Peter Reich, David

Tilman, Sarah Hobbie, Stephen Pacala, Anurag Agrawal,



Sharon Strauss, Dan Faith, Brian Enquist and three

anonymous referees. J.C.B. thanks the Department of

Ecology and Evolutionary Biology at Princeton University

for hosting her as a visiting fellow.

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Editor, Brian Enquist

Manuscript received 24 October 2008

First decision made 26 November 2008

Second decision made 14 February 2009

Manuscript accepted 4 March 2009



frontiers and foundations in ecology

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