Resource competition among >2 species

• One resource– species with lowest R* excludes all others

– example: species 1 excludes all others

Resource competition among >2 species

• Two resources, essential• Constant, homogeneous environment• Two resources - two coexisting species

at equilibrium– which two species depends on resource

ratios– each species is best competitor for a

particular ratio of resources

R1

R2 sp.1

sp.2

sp.3

sp.4

1 & 21

2

3

2 & 3

3& 4

4

12

23

43

Resource competition, >2 species

New effect: spatial variation

• Suppose resource ratios vary locally– natural heterogeneity in soil nutrients– consequences for coexistence?

• When there is local spatial variation in resource ratios, >2 species can coexist – with local spatial segregation (patchiness)– More species than resources

R1

R2 sp.1

sp.2

sp.3

sp.4

12

23

43

1, 2, 3, & 4

Variation in resource ratios

Spatial variation• Local variation fosters diversity• More species than resources possible• Dependent on extent of variation• Plant communities

– often 100’s or 1000’s species– only about 12 essential resources– often patchy

• Variance in Resource Ratios Hypothesis (VRR)

What is the effect of nutrient enrichment?

• Relationship of diversity & productivity• Unimodal vs. Monotonic• Mechanisms producing relationships

– Unimodal– particularly decrease in diversity with

productivity

R1

R2sp.1

sp.2

sp.3

sp.4

12

23

43

1, 2, 3, & 4

2 & 3

4 only1 only

Enrichment and coexistence

Nutrient enrichment• Increase all resources uniformly

– local variation in resource ratios allows coexistence of fewer species

• Increase one resource– necessarily makes resource ratios more extreme– raises, then lowers number of coexisting species

• Assumes resources increase without increasing variation

• “Paradox of enrichment” – enrichment = reduced diversity

Switching resources• Does VRR predict coexistence of many

species on 2 switching resources?– species don’t specialize on ratios– each species consumes one resource or the other

only

• At equilibrium there are 2 species, each consuming and limited by one resourse – Fundamental difference between animal and plant

communities

R1

R2

sp.1

sp.2

sp.3

1

4

1 & 4sp.4

Switching resources

Plants vs. Animals• Plants use essential resources• VRR predicts high species:resources

ratio• Animals use switching resources• Theory predicts species:resources ratio

= 1

Coexistence and evolution• Competitive coevolution

– 2 spp. competing for 1 resource cannot coexist– if individuals vary in resource use– if that variation is heritable– competition creates selection

• May select for increasing efficiency– selection for better resource use (lower R* )– a “race” to be most efficient– end result is still exclusion

Coexistence and evolution• Competition may select for divergence in

resource use– individuals exploiting an alternative resource

favored (not affected by competition)– alternative resources could be different spatially,

temporally, in size– for substitutable or switching resources– evolution of divergence may avoid exclusion

Example: Divergence in prey size

size of prey

freq

. of

use

size of prey

freq

. of

use

selection against

time

Evolution of divergence in resource use

R1

R2

sp. 1

sp. 2

unstable

sp. 2

sp. 1

Evolution of divergence in resource

use

R1

R2 sp. 1

sp. 2

unstable

R2 sp. 1

sp. 2

stable

R2 sp. 1

sp. 2

stable

Competitive character displacement

• Competition selects for divergence in a morphological feature– presumably results in divergence of

resource use– often held to be the best evidence for the

importance of competition– Example: Sitta nuthatches

Nuthatches

– Example: Sitta nuthatches– Asia & Europe– Ranges include regions of allopatry (no

contact)– also regions of sympatry (co-occur)– Sitta neurenmayer (Europe)– Sitta tephronata (Asia)– Sympatry in Iran

Nuthatches

• Bill size– related to prey size– data suggest character displacement on bill

size• S. neurenmeyer S.

tephronta• Allopat. 25 mm 25

mm• Sympat. 22 mm 28 mm

Prediction of character displacementbi

ll le

ngth

(m

m)

site (longitude)

S. tephronata

S. neurenmayer

Actual pattern (Grant 1972)bi

ll le

ngth

(m

m)

site (longitude)

S. tephronata

S. neurenmayer

Nuthatches

• No shift in cline of bill size when region of sympatry is reached

• Bill sizes vary geographically in a continuous fashion

• Not much evidence for character displacement

Hydrobia snails

• intertidal mud snails– particle feeders (diatoms, sediment)

• Allopatry– H. ventricosa mean length = 3.1 mm– H. ulvae mean length = 3.3 mm

• Sympatry– H. ventricosa mean length = 2.8 mm– H. ulvae mean length = 4.5 mm

Hydrobia snailsQuestions

• Character displacement?• Competition for food particles?• Levinton - does particle size affect

growth?– larger species does best on larger

particles?• Result: No difference in growth for

different particle sizes

Hydrobia snails: More questions

• H. ulvae & H. ventricosa sympatric in lagoons• H. ulvae alone in intertidal• Lagoon H. ulvae

– alone … 1.2 X larger than intertidal H. ulvae– w/ H. ventricosa … 1.4 X larger than intertidal H.

ulvae

• size difference due to physical environment?• lagoons: low reproduction, high growth

Character displacement• Classic cases of character displacement now

questioned• Probably not a widespread phenomenon• Morphology (size) presumed related to resource

use• Competition presumed to be the driving force• Examples of size differences reducing

competition?

Caribbean AnolisPacala & Roughgarden 1985

• St. Maarten• A. gingivinus

– SVL = 41 mm• A. wattsi

– SVL = 38 mm

• St. Eustatius• A. bimaculatus

– SVL = 53 mm• A. wattsi

– SVL = 40 mm

Caribbean Anolis

• Predict less competition on St. Eustatius

• Note: size strongly correlated with prey size

Experiment

60 Ag100 Aw

60 Ag100 Aw

60 Ag 60 Ab100 Aw

60 Ab100 Aw

60 Ab

60 Ag 60 Ab

St. Maarten St. Eustatius

12 X 12 m enclosures; fenced 1.5 m; clear lizards

Caribbean Anolis

• St. Maarten• A. gingivinus + A. wattsi

– less food in stomach– lower growth rate (0.5X)– perch height higher (2X)

• compared to A. gingivinus alone

• Interspecific effect strong

• St. Eustatius• A. bimaculatus + A. wattsi

– same amount in stomach– same growth rate– same perch height

• compared to A. bimaculatus alone

• Interspecific effect absent

Alternative interpretation• Suppose competition is absent on St. Eustatius

– large resource base, abundant food– predators reduce density

• A. bimaculatus enclosures– escapes occurred over time– density: 60 45 30 lizards– 1 mo 2 mo– as density drops growth increases; competition

Conclusion

• Size difference reduced competition• One case, but it shows this effect is possible• Authors do NOT claim size difference evolved

due to competition• Has not established that size would evolve in

response to competition

Morphological evolution & competition (Schluter 1994)

Sticklebacks

• species complex• extreme body forms

– limnetic - feed on plankton (e.g., Daphnia)– benthic - feed on benthic invertebrates

                                        Representative limnetic (top) and benthic (bottom) stickleback from Lake Enos in British Columbia, Canada. Click to enlarge. Posted with permission from Paul J. B. Hart and Andrew B. Gill, "Evolution of Foraging Behaviour int the threespine stickleback," in The Evolutionary Biology of the Threespine Stickleback, eds. Michael A. Bell and Susan A. Foster, (Oxford: Oxford University Press), 1994, p. 211. © Oxford University Press

see also Robinson & Wilson 1994

Sticklebacks

• Morphological intermediates exist• 1 sp. in a lake -- typically intermediate

morph• 2 spp. in a lake -- typically 2 morphs• Morphology is related to feeding

efficiency and growth• Hypothesis: evolved morphological

divergence due to competition (Character displacement)

Experiment• 23 X 23 m ponds• Target species intermediate in morphology• produced by hybridization

Morphology

intermediate X benthic

intermediate X intermediate

intermediate X limnetic

Hypothesis• Competition with a limnetic will have greatest

effect on survival and growth of forms morphologically similar to limnetic

Morphology

LimneticTarget

Morphology

LimneticTarget

time

Experiment• Hybrids add variation on which selection

can work

Morphology

intermediate X benthic

intermediate X intermediate

intermediate X limnetic

Implication

• If hypothesis is supported, selection for character divergence is occurring via competition

Experiment

Experimental1800 target1200 limnetic

Control1800 target X 2 ponds

Data collection• 3 months• Collect fish, measure Target• Growth rate reduced by density

– competition occurs• Regression of growth vs. morphology• Slope = growth differential between

more benthic and more limnetic

Results

I x B I x I I x L

Gro

wth Control

Competitor

morphology

Results• Growth differential

– significant for 1 experimental group– nearly so for a 2nd experimental group– clearly not significant for both controls

• Survival differential– some evidence for an effect in 1 pond

• Target individuals with limnetic morphology fare worst

Conclusions• Experimental evidence for character

displacement• Caveats:

– pseudoreplication – statistical weakness

Lake whitefish Coregonus lavaretus

dwarf, limnetic

benthic

Null models in community ecology

• Experiments– show that a process occurs– may show it can cause effects on distribution,

abundance, fitness of a limited set of species– Does that process structure the community as a

whole?– experiments rarely can test that

• If interspecific competition is important, what patterns would be predicted for communities?

Community patterns

• Competition favors differences in resource use among co-occurring species

• Predict: co-occurring species should be more different in resource use than expected if species were placed together randomly.

• Should be present across similar species within a community

G. E. Hutchinson • Co-occurring European Corixids• Body lengths – ratio of larger to

smaller tended to be >1.3• Morphology as a surrogate for

resource use• Origin of idea of limiting

similarity

Morphological pattern

• Predict: co-occurring species should be more different in morphology than expected if species were placed together randomly.

• "Community-wide character displacement"• How do you tell?• Null models or Neutral models of communities• Morin 98-103; Chase & Leibold 117-122

Statistical Null hypotheses• Hypothesis of only chance affecting outcome• e.g., c2 for mendelian assortment

– coat color… Red White Roan– RR rr Rr

• Cross two Roan: Rr x Rr• Expect: RR = 0.25; Rr = 0.50; rr = 0.25• observe: RR = 0.26; Rr = 0.38; rr = 0.36• c2 = 7.76, P<0.05 … significant departure from

(null) expectation

Statistical Null hypotheses• Expected: assumption of random sampling of

alleles• P<0.05: results deviating as far (or farther) than

observed expected <5% of the times if only random processes are involved

• conclude: some non-random process is structuring alleles at this locus

• Same general pattern in community ecology, but the model and math are more complex

Example – Dytiscid beetles(Juliano & Lawton 1990)

• 28 species, Northern England• 9 different sites have 8 to 16 species• interspecific variation in size and shape• Are co-occurring species more different in

morphology than expected?

Hygrotus inaequalis

Hyphydrus ovatus

Hydroporus planus

Issues for null models• What is the character of interest?

– Resource use– Morphology

• one variable• many variables• correlation of variables

– Co-occurrence (do pairs of species co-occur less often than expected … “forbidden combinations”)

Issues for null models• What is the source pool of species?

– Islands• Mainland fauna• All species on similar islands

–Limits of source pool• Taxonomic• Geographic• Trophic

Issues for null models

• What is the source pool of species?–Real species (discrete values)

• Randomization tests–Statistical distributions (continuous)

• Monte Carlo methods; simulations

Issues for null models• Identifying the assemblage present

–presence/absence–abundance

• rare species may transients, not integrated into the community

• rarity may be a result of inappropriate morphology or resource use

Issues for null models• Test statistic – measure of differences

– Size ratios (Univariate only)– Morphological nearest neighbor distance– Minimum spanning tree

• Mean vs. Variation– predict mean difference larger than expected– predict variation of difference smaller than

expected (regularity of species spacing)– combination

Issues for null models

• Constraints on randomization– Stratify by other factors, e.g., genera within

families– Overall distribution – widespread species more

likely to be included– Dispersal ability – good dispersers more likely

to be included

Source pool : The narcissus effect• Colwell & Winkler 1984• What if assemblages at all locations are affected

by competition– morphologies are more distinct than expected– randomly draw real species … that effect is

incorporated into randomly drawn assemblages– real assemblages do not differ from randomly drawn

because both include the effect of competition on morphology

Source pool issues: The narcissus effect• Solution?• Synthetic species (unlike any real species, but

within the range of variation)• Draw from continuous distributions of

morphological variables (match discrete distributions)

size

# s

pe

cie

s

size

# s

pe

cie

s

Dytiscid morphology• length, width, depth, head width

– correlated in real species

• for real species, choose at random, and allocate to community– each species brings correlated morphological

measurements

• Cannot simply choose length, width, depth, head– omits correlation structure

• Canonical discriminant function– produces uncorrelated variables (up to 4)– choose canonical variates

Dytiscid beetles

Test: randomization• real community with S species

– calculate nearest neighbor distance (NND) in morphological space for

all species– get mean NND and SD NND

• draw S species from pool– calculate NND in morphological space for all species– get mean NND and SD NND

• Repeat many (500 or 1000) times• Test stat [Mean NND – SD NND] =D• Is real D large compared to those drawn at random?

Test: Monte Carlo

• real community with S species– calculate nearest neighbor distance (NND) in morphological

space for all species– get mean NND and SD NND

• draw S species from distributions of Canonical functions– calculate NND in morphological space for all species– get mean NND and SD NND

• Repeat many (500 or 1000) times• Test stat [Mean NND – SD NND] =D• Is real D large compared to those drawn at random?

Test statistic• Reject H0 if observed >95% of all others• Result …For one site, there was a significant pattern

of large mean NND and large D, but not of small SD NND

• Species at one site are more dissimilar than expected by chance– and given average dissimilarity, the are less variable than

expected by chance (D)• using synthetic species (vs. real) null hypothesis is

rejected slightly more frequently (narcissus effect)

Null distribution and real

communties

Real species

Synthetic species

Other results

• Significant– Hawks (Accipter spp.)– Middle eastern cats– Some tiger beetle (Carabidae) assemblages– Desert Rodents

• Not significant– Birds (Tres Marias & Channel Islands)– Most tiger beetle assemblages– Multiple passerine bird assemblages

What does it show?

• A significant result establishes that there is a pattern, consistent with prediction.

• Does not establish what the mechanism is.• Experiments to test mechanisms where patterns

exist– e.g., experiments like Pacala & Roughgarden

Exploitation mostly predation

Exploitation mostly predation

• Predator: kills and eats victim• Parasite: lives intimately with victim and

usually does not necessarily kill victim• Herbivore/Carnivore distinction not that

important for dynamics

Exploitation

• How does the presence / absence of a predator affect:– species populations– assemblages of prey species– evolution of prey

• Does predation contribute to community patterns?

Predation & population dynamics

• Predators eat prey; prey die due to predation• How does this affect population dynamics?• Lotka-Volterra predator-prey model• Starting point• N = number in prey population• P = number in predator populatio

Lotka-Volterra predator-prey• Without predation, prey grow exponentially

dN / dt = r1 N • Predation is an increasing function of N & P• Effect of predation on prey population = C1 NP

• C1 is the capture efficiency

• So, with predation…

dN / dt = r1 N - C1 NP

Lotka-Volterra predator-prey• Without prey, predators starve to death

exponentially

dP / dt = - r2 P• Predation is an increasing function of N & P• Effect of predation on predator population=C2 NP

• C2 = product of capture & conversion efficiencies

• So, with prey …

dP / dt = C2 NP - r2 P

Lotka-Volterra predator-prey:Equilibrium predictions

• At equilibrium• dN / dt = 0 and dP / dt =0• there is a specific, constant density of

predators, above which prey cannot increase• there is a specific, constant density of prey,

below which predator cannot increase

Lotka-Volterra predator-prey isoclines

Pre

dato

r (P

)

Prey (N)

dN / dt < 0

dN / dt > 0

dN / dt = 0

PREY ISOCLINE

Pre

dato

r (P

)Prey (N)

dP / dt < 0

dP / dt > 0

dP / dt =

0PREDATOR ISOCLINE

Lotka-Volterra predator-prey isoclines

dN / dt = 0

Pre

dato

r (P

)

Prey (N)

dP / dt =

0

equilibrium

Lotka-Volterra predator-prey isoclines

dN / dt = 0

Pre

dato

r (P

)

Prey (N)

dP / dt = 0

START HERE

Lotka-Volterra predator-prey dynamics

Time (t )

Den

sity

(N

or

P

)

Predator-prey cycles in real data• Hare & Lynx• What assumptions are

built into Lotka-Volterra predator-prey models?

Simplifying Assumptions

• Simplifying Environmental– Constant in time– Uniform or random in space

• Simplifying Biological– Individuals are identical & constant in time– Exponential prey growth– Prey limited only by predation– Predator growth dependent only on predation

Explanatory Assumption• Predators and prey encounter each other at

random, like bimolecular collisions– Frequency of encounter proportional to product of

densities

• Individual predator feeding rate increases linearly as N increases– No limit on increase in feeding rate

Unrealistic elements• No limits on prey except predation

– expect real prey may be limited by food, space, etc. when abundant

– upper limit ( K ) for prey even with no predators

• Predators do not saturate with prey– expect real predators to hit a maximum number eaten– expect an upper limit for predators with maximal food (KP )

Gause’s predator-prey experiments

Didinium

Paramecium

ParameciumPrey

Didinium Predatory ciliate

Didinium - Paramecium predator-prey experiment

Time (t )

Den

sity

(N

or

P

)

Paramecium

Didinium

Gause’s Predator-Prey experiments

• Predator and prey in a simple environment• No cycles (stable or otherwise)• Predator exterminates prey• Predator dies out shortly after• Inconsistent with Lotka-Volterra predator-prey

models

Gause’s Modified Predator-Prey experiments

• Regular immigration of Paramecium• Produces cycles of predator & prey• Consistent with Lotka-Volterra predator-prey

models?• No

– violates simplifying assumptions– prey population now not soley governed by

exponential growth and predation

Huffaker’sPredator-Prey experiments

• Mites– predator Typhlodromus– prey Eotetranychus

• on oranges• With oranges evenly

spread on a tray– no cycles– prey extinction, then

predator extinction

Huffaker’s modifiedPredator-Prey experiments

• Add barriers to dispersal• rubber balls, vaseline

– cycles

• Confirms Lotka-Volterra prediction?

• NO– violates simplifying

environmental assumption

Predator-Prey models & experiments: Conclusions

• Lotka-Volterra models are largely inadequate• lab systems meeting assumptions -- no cycles• Stable oscillations when system is “fixed”• Conceptual error:

– Design experiments to meet assumptions, then test predictions

– Don’t manipulate experiments until they confirm theory

Improved Predator-Prey models • Self limitation of prey and predators• Asymptotic prey consumption by

predators• Spatial refuges for prey• graphical approach

– Rosezweig & MacArthur (1963)• mathematical approach

– Williams (1980) Grover (1997)– Gilpin & Ayala (1973) Populus 5.4