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488

Conservation Biology, Pages 488–499Volume 17, No. 2, April 2003

Additive Partitioning of Species Diversity across Multiple Spatial Scales: Implications for Regional Conservation of Biodiversity

JON C. GERING,* THOMAS O. CRIST, AND JOSEPH A. VEECH

Department of Zoology, Miami University, Oxford, OH 45056, U.S.A.

Abstract:

Ecologists and conservation biologists are keenly interested in how patterns of species diversitychange across spatial scales. We examined how additive partitioning can be used to statistically evaluate spa-tial patterns of species diversity and develop conservation strategies. We applied additive partitioning to dataon arboreal beetle diversity (richness, Shannon, Simpson) collected from a nested design consisting of four hi-erarchical levels—trees, forest stands, sites, and ecoregions—that corresponded to increasingly broader spa-tial scales within the eastern deciduous forest of Ohio and Indiana ( U.S.A.). A significant percentage (relativeto that of randomization tests) of total species richness and Shannon and Simpson diversity was attributed tobeta diversity between ecoregions and, to a lesser extent, among sites (parks and nature preserves) withinecoregions. Hierarchical cluster analysis corroborated these findings. We also found differences between rarespecies (

�

0.05% of total abundance) and common species (

�

0.5% of total abundance) in the overall per-centage of richness explained by each spatial scale. Rare species accounted for the majority (45%) of the 583total beetle species in our study and were strongly influenced by broad spatial scales (i.e., ecoregions), whereasthe richness of common species was significantly greater than expected across the range of spatial scales ( fromtrees to ecoregions). Our results suggest that the most effective way to preserve beetle diversity in the easterndeciduous forest of the United States is to acquire and protect multiple sites within different ecoregions. Moregenerally, we advocate the use of diversity partitioning because it complements existing models in conserva-tion biology and provides a unique approach to understanding species diversity across spatial scales.

División Aditiva de la Diversidad de Especies en Escalas Espaciales Múltiples: Implicaciones para la Conservaciónde Biodiversidad Regional

Resumen:

Los ecólogos y biólogos de la conservación están muy interesados en la manera en que cambianlos patrones de diversidad de especies a través de escalas espaciales. Examinamos como se puede utilizar ladivisión aditiva para evaluar patrones espaciales estadísticamente y desarrollar estrategias de conservación.Aplicamos la división aditiva a datos de diversidad de escarabajos arbóreos (riqueza, Shannon, Simpson)recolectados con un diseño anidado que consiste de cuatro niveles jerárquicos—árboles, bosques, sitios yecoregiones—que correspondían a escalas espaciales progresivamente mayores en el bosque deciduo de Ohioe Indiana (E.U.A.) Un porcentaje significativo (relativo a pruebas al azar) del total de la riqueza de especiesy la diversidad de Shannon y Simpson se debe a la diversidad beta entre ecoregiones y, en menor extensión,entre sitios (parques y reservas naturales) dentro de las ecoregiones. Análisis de cluster jerárquicos corrobo-raron estos hallazgos. También encontramos diferencias entre especies raras (

�

0.05% de la abundancia total)y comunes (

�

0.5% de la abundancia total) en el porcentaje total de riqueza explicada por cada escala espa-cial. Las especies raras fueron la mayoría (45%) del total de 583 especies de escarabajos en nuestro estudio yestuvieron fuertemente influidas por escalas espaciales amplias (es decir, ecoregiones), mientras que la riquezade especies comunes fue significativamente mayor que la esperada en todo el rango de escalas espaciales (desdeárboles a ecoregiones). Nuestros resultados sugieren que la manera más efectiva de preservar la diversidad deescarabajos en el bosque deciduo oriental de Estados Unidos es adquirir y proteger múltiples sitios dentro de

*

Current address: Division of Science, Truman State University, Kirksville, MO 63501, U.S.A., email [email protected] submitted September 24, 2001; revised manuscript accepted April 18, 2002.

Conservation BiologyVolume 17, No. 2, April 2003

Gering et al. Additive Partitioning across Spatial Scales

489

diferentes ecoregiones. Más ampliamente, recomendamos el uso de la división aditiva porque complementa alos modelos existentes en biología de la conservación y proporciona una aproximación única al enten-

dimiento de la diversidad de especies a lo largo de escalas espaciales.

Introduction

Conservation biologists and land managers frequentlyuse ecological models to determine strategies for conser-vation. The most popular models are the species-area re-lationship (MacArthur & Wilson 1967), metapopulationmodels (Levins 1969; Hanski & Gilpin 1991), source-sinkmodels (Pulliam 1988), and population viability models(Shaffer 1991). Collectively, these models have had a pro-found effect. For example, metapopulation and source-sink models have illustrated the importance of managinglandscapes and networks of habitat, whereas populationviability analyses have identified the importance of de-mographic and environmental stochasticity on the long-term persistence of populations. Despite their growinguse and importance in conservation biology ( Hunter1996; Gaona et al. 1998), these models are not very ap-plicable to the conservation of biodiversity because theyemphasize processes (movement, population growth)more than patterns (diversity), single species more thancommunities, and the effects of landscape design on asingle spatial scale (e.g., arrangement of patches with areserve) more than effects over multiple spatial scales.In essence, the models convey little information abouthow species diversity is affected by spatial scale. Yet it isclear that ecologists and conservation biologists havebeen striving to understand how spatial scale influencesbiodiversity (Shmida & Wilson 1985; Peltonen et al. 1998;Peterson & Parker 1998; Wagner et al. 2000). Palmer andWhite (1994), for example, used a nested series of sam-pling plots to assess how the species-area relationship—a model critical for the design of nature preserves ( Dia-mond and May 1981)—was affected by the spatial scaleof sampling.

Whittaker (1960) first acknowledged the link betweenspatial scale and diversity when he popularized alpha,beta, and gamma diversity. MacArthur (1965) later equatedwithin-habitat diversity to Whittaker’s alpha diversity andbetween-habitat diversity to beta diversity ( Magurran1988). Although their terminology continues to pervadeecological literature and is described in conservation bi-ology texts (e.g., Hunter 1996), there have been few at-tempts to apply the conceptual framework of diversitycomponents to determining how species diversity is gen-erated over spatial scales ( but see Wagner et al. 2000).This is because Whittaker used a multiplicative relation-ship to relate alpha and beta diversity to regional diver-sity ( i.e., gamma diversity; regional

�

alpha

�

beta ).The practical disadvantage of this relationship—and the

reason it is not used more often by ecologists and con-servation biologists—is that diversity components arenot weighted equally when they are partitioned acrossmore than one spatial scale ( Lande 1996). However, anadditive relationship between diversity components (i.e.,regional

�

alpha

�

beta) makes it possible to calculatethe relative contributions of alpha and beta diversityto overall diversity across a range of spatial scales (Allan1975

a

; Lande 1996). Wagner et al. (2000) used additivepartitioning and concluded that beta diversity amongland-use types is more critical than beta diversity be-tween patches of the same land-use type in generatingplant species richness in agricultural landscapes. Otherresearchers have used additive partitioning to examinehow the species diversity of fruit-feeding butterflies isdistributed among and within habitats of tropical forests( DeVries et al. 1997; 1999).

We build on these studies in three ways. First, we con-duct statistical tests on additive partitioning of diversityby using a randomization approach. To date, additive par-titioning has been used primarily as a descriptive tool toquantify how diversity is partitioned among spatial (Wag-ner et al. 2000), temporal (DeVries & Walla 2001), orvertical (DeVries et al. 1997) dimensions. Second, weused the results of the statistical analyses to consider thesampling designs and conservation strategies that will bemost effective in maintaining the regional diversity of in-sect communities. Our study organisms—beetles in treecrowns—are the most diverse animal taxa in the world( Erwin 1982, 1983, 1998; Hammond 1992) and havefunctional roles as defoliators, predators, xylophages( i.e., wood feeders ), and detritivores in forest ecosys-tems ( Dajoz 2000 ). It is critical that we understandwhich spatial scales most strongly influence the diversityof beetles and other organisms with important functionalroles so that we can improve management strategies andmaintain the health of forest ecosystems. Finally, we dis-cuss how additive partitioning can be used to strengthenconservation strategies for biotic communities.

We tested the null hypothesis ( that our observed al-pha and beta diversity are obtained by a random distri-bution of individuals among samples at all hierarchicallevels) against three alternative hypotheses by analyzingspecies-richness data collected across nested spatialscales—trees, forest stands, sites, and ecoregions—in theeastern deciduous forest of the United States. The firstalternative hypothesis was that diversity is generated onfine spatial scales (e.g., individual trees within a foreststand) because of host-tree differences in community

490

Additive Partitioning across Spatial Scales Gering et al.


composition ( Mawdsley & Stork 1997; Wagner 1997;Gering & Crist 2000). A second alternative was that in-termediate spatial scales ( i.e., forest stands and sites )have stronger effects on beetle diversity because of di-versity in tree communities and differences in manage-ment history. For example, sites separated by

�

20 kmmay result in beetle communities being

�

10% similar( Davies et al. 1997). The third alternative was that thebroad-scale effects of ecoregions have the strongest in-fluence on beetle richness because biogeographical pro-cesses and historical factors may be most important indetermining community structure (Ricklefs & Schluter1993; Lawes et al. 2000; Smith 2001).

Methods

Sampling Design and Study Sites

We used a hierarchically nested design to sample insectsfrom tree crowns in the forests of southern Ohio andsoutheastern Indiana. Four hierarchical levels (correspond-ing to spatial scales) were represented in this design: ecore-gions, sites, stands, and trees. The highest level ( broadestspatial scale) was represented by two ecoregions ( Bailey1998) that differ in their glacial history and present-dayforest composition, topography, and soil types (Fig. 1).The forests of the north-central Tillplain ecoregion ( NCT)correspond to the beech-maple designation of Braun(1950) and are dominated by American beech (

Fagusgrandifolia

) and sugar maple (

Acer saccharum

) and toa lesser extent by red oak (

Quercus rubra

), white oak(

Quercus alba

), elms (

Ulmus

spp.), and ash (

Fraxinus

spp.) ( Ray & Vankat 1982; Delcourt & Delcourt 2000).The ecoregion is dominated by agriculture and is rela-tively flat as a result of glacial scouring. The topographyis characterized by ridges with shallow (10–15 m), slop-ing drainages. The forests of the Western Allegheny Pla-teau ecoregion (WAP) are typical of the mixed meso-phytic designation of Braun (1950) and are dominatedby oaks (

Quercus

spp.) and hickory (

Carya

spp.) in xe-ric areas and American beech, tulip poplar (

Lirioden-dron tulipifera

), and hemlock (

Tsuga

spp.) in mesic ar-eas (Delcourt & Delcourt 2000). Maples (

Acer

spp.) occurin both mesic and xeric areas. The ecoregion is unglaciatedand has variable soils and a topography characterized bysteep ridges and long, narrow drainages.

Three sites were nested within each of the ecoregions(Fig. 1). Hueston Woods State Park (HWSP; Preble County,Ohio ), Brookville Reservoir (BROK; Franklin County,Indiana), and Caesar Creek State Park (CACR; WarrenCounty, Ohio) were located in the NCT, and Clear CreekMetro Park ( CLCR; Fairfield County, Ohio ), ShawneeState Forest (SSFO; Scioto County, Ohio), and Edge-of-Appalachia Nature Preserve (EOAP; Adams County, Ohio)were located in the WAP (Fig. 1). We selected these parks

and nature preserves as representative of the forest typesin each ecoregion and because they have considerableconservation importance. The HWSP contains approxi-mately 100 ha of Ohio’s oldest (

�

200 years old) beech-maple forest, SFFO is the largest (24,300 ha) of Ohio’s20 state forests, and EOAP (486 ha) contains 50 rareplant and animal species and three plant communitiesthat are globally rare. Within each site, we selected fourstands (0.5–1 ha) that represented typical mesic and xe-ric areas. These stands were selected by extensive visualsurveys of differences in tree communities within sites.From those stands, we selected four individual trees torepresent the lowest hierarchical level (i.e., finest spatialscale) in the study. The selected trees were representa-tive of the dominant tree genera within the stand, as deter-mined by our surveys.

Quercus

,

Acer

,

Fagus

, and

Carya

were common, whereas

Liriodendron

,

Celtis,

and

Fraxi-nus

were encountered less frequently.

Insect Sampling

We sampled the insect communities from each tree dur-ing two sampling periods in the summer of 2000: 22May–20 June (early ) and 2–25 August ( late). We sam-pled twice during the summer because temporal changehas a significant effect on beetle community composi-tion (Gering & Crist 2000). Hence, there are two sepa-

Figure 1. A map of Ohio (OH) and surrounding states (IN, Indiana; KY, Kentucky; WV, West Virginia) show-ing the location and relative distances among the three sampling sites in each ecoregion. The sites are numbered as follows: 1, Hueston Woods State Park; 2, Brookville Reservoir; 3, Caesar Creek State Park; 4, Clear Creek Metropark; 5, Edge-of-Appalachia Nature Preserve; 6, Shawnee State Forest. Solid lines represent state boundaries, and dashed lines represent bound-aries among ecoregions.


Gering et al. Additive Partitioning across Spatial Scales

491

rate estimates of richness for each individual tree, fora total of 192 records (96 trees

�

2 sampling periods).We used the insecticide fogging technique to sampleeach tree because it is relatively unselective, does not de-pend on arthropod activity, and effectively samples adultbeetles (cf. Basset et al. 1997; Stork & Hammond 1997).At dawn on windless mornings, the crown of each treewas inundated for 3 minutes with 0.5 L of a 0.5% pyre-thrin-based insecticide (Pyrenone 50, AgrEvo Products,Berlin, Germany) emitted from a radio-controlled CurtisDyna-Fogger. During the following 2 hours, insects fellinto a ground-based array of 12, 0.5-m

2

collecting fun-nels. The funnels were located beneath each tree crownso that insects from neighboring tree crowns were un-likely to be collected. Our sampling protocol was basedon previous studies (e.g., Davies et al. 1997; Harada &Adis 1997; Wagner 1997; Gering & Crist 2000) and thedetailed evaluation of drop time, insecticide concentra-tion, and recovery time provided by Stork and Ham-mond (1997). An important aspect of our protocol wasthat collecting effort was standardized (6 m

2

) for eachtree. This enabled us to make valid statistical compari-sons of beetle diversity across trees, stands, sites, and ecore-gions, although it did not ensure an equal number of indi-viduals in each sample.

Insect Processing

We sorted beetle specimens and identified them to fami-lies and recognizable taxonomic units (RTUs or morphospe-cies; Oliver & Beattie 1993, 1996). Species grouped bycoarse morphological features often correspond closelyto expert taxonomic identification (Longino & Colwell1997), although this may vary among taxa. To validateour morphospecies designations, we sent 126 morphospe-cies to a Coleopteran systematist (D. K. Young, Universityof Wisconsin-Madison), who identified 140 actual species.Therefore, our estimates of species richness were con-servative. Most of the lumping within this subset of mor-phospecies occurred in one weevil genus (Curculionidae:

Curculio

) and one darkling beetle genus (Tenebrionidae:

Platydema

). Family and subfamily designations follow thesystematic relationships of Lawrence and Newton (1995),which differ somewhat from the familial relationships ofDownie and Arnett (1996).

Data Analysis

GENERAL

COMMUNITY

PATTERNS

We tallied species richness and abundance for the entirestudy and separately for ecoregions and sites within sam-pling periods. We also subdivided the entire richness intofamily-specific richness and identified the most abundantbeetle species ( by number of individuals).

SPECIES

-

ACCUMULATION

CURVES

We constructed species-accumulation curves to assessthe adequacy of our sampling. Species-accumulation curvesrelate sampling effort (e.g., number of trees) to the cumula-tive number of species to evaluate sampling effective-ness (e.g., Longino & Colwell 1997; Wagner 1997). Weconstructed accumulation curves with PC-ORD ( McCune& Mefford 1999), which subsamples the entire sample( the community of each tree) 500 times to determinethe number of species as a function of subsample size.Five separate accumulation curves were used to evaluatethe effects of sampling across space and time: one foreach ecoregion across both sampling periods, one foreach sampling period across both ecoregions, and onefor the entire study.

ADDITIVE

PARTITIONING

OF

DIVERSITY

Allan (1975

a

) and Lande (1996) demonstrated that re-gional diversity is the sum of alpha and beta diversitywhen alpha is the average diversity within the samplingunits in the region and beta is diversity among samplingunits. This differs from Whittaker’s (1960, 1977) multi-plicative relationship and allows researchers to additivelypartition the total diversity in a region into scale-specificdiversity components ( Fig. 2). Within the context of ourstudy, alpha and beta diversity maintain their traditionalinterpretations as within-unit diversity and between-unitdiversity on a given scale, respectively. For example,alpha

2

represents the mean number of beetle speciesamong the 24 stands, whereas beta

2

represents diversityin species among the 24 stands and beta

3

represents di-versity in species among the six sites. Because alpha di-versity at a given scale is the sum of the alpha and betadiversity at the next lowest scale (i.e., alpha

2

�

alpha

1

�

beta

1

; Allan 1975

a

; Lande 1996), the overall beetle diver-sity in our study can be described by the following for-mula: alpha

1

�

beta

1

�

beta

2

�

beta

3

�

beta

4

( Fig. 2).Lande ( 1996 ) demonstrated that any metric can be

partitioned into its components provided that it exhibitsstrict concavity, which means that the overall value ofthat metric for a pooled set of communities equals or ex-ceeds the average diversity within communities. Speciesrichness, Simpson diversity, and Shannon diversity areall strictly concave. We used all three metrics in ourstudy to account for the pure effects of species (speciesrichness) and the combined effects of richness and abun-dance (Shannon and Simpson diversity). An importantdifference between the Shannon and Simpson indexes istheir relative sensitivity to rare species. The Simpson in-dex is a dominance measure weighted toward commonspecies, whereas the Shannon index is an informationstatistic weighted equally toward rare and common spe-cies ( Magurran 1988). The Shannon index generally var-ies from 1 ( low diversity) to 5 (high diversity), whereas

492

Additive Partitioning across Spatial Scales Gering et al.


the Simpson index is always

�

1 because it is the proba-bility that two individuals drawn from the sample be-long to the same species. Both indices are calculatedfrom the proportional abundance,

P

i

, of all species inthe sample. The Shannon index is forspecies

i

�

1 to

S

n

, where

S

n

equals the number of spe-cies in the sample. The Simpson index is which is also known as the Gini coefficient ( Peet 1974;Lande 1996). Using these diversity indices, we conductedadditive partitions for the entire community in both sam-pling periods for a total of six partitions (3 metrics

�

2 sam-pling periods) by using a computer program, PARTITION.

The utility of PARTITION is that the statistical signifi-cance of level-specific alpha and beta estimates can betested through a randomization procedure. This processis called complete randomization because the numbersof individuals and species in samples at all hierarchicallevels are determined by the random placement of indi-viduals into any of the samples at the lowest level ( i.e.,the randomization is unrestricted) ( T.O.C. et al., unpub-lished data). Briefly, the species abundances from all sam-ples at a given level were combined to create a single spe-cies-abundance distribution (Solow 1993; Wiens et al.1996). The distribution is then used to randomly assignindividuals (without replacement) to samples such thatthe initial size (number of individuals) of the sample ismaintained. As with the actual data, the randomized data(samples) were partitioned and the diversity estimatesobtained. This process was repeated 10,000 times to forma null distribution of each alpha and beta estimate ( for

Pi lnPi( )∑[ ]–

1 Pi2,∑–

species richness or for Shannon or Simpson diversity) ateach level of analysis. Each of the level-specific estimateswas then compared with the appropriate null distribu-tion and used to test the null hypothesis that the ob-served alpha and beta diversity are obtained by a randomdistribution of individuals among samples at all hierarchi-cal levels.

Statistical significance was assessed by the proportionof null values that are greater than (or less than) the ac-tual estimate. For instance, if 30 out of 10,000 null val-ues were greater than or equal to an observed estimate,then the probability of obtaining ( by chance) an estimateas great or greater than the observed value was 0.003. Insuch a case, the actual estimate was significantly large.The probabilities obtained from randomization tests canbe interpreted as

p

values in traditional significance tests( Manly 1997 ). The randomization test conserves the sizeof each sample and the overall abundance of each spe-cies. This approach, together with the equal sampling ef-fort, negates the need for adjusting for unequal samplesize by rarefaction, but it does not remove differentialbias in species richness caused by different sizes amongsamples.

In addition to overall richness and diversity, we werealso interested in how spatial scale affected the richnessof rare and common species. Thus, we subdivided theentire community into rare and common species, whererare species were those with an abundance of

�

0.05%of the total community abundance within a samplingperiod and common species were those with an abun-dance of

�

0.5% of the total community abundancewithin a sampling period. Only species richness was usedin the partitioning of groups of rare and common species,for a total of four partitions ( 2 groups

�

2 samplingperiods).

The complete randomization approach is relevant totesting theory and mechanisms (e.g., patterns of aggre-gation, species distribution, and abundance) that influ-ence observed partitions of diversity (T.O.C. et al., un-published data ). An alternative approach—restrictedrandomization—can be performed by PARTITION to con-duct statistical tests on observed components of diver-sity against a null hypothesis that the observed alpha andbeta diversity at each level

k

are obtained from a randomdistribution of

k

�

1 sample units among

k

samples thatform a

k

�

1 sample. In essence, restricted randomiza-tion determines whether an observed component of di-versity at a level is greater or less than expected by ran-dom draws from the samples at the next lowest level.Restricted randomization is appropriate for testing somenull hypotheses, but it generally has less statistical powerthan complete randomization. On the regional level, forexample, we found that restricted randomization hadlimited power to detect departures from the null hy-pothesis because fewer samples were randomized thanwith complete randomization (results not shown). Be-

Figure 2. Relationships among hierarchical levels in our additive partitioning model (alpha1-5 and beta1-4 ), Whittaker’s (1960) terminology (in parentheses), and MacArthur’s (1965) designations (in brackets) of di-versity. Because of the additive relationship between levels (e.g., point � pattern � alpha, alpha � beta � gamma), we can use substitution among levels to ar-rive at the following equation (illustrated by arrows and mathematical operators) to describe the total(i.e., regional or alpha5) diversity: alpha1 � beta1 � beta2 � beta3 � beta4.


Gering et al. Additive Partitioning across Spatial Scales 493

cause we were interested in comparing patterns of sig-nificance for the partitions of rare and common species,we used the more powerful complete randomization ap-proach.

SITE CLASSIFICATION

To examine the similarity of beetle communities betweensampling periods and among sites and ecoregions, weused hierarchical cluster analysis with the Jaccard indexof similarity (Magurran 1988). The Jaccard index com-pares samples based on the presence or absence of spe-cies. We selected this similarity index to emphasize spe-cies composition and because it does not dilute theimportance of rare species, which can be numerous in can-opy beetle communities (e.g., Gering & Crist 2000). Wecombined the four stands from within each site to arrive ata composite community for that site. We performed thecluster analysis using the average linkage method in PC-ORD ( McCune & Mefford 1999).

Results

General Community Patterns

We recorded 15,907 individuals representing 583 spe-cies. Richness was not distributed evenly in time orspace. It was higher in the early than in the late sam-pling period and slightly higher in the NCT than in theWAP (Table 1). The species-abundance distribution wascharacterized by a high percentage of singletons ( i.e.,species represented by one individual) and a few domi-nant species; approximately one-third (185) of the 583total species were singletons. A similar percentage (37–46%) of species was found as singletons within ecore-gions and sampling periods (Table 1).

The dominant families in terms of species richness wereweevils (Curculionidae ), long-horned beetles (Cer-ambycidae), leaf beetles (Chrysomelidae), and click bee-tles (Elateridae) (Table 2). There was considerable varia-tion in the percentage of singletons represented withineach family ( e.g., 10% for Scarabaeidae to 47% forCerambycidae ). The dominant species ( in terms ofabundance) included two exotic species, the Asiatic oakweevil [Cyrtepistomus castaneus (Roleofs)] and the Asianladybird beetle (Harmonia axyridis Pallas). Together,they accounted for more than one-third of all individuals inthe late sampling period and approximately 20% of all indi-viduals across both sampling periods. Other dominant spe-cies included a tenebrionid, a minute brown scavengerbeetle (Latridiidae), and a carabid.

Species-Accumulation Curves

The accumulation curves showed little evidence of ap-proaching an asymptote (Fig. 3), suggesting that we didnot sample total species richness in any of the communi-ties despite the spatial and temporal extent of our sam-pling design.

Additive Partitioning

The most noticeable result from the additive partitioningwas that the highest beta component (beta4) in the modelwas always greater than expected by chance, whereas the

Table 1. Observed species richness and number and percentage of singletons of 583 beetle species (15,907 individuals) collected from 96 trees (16 in each site) sampled by insecticide fogging during early (22 May–20 June) and late (20 August – 5 September) sampling periods in six sites and two ecoregions in Ohio and Indiana.

Richness

SingletonsSingletons

(%)

Ecoregion and site* early late early late early late

North-central Tillplain 336 243 127 100 37.7 41.1HWSP 194 148 85 67 43.8 45.3BROK 190 108 77 44 41.0 41.0CACR 176 146 68 66 38.6 45.2

Western Allegheny Plateau 323 229 104 104 32.2 45.4EOAP 178 128 77 59 43.2 46.0SSFO 218 116 71 53 32.6 45.6CLCR 182 120 83 56 45.6 46.6

*Abbreviations: HWSP, Hueston Woods State Park; BROK, BrookvilleReservoir; CACR, Caesar Creek State Park; EOAP, Edge-of-AppalachiaNature Preserve; SFFO, Shawnee State Forest; CLCR, Clear CreekMetropark.

Table 2. Dominant families (species richness) and number of singletons within each family for beetles collected by insecticide fogging from 96 trees nested within two ecoregions in southern Ohio and southeastern Indiana.

FamilyNo. of

species*No. of

singletons

Curculionidae (snout beetles and weevils) 70 19

Cerambycidae ( long-horned beetles) 51 24

Chrysomelidae ( leaf beetles) 47 5Elateridae (click beetles) 47 13Anobiidae (death-watch beetles) 23 4Coccinelidae ( ladybird beetles) 21 4Tenebrionidae (darkling beetles) 21 5Mordellidae (tumbling flower

beetles) 20 3Cleridae (checkered beetles) 20 7Staphylinidae (rove beetles) 20 7Buprestidae

(metallic wood boring beetles) 14 3Carabidae (ground beetles) 14 6Cantharidae (soldier beetles) 13 4Nitidulidae (sap-feeding beetles) 11 5Scarabaeidae (scarab beetles) 10 1

*Cumulative value for sampling conducted during early (22 May–20 June) and late (20 August–5 September) sampling periods.

494 Additive Partitioning across Spatial Scales Gering et al.


alpha component was always lower than expected (Ta-ble 3). This was evident across all combinations of group,index, and sampling period, despite the fact that the al-pha component accounted for a substantial proportionof the richness of common species (Fig. 4) and a largeproportion of the Shannon and Simpson diversity for theentire community ( Fig. 5). There were also differencesbetween Shannon and Simpson diversity in the percent-age of total diversity accounted for by alpha1, which wasgreater for Simpson diversity than for Shannon diversity(Fig. 5).

Differences also occurred between rare and commonspecies in the percentage of overall richness distributedamong levels of the hierarchical model (Table 3; Fig. 4).Deviations from expected values were positive for rare spe-cies only at the highest level in the partition, whereas devi-ations from expected values were always positive for com-mon species throughout the higher levels in the partition.The reverse was true at lower levels. Only beta4 was consis-tently greater than expected for rare species (Table 3).

Site Classification

As expected from previous studies, our cluster analysisidentified strong differences in community compositionbetween sampling periods ( Fig. 6). Sites were grouped

according to their ecoregions in both sampling periods.In general, there was a higher degree of similarity be-tween ecoregions and among sites in the late samplingperiod than in the early sampling period.

Discussion

In principle, additive partitioning is simply a mathemati-cal approach to describing the relative contributions ofcomponents to a sum total. It can be used on a variety ofmetrics and can quantify spatial and temporal patternsof diversity, size (e.g., basal area), abundance, and otherecological data. In practice, however, this approach hasnot been applied to many ecological phenomena. Theexceptions include Wagner et al.’s (2000) study of plantspecies richness in agricultural landscapes, DeVries etal.’s studies (1997, 1999; see also DeVries & Walla 2001)of temporal and spatial patterns of butterfly diversity inrainforests, and Allan’s (1975b) study of benthic insectdiversity in an alpine stream. Additive partitioning of di-versity has also been used in other studies, but wasclearly not the main emphasis of the research (e.g., Hol-land & Jain 1981; Barker et al. 1983). Even so, it has con-siderable potential because it allows conservation biolo-gists to understand the contributions of alpha and betadiversity to total diversity over a range of user-definedspatial scales.

Our finding that broad-scale beta components of di-versity were greater than expected supports the hypoth-esis that the effects of ecoregions structure the richnessand composition of arboreal beetles in the eastern decid-uous forest. This is supported by our cluster analysis,

Figure 3. Accumulation curves for beetle species richness from 96 trees sampled by insecticide fogging during early (22 May–20 June) and late (2–25 August) sam-pling periods in two ecoregions (NCT, northcentral Tillplain; WAP, Western Allegheny Plateau) in Ohio and Indiana. Each ecoregion contained 48 trees in each sam-pling period, for a total of 192 trees across both seasons(overall accumulation curve). Error bars on the overall accumulation curve represent one standard error.

Table 3. Significance values* for tests of actual diversity estimates from additive partitioning against null estimates from the PARTITION program.

Richness Shannon Simpson

Group Level E L E L E L

Entire community beta4 � � � � � �beta3 � ns � � � �beta2 � � � � � �beta1 � � � � � �alpha � � � � � �

Rare species beta4 � �beta3 � �beta2 � � na nabeta1 � �alpha � �

Common species beta4 � �beta3 � �beta2 � � na nabeta1 ns nsalpha � �

*All values determined at the 0.05 level. Abbreviations: �, signifi-cantly small; �, significantly large; ns, not significant; E, early sam-pling period; L, late sampling period; na, partition not conducted.



Figure 4. Percentage of to-tal beetle species richness explained by alpha and beta components of diver-sity on four spatial scales: trees, forest stands, sites, and ecoregions. The contri-butions to the total richness for each scale were deter-mined by the additive parti-tioning of diversity. Total species richness for each of the three groups (denoted on the x-axis) is the num-ber at the top of each bar. Early (22 May–20 June.) and late (2–25 August) are sampling periods.

Figure 5. Percentage of total Shannon and Simpson diversity explained by al-pha and beta components of diversity on four spatial scales: trees, forest stands, sites, and ecoregions. Contributions to to-tal diversity for each scale were deter-mined by an additive partitioning of di-versity.



which identified strong differences in community com-position between ecoregions and among sites. Thesetwo findings point to the importance of ecoregionalfactors in determining community composition andrichness. The NCT and WAP differ in topography, soils,dominant tree species, and land-use patterns because oftheir biogeographic histories (Bailey 1998; Delcourt &Delcourt 2000). Any one of these factors alone is un-likely to explain the differences in overall beetle com-munity composition, although certain factors may explainthe differences in some taxonomic groups. Soil type, forexample, may influence the richness of beetle families(e.g., Scarabaeidae) that have soil-dwelling larvae, just astree composition may be important to herbivorous bee-tle families (e.g., Curculionidae). Land-use factors alsoinfluence beetle communities (Romero-Alcaraz & Avila2000) so that the observed regional differences in beetlecommunities might also be explained by the greater ag-ricultural land use in the NCT than in the WAP. In es-sence, additive partitioning identifies a pattern that en-ables conservation biologists to more readily identify theprocesses that might be responsible for observed spe-cies diversity ( Wagner et al 2000). Here it appears thatmore detailed studies on the effects of tree communitycomposition, soils, or land use on beetle diversity may en-hance our understanding of the regional processes thatgenerate beetle diversity.

In addition to identifying the importance of broad-scale effects, additive partitioning also identified signifi-cant differences between rare and common species inthe percentage of overall richness explained by levels inthe hierarchical model. The richness of rare species wasenhanced (i.e., greater than expected) only at the high-est levels in the model, whereas significant enhance-ment of common species richness was evident through-out all levels (except tree-level alpha) in the models. Weinterpret this as evidence that the richness of rare spe-cies was strongly influenced by beta diversity betweenecoregions and among sites. More important, the parti-tioning results for the entire community mirrored thoseof the rare species, indicating that rare species maybe driving the patterns of the entire community. This isprobable, because the rare species, as we have definedthem, accounted for a high percentage (36–47%) of thespecies in the community. It is unclear whether the rarespecies in our study are sampling artifacts, biologicallymeaningful, or truly rare (Rabinowitz 1981; Gaston 1994),but the proportion of singletons we recorded is typical ofother canopy insect communities. Despite working in dif-ferent locations, Allison et al. (1997; Papau New Guinea)and Davies et al. (1997; Venezuela) recorded 40–50% sin-gletons in their studies or found high diversity values thatindicated a high proportion of singletons.

The consistent proportion of rare species in insecti-cide fogging studies (Erwin 1998) can be explained, inpart, by our partitions of beetle diversity. For example,our finding that the species-accumulation curve did notreach an asymptote suggested that our sampling de-sign—despite its spatial extent—was not sufficient to ac-count for all the species present in the sampling area.The partitioning of richness for the rare species, and to alesser extent for the entire community, provides an ex-planation for this well-documented pattern. As samplingdesigns incorporate a greater spatial extent, saturationof accumulation curves is less likely because rare specieswill be encountered more frequently at the broadest scales.For this reason, accumulation curves should not be ex-pected to become saturated in spatially extensive stud-ies of hyperdiverse communities (Palmer 1995; Novotny& Basset 2000; Summerville et al. 2001). The only wayto force accumulation curves for hyperdiverse commu-nities toward saturation is to sample intensively over alimited spatial area. Basset and Arthington (1992), for ex-ample, nearly flattened their cumulative saturation curvesby sampling (using restricted canopy fogging) and resam-pling (eight times) the same individual trees in a 35-hastand of warm subtropical forest.

The preponderance of rare species in spatially exten-sive sampling designs presents conservation biologistswith a peculiar dilemma. In most cases, the first step inconservation programs is to produce a comprehensivespecies list within the region of interest. The best way toaccomplish this is to sample intensively over a limited

Figure 6. Degree of similarity between beetle commu-nities in six different sites and two different ecoregions of the eastern deciduous forest in southern Ohio and southeastern Indiana. Early (22 May–20 June) and late (2–25 August) are sampling periods. Abbrevia-tions: HWSP, Hueston Woods State Park; BROK, Brookville Reservoir; CACR, Caesar Creek State Park; EOAP, Edge-of-Appalachia Nature Preserve; SFFO, Shawnee State Forest; CLCR, Clear Creek Metropark. The distance measure is percent similarity based on the Jaccard coefficient.



spatial area, as indicated above. Yet our diversity parti-tioning suggests that a significant percentage of speciesrichness is generated by diversity among sampling units(i.e., beta diversity) at relatively broad scales. Therefore,there is a trade-off between the spatial extent of sam-pling and the thoroughness of the species inventory. Aspatially intensive sampling design will probably pro-duce a thorough species list but miss many rare speciesthat occupy neighboring habitats. Spatially extensivesampling designs, in contrast, produce unsaturated accu-mulation curves but provide a better assessment of theheterogeneity of species diversity. Palmer and White (1994)reject the idea of a “regional” species-area curve and pointout, as we have, that scale-dependent processes (e.g., dis-proportionate accumulation of rare species at broadscales) can render accumulation curves ineffective forestimating the number of species in a given area. Addi-tive partitioning was particularly helpful in arriving atthis conclusion because it identified significantly largebeta diversity as the reason for the unsaturated accumu-lation curves.

With a spatially intensive sampling design, we mayhave concluded that tree-crown beetle communities areoverwhelmed by a few dominant and exotic speciessuch as the Asiatic oak weevil. In fact, our partitioning ofSimpson diversity indicated the extent to which finespatial scales are dominated by common (and exotic )species. Shannon diversity reflected this pattern to alesser extent because it gave equal weight to rare andcommon species. An important point, then, is that dif-ferent types of diversity indices (e.g., dominance indicesand evenness indices) should be used with species rich-ness to gain a full understanding of how rare and com-mon species contribute to overall regional diversity. Forexample, we were able to determine that rare speciesrepresent a critical component of the community andcontribute to differences between ecoregions, whereasthe richness of common species was explained by alphadiversity at the finest spatial scales.

These findings emphasize the need for programs of re-gional conservation planning. For example, the protec-tion and acquisition of additional sites within an ecore-gion will be more effective in conserving insect diversitythan local-scale management approaches that strive toincrease tree species diversity within stands. Our find-ings further suggest that management approaches forrare species will be sufficient to maintain common spe-cies because the important spatial scale for rare species( i.e., ecoregions) also encompasses the spatial scalesthat appear to be important for the richness and diver-sity of common species. This is noteworthy becausesuch management accomplishes two goals: conservationof species richness, which is produced by rare species,and maintenance of the functional aspect of forest insectcommunities, which is driven by common species thathave greater effects on host trees and food-web interac-

tions. Thus, even the alpha diversity produced by com-mon and exotic species has an important role in conser-vation strategies.

Finally, additive partitioning represents a contrast tosource-sink and metapopulation approaches because itis a multispecies method of analyzing biodiversity. Insome cases, the patterns of species richness and diver-sity—not the processes that determine them—will bemore useful for determining conservation strategies. Thespecies-area relationship, for example, simply describesspecies richness as a function of area without making as-sumptions about the processes that may be driving therelationship, even though it is clear that colonization, spe-cies coexistence, and numerous scale-specific processescan affect the shape of the curve ( MacArthur & Wilson1967; Shmida & Wilson 1985; Palmer & White 1994).Similarly, additive partitioning will be useful in situationswhere researchers wish to describe change in speciesrichness or diversity over spatial or temporal scales with-out invoking specific processes. Source-sink and meta-population models will continue to be more useful insingle-species studies, in which processes such as dis-persal and mortality are critical for determining conser-vation strategies. These differences suggest that additivepartitioning is a valuable tool for conservation biologistsbecause it complements existing approaches while pro-viding a unique way to understand community diversityover space and time.

Acknowledgments

The Nature Conservancy’s Ecosystem Research Program,the Miami University Committee on Faculty Research,and the Ohio Board of Regents Research Challenge Pro-gram generously provided funding for this project. C.Yeager, N. Anderson, J. Kahn, J. Veech, K. Summerville,and D. Golden helped with insect sampling. N. Andersonalso contributed greatly to insect processing. D. Claus-sen, A. Rypstra, M. Vanni, J. Vankat, K. Summerville, andK. McGrath provided comments on the experimental de-sign and the general format of the manuscript. R. Landeand P. DeVries also reviewed the manuscript; we thankthem for their valuable and insightful comments. We aregrateful to the landowners and managers of the stateparks, metroparks, reservoirs, and nature preserves usedin this study. Without their cooperation, it would nothave been possible to conduct this study. This paperwas written in partial fulfillment of the requirements forthe doctoral degree of J. Gering.

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