Food Webs, Body Size, and Species Abundance in Ecological Community Description TOMAS JONSSON, JOEL E. COHEN, AND STEPHEN R. CARPENTER I. Summary............................................... 2 A. TrivariateRelationships................................ 2 B. BivariateRelationships ................................ 3 C. UnivariateRelationships............................... 4 D. EVectof FoodWeb Perturbation ........................ 4 II. Introduction ............................................ 4 A. Definitions.......................................... 7 III. Theory: Integrating theFoodWeb andthe Distributions of Body Sizeand Abundance ...................................... 9 A. PredictingCommunity Patterns.......................... 10 B. TheDistribution of Body Sizes.......................... 13 C. Rank-Abundanceand FoodWeb Geometry................ 15 D. Linkingthe FoodWeb to the Relationship BetweenBody Size andNumerical Abundance ............................. 16 E. Trophic Pyramidsand theRelationship BetweenConsumer andResource AbundanceAcross Trophic Levels ............ 18 IV. Data:TuesdayLake ...................................... 20 A. TheManipulation.................................... 21 B. TheData........................................... 22 V. Results: Patternsand Relationships in the PelagicCommunity of TuesdayLake ........................................... 25 A. TrivariateDistributions: FoodWeb, BodySize, and Abundance 25 B. BivariateDistributions................................. 29 C. UnivariateDistributions ............................... 51 VI. EVects ofa FoodWeb Manipulation onCommunity Characteristics. 60 A. SpeciesComposition andSpecies Turnover................. 62 B. FoodWeb,Body Size, andAbundance.................... 62 C. FoodWeband Body Size.............................. 62 D. FoodWeband Abundance............................. 63 E. BodySize andAbundance.............................. 63 F. FoodWeb.......................................... 64 G. BodySize........................................... 65 H. Abundance ......................................... 65 I. ConclusionsRegarding theManipulation.................. 67 VII. Data Limitationsand EVectof Variability ..................... 68 ADVANCESINECOLOGICALRESEARCHVOL.36 (cid:1)2005byTomasJonsson,JoelE.Cohen, 0065-2504/05$35.00 andStephenR.Carpenter Allrightsreserved 2 T. JONSSON, J.E. COHEN, AND S.R. CARPENTER VIII. Conclusions............................................. 72 Acknowledgments ............................................. 73 Appendices................................................... 74 References ................................................... 78 I. SUMMARY Thischapterdemonstratesthatmethodstodescribeecologicalcommunities can be better understood, and can reveal new patterns, by labeling each species that appears in a community’s food web with the numerical abun- danceandaveragebodysizeofindividualsofthatspecies.Weillustrateour newapproach,andrelateittopreviousapproaches,byanalyzingdatafrom the pelagic community of a small lake, Tuesday Lake, in Michigan. Although many of the relationships we describe have been well studied individually, we are not aware of any single community for which all of theserelationshipshavebeenanalyzedsimultaneously.Anoverviewofsome of the results of the present study, with further theoretical extensions, has been published elsewhere (Cohen et al., 2003). Ournewapproachyieldsfourmajorresults.Thoughmanypatternsinthe structure of an ecological community have been traditionally treated as independent, they are in fact connected. In at least one real ecosystem, many of these patterns are relatively robust after a major perturbation. Some of these patterns may be predictably consistent from one community to another. Locally, however, some community characteristics need not necessarily coincide with previously reported patterns for guilds or larger geographicalscales. We describe our major findings under these headings: trivariate relation- ships (that is, relationships combining the food web, body size, and species abundance);bivariaterelationships;univariaterelationships;andtheeVects of food web perturbation. A. Trivariate Relationships SpecieswithsmallbodymassoccurlowinthefoodwebofTuesdayLakeand are numerically abundant. Larger-bodied species occur higher in the food web and are less numerically abundant. Body size explains more of the variation in numerical abundance than does trophic height. Body massvariesalmost12ordersofmagnitudeandnumericalabundancevaries by almost 10 orders of magnitude, but biomass abundance (the product of body mass times numerical abundance) varies by far less, about FOODWEBS,BODYSIZE,ANDSPECIESABUNDANCE 3 5ordersofmagnitude.Thenearlyinverserelationshipbetweenbodymassand numericalabundance,andtherelativeconstancyofbiomass,areillustratedby anewfoodwebgraph(Fig.3), which shows the food web in the plane with axescorresponding tobody mass and numerical abundance. B. Bivariate Relationships The pelagic community of Tuesday Lake shows a pyramid of numbers but notapyramidofbiomass.Thebiomassofspeciesincreasesveryslowlywith increasing body size, by only 2 ordersof magnitude as body mass increases by12ordersofmagnitude.The biomass-body sizespectrumisroughly flat, as in other studies at larger spatial scales. Prey body mass is positively correlatedtopredatorbodymass.Preyabundanceandpredatorabundance are positively correlated for numerical abundance but not for biomass abundance. Body size and trophic height are positively correlated. Body size and numerical abundancearenegatively correlated. The slope of the linear regression of log numerical abundance as a func- tionoflogbodysizeinTuesdayLakeisnotsignificantlydiVerentfrom(cid:1)3/4 across all species but is significantly greater than (cid:1)1 at the 5% significance level. This (cid:1)3/4 slope is similar to that found in studies at larger, regional scales,butdiVerentfromthatsometimesobservedatlocalscales.Theslope within the phytoplankton and zooplankton (each group considered sepa- rately) is much less steep than (cid:1)3/4, which is in agreement with an earlier observation that the slope tends to be more negative as the range of body massesoftheorganismsincludedinastudyincreases.Anovelcombination of thefood web with dataon body size and numerical abundance, together with an argument based on energetic mechanisms, refines and tightens the relationship between numerical abundance and body size. The regression of log body mass as a linear function of log numerical abundanceacrossallspecieshasaslopenotsignificantlydiVerentfrom(cid:1)1, butsignificantlylessthan(cid:1)3/4.TheestimatedslopeissignificantlydiVerent from the reciprocal of the estimated slope of log numerical abundance as afunctionoflogbodymass.Thus,iflogbodymassisviewedasanindepen- dentvariableandlognumericalabundanceisviewedasadependentvariable, theslopeofthelinearrelationshipcouldbe(cid:1)3/4butcouldnotbe(cid:1)1atthe5% significance level. Conversely, if log numerical abundance is viewed as an independent variable and log body mass as a dependent variable, the slope of the linear relationship could be (cid:1)1 but could not be (cid:1)4/3 (which is the reciprocal of (cid:1)3/4) at the 5% significance level. While a linear relationship is a good approximation in both cases, Cohen and Carpenter (in press) showedthatonlythemodelwithlogbodymassastheindependentvariable meets the assumptions of linear regressionanalysis for these data. 4 T. JONSSON, J.E. COHEN, AND S.R. CARPENTER C. Univariate Relationships The food web of Tuesday Lake has a pyramidal trophic structure. The number of trophic links between species in nearby trophic levels is higher than would be expected if trophic links were distributed randomly among the species. Food chains are shorter than would be expected if links were distributed randomly. Species low in the food web tend to have more pre- datorsandfewerpreythanspecieshighintheweb.Thedistributionofbody size is right-log skewed. The rank-numerical abundance relationship is approximately broken-stick within phytoplankton and zooplankton while the rank-biomass abundance relationship is approximately log-normal across all species. The slope of the right tail of the body mass distribution is much less steep than has been suggested for regional scales and not log-uniform asfound at local scalesfor restricted taxonomicgroups. D. EVect of Food Web Perturbation The data analyzed here were collected in 1984 and 1986. In 1985, three speciesofplanktivorousfisheswereremovedandonespeciesofpiscivorous fishwasintroduced.ThedatarevealsomediVerencesbetween1984and1986 inthecommunity’sspeciescompositionandfoodweb.Mostothercommu- nity characteristicsseem insensitiveto this major manipulation. DiVerentfieldsofecology havefocusedondiVerentsubsetsofthebivari- ate relationships illustrated here. Integration of the relationships as sug- gested in this chapter could bring these fields closer. The new descriptive data structure (food web plus numerical abundance and body size of each species) canpromotetheintegrationoffoodweb studieswith, forexample, population biology andbiogeochemistry. II. INTRODUCTION Anecologicalcommunityisasetoforganisms,withinamoreorlessdefined boundary, that processes energy and materials. There are many diVerent notionsofanecologicalcommunityandmanyapproachestodescribingand understandingcommunitystructureandfunction(Paine,1980;May,1989). Here we integrate some of these approaches. A food web lists the kinds of organisms in a community and describes which kinds of organisms eat which other organisms. The food web ap- proach(e.g.Cohen,1989;Lawton,1989)triestounderstandthecommunity throughadetailedstudyofthetrophicinteractionsamongthespecieswithin the community. Sometimes, it focuses on the population dynamic eVects of species on each other (e.g. Pimm, 1982). FOODWEBS,BODYSIZE,ANDSPECIESABUNDANCE 5 The pattern catalog approach tries to understand communities through patternsinthedistributionofspeciescharacteristicsindiVerentcommunities and under diVerent circumstances. For example, rank-abundance relations, bodysizedistributions,abundance-bodysizeallometry,andbiomassspectra are all examples of community characteristics that emerge from species characteristics. How the trophic relations among the species aVect these patternsand vice versa haslargelybeen ignored. In this chapter, we integrate these diVerent approaches. We augment a traditional food web with information on two species characteristics, body size, and abundance, without presenting or testing a particular theory ofcommunityorganization.Instead,weadvocatetheideathatmanyprevi- ously studied relationships and distributions can be better understood by connecting thefoodweb with speciesabundance and body size. This approach will be illustrated and tested by data on the pelagic com- munity of Tuesday Lake, a small lake in Michigan, in 1984 and 1986. In 1985,thelakewassubjectedtoamajorperturbation(seeSectionIV.A):the three incumbent fish species were removed and a new fish species was introduced.ThemanipulationsignificantlyaVectedanumberofparameters (e.g.,primaryproduction,chlorophyllconcentration,zooplanktonbiomass; Carpenter and Kitchell, 1988). Until the present analysis, the eVects of the manipulation on community characteristics, such as the distributions of bodysizeandabundanceortherelationshipbetweenthem,wereunknown. WeanalyzehowtheperturbationaVectedseveralcommunity-levelpatterns. Cohen (1991) suggested that body size and abundance of the species in a community could be related to a ranking of the body size of the species by simple allometric or exponential functions. If this relation is confirmed by empirical data, it raises the possibility of predicting a large number of community patterns using only a few input variables. For example, the distributions of body size and abundance in a community could then be approximated from a single variable, the number of species, and a small numberofcoeYcients.UsingthedataofTuesdayLake,wedemonstratethe existence of simple relationships that could be tested in other communities. If these relationships are subsequently found to hold in general, they could then be used topredict thestructure of additionalecological communities. Many studies of relationships among species characteristics have focused ongeographicalscalesotherthanthat ofthelocalecosystem. Forexample, thebodysize-abundancerelationshipisoftenstudiedusingdatafromalarge setofcommunities(e.g.Damuth,1981).Suchstudiesarehamperedbyalack of information on the ecological constraints operating on species within a particular local community because the studies average data over several communities.Otherstudieshavefocusedonparticulartaxaorguildswithin acommunity.Thisfocusreducesthenumberofspecies,rangeofbodysizes, or range of trophic levels included when compared to a whole community. 6 T. JONSSON, J.E. COHEN, AND S.R. CARPENTER The present study combines data on virtually all the nonmicrobial pelagic species of Tuesday Lake. The organisms, from phytoplankton to fish, span approximately12ordersofmagnitudeinbodymass andupto10ordersof magnitude in numerical abundance. We compare some community charac- teristics in the local community of Tuesday Lake with previously reported patterns forspecific taxaor largergeographic scales. ThischapterisnotprimarilyaboutTuesdayLake.Othershavedescribed Tuesday Lake in much more detail (e.g. Carpenter and Kitchell, 1988, 1993a). Rather, we use Tuesday Lake to illustrate how many previously unrelated descriptions of communities can be brought together (Table 1). The main theme of the chapter is that when data on body size and abun- dance are associated with each species in a food web, then the community- wide distributions of body size, abundance, and feeding relations become Table 1 Descriptionsofanecologicalcommunitythatcombineinformationonthe foodweb,bodysize,andabundance(numberofindividualsorbiomass) Distributions and Food Body Section relationships analyzed web size Abundance discussed Foodweb statistics The distribution of trophiclinks The distribution of chainlengths U V.C.1 Trophic generality and vulnerability The distribution of bodysize U V.C.2 Rank-bodysize The distribution of numericaland U V.C.3 biomassabundance Rank-abundance Predator-prey body size allometry Body size vs. trophicheight Trophic generality and U U V.B.1 vulnerability vs.body size Abundance-body size allometry Abundance-body size spectrum U U V.B.2 Diversity, bodysize and abundance Predator-prey abundance allometry Abundance vs. trophicheight Ecological pyramids U U V.B.3 Trophic generality and vulnerability vs.abundance Trophic position, body size U U U V.A andabundance ReprintedfromCohenetal.(2003)withpermissionfromtheNationalAcademyofSciences. FOODWEBS,BODYSIZE,ANDSPECIESABUNDANCE 7 connected, orderly, and intelligible in new ways. Since the relationship among these three attributes aVects many other aspects of an ecological community, awareness of these connections contributes to a better overall understanding of communitystructure and function. This chapter is organized as follows. Section II.A presents crucial defini- tions. Section III presents some theoretical predictions for the relationships among the food web and the distributions of body size and abundance. Section IV describes Tuesday Lake, how the data on the food web, body size, and abundance of the species were collected, and the manipulation in 1985. SectionVpresentsand analyzesthedataon TuesdayLake,including the data from 1984 and 1986 but emphasizing the data of 1984. Section VI comparesthedataof1984and1986toseetheeVectsoncommunitypatterns of the 1985 perturbation. Section VII discusses limitations in the data and theeVectofvariability.SectionVIIIsummarizesthenewinsightsgainedby an integrated trivariateapproach. A. Definitions Body mass is the average body mass (kg) of an individual of a species. Allindividualsareincluded,notonlyindividualsconsideredadults.Numer- ical abundance means the concentration of individuals (individuals/m3). Biomass abundance is the total amount of biomass per volume (kg/m3) of a species.Bothnumericalabundanceandbiomassabundancedependcrucially on the reference volume of water in which average concentration is esti- mated. Section IV.B describes how these characteristics were measured for diVerent species in Tuesday Lake. Throughout this chapter, the reference volumeofwaterforbothestimatesofabundanceistheepilimnion,whichis roughly equivalentto the photic zone,in Tuesday Lake. A basal species is a species recorded as eating no other species. Usually a basalspeciesisautotrophic,buttheabsenceofevidencethatagivenspecies consumes any other species may be due to incomplete observation (for example, of endosymbionts). A top species is a species recorded as having no other species as predators or consumers. The absence of evidence that a given species is eaten by any other species may be due to incomplete observation (for example, of parasites inside individuals of the species). An intermediatespeciesisaspeciesthatconsumesatleastoneotherspeciesand isconsumedbyatleastoneotherspeciesintheweb.Anisolatedspeciesisa speciesthat hasno otherspecies reported as predators orprey. Afoodchain(A,B,C,(cid:2)(cid:2)(cid:2),X,Y,Z)isanorderedsequenceofatleasttwo speciesA,B,C,(cid:2)(cid:2)(cid:2),X,Y,Z,whereAisabasalspeciesandZisatopspecies such that each species (except the last, here denoted Z) is eaten by the next speciesinthelist. The trophic position ofa speciesinafoodchainis1þthe 8 T. JONSSON, J.E. COHEN, AND S.R. CARPENTER numberofspeciesprecedingitintheorderedlistofspeciesinthechain.For example, in the food chain (A, B, C,(cid:2)(cid:2)(cid:2), X, Y, Z), species A has trophic position1,speciesBhastrophicposition2,speciesChastrophicposition3, and the trophic position of Z is equal to the number of species in the list. Trophic height isthe average trophicposition of aspecies in all food chains ofwhichitisapart.Probablybecauseoflargesize(duetocolonialityand/or spines), a few phytoplankton species were not eaten by the herbivores in Tuesday Lake. These isolated species are left out of some analyses. A food web is a collection of cross-linked food chains and sometimes includes, in addition,isolatedspecies.Connectanceiscalculatedas2(cid:4)L/(S2(cid:1)S),where L isthenumberofnoncannibalisticlinks andSisthenumber ofconnected (that is, nonisolated) species in a food web. The unlumped web of Tuesday Lake refers to the food web describing the trophic interactions among the species listed in Appendices 1A and 2A. In the trophic-species webs, species withidenticalsetsofpreyandpredatorsareaggregatedintotrophicspecies. Linkage density (d) is the number of links per species (i.e., d ¼ L/S). The trophic vulnerability (V) and the trophic generality (G) of a species are the number of predators and the number of prey, respectively, that species has (Schoener, 1989). For each consumer species j that eats a nonempty set of resource species R, we define the available resource biomass B and the available resource j j productivityP asthesumoftheavailableresourcebiomassortheavailable j resource productivity, respectively, of each of the resource species eaten by consumer j, that is, B ¼XBAi ¼XNAi(cid:4)BMi ð1Þ j V V i2Rj i i2Rj i and P ¼XPi ¼XNAi(cid:4)BMi3=4(cid:2) ð2Þ j V V i2Rj i i2Rj i The available biomass abundance of a resource species i is calculated as thetotalbiomassabundanceBA ofspeciesidividedbythetrophicvulnera- i bilityV,that is,numberofconsumer speciesthat theresourcespeciesihas i (including, of course, consumer species j). The available productivity of a resourcespeciesiiscalculatedasthetotalproductivityP ofspeciesidivided i by V. The total productivity (kg (cid:4) year(cid:1)1/m3) of a resource species is i calculated as the numerical abundance (NA) of the resource species times i the productivity of an individual, approximated by BM3/4. The available i resourcebiomassB andtheavailableresourceproductivityP bothrequire j j trivariate information regarding the food web (the resource species of each consumer,andtheconsumerspeciesofeachofthoseresourcespecies),body FOODWEBS,BODYSIZE,ANDSPECIESABUNDANCE 9 masses, and numerical abundance. In these measures, dividing by the num- ber of consumer species V reflects the crude assumption, made for want of i better information, that each consumer of a given resource species gets an equalshareoftheresource’sbiomassorproductivity.Thiscrudeassumption could be refined if quantitative data were available on the flows of energy along each trophiclink. A random variable, its frequency distribution, or a set of numbers is said to be right-skewed if its third central moment is positive, left-skewed if its third central moment is negative, and symmetric if its third central moment is zero. (The third central moment is the sum of the cubes of the deviations of each number from the mean.) A random variable is said to be right-log skewed if the logarithm of the random variableisright-skewed. Departure from normality of a distribution is assessed using measures of kurtosis and symmetry (D’Agostino and Pearson, 1973). Characteristics of the observed food web are compared with predictions of a null-model. An appropriatenull-modelforthetrophic-specieswebisthecascademodel(see SectionIII.A.1).Thecascademodel’spredictionsforthemeanandexpected maximal foodchainlength,numberofbasal,intermediate,andtopspecies, andnumberoflinksamongthesespeciescategorieswerecalculatedusingthe formulasinCohenetal.(1986).Alllogarithmsinthischapterarecalculated with base10. III. THEORY: INTEGRATING THE FOOD WEB AND THE DISTRIBUTIONS OF BODY SIZE AND ABUNDANCE This section outlines quantitative models and qualitative theoretical argumentsto guide theanalysis ofthe datain subsequentsections. A basic question of community ecology is whether ‘‘the populations at a site consist of all those that happened to arrive there, or of only a special subset, those with properties allowing their coexistence’’ (Elton, 1933). Many ecologists probably agree that communities are not purely randomly constituted, apart from stochastic processes (e.g., those related to coloniza- tion and extinction, MacArthur and Wilson, 1967). For example, it is well known that large species usually are less numerically abundant and are positionedhigherin a food web than small species. Our goal is to shed additional light on the structure of an ecological community by looking in detail at the univariate, bivariate, and trivariate patterns that involve the food web and the distributions of body size and abundancein acommunity(Table 1). Thistheoretical section reviewssome simple models of these patterns. The models use only a few input 10 T. JONSSON, J.E. COHEN, AND S.R. CARPENTER variables.ThemodelswillbetestedinsectionVusingthedatadescribedin Section IV. A. Predicting Community Patterns 1. The CascadeModel The cascade model offoodweb structure tries topredictmultiplefoodweb properties from the simplest assumptions possible. A leisurely nontechnical summaryofthecascademodelanditsmotivationisgivenbyCohen(1989). Cohen et al. (1990) give a detailed theoretical and empirical exposition. Carpenter and Kitchell (1993a) also use the term ‘‘cascade model.’’ Their model describes the dynamics of multiple populations interacting through food webs following major perturbations. As an example of a ‘‘trophic cascade’’ in Carpenter’s sense, an increase in the abundance of the top trophic level leads to alternating decrease and increase in the abundance of trophic levels below. In this chapter cascade refers only to the following strictlystaticmodeloffoodwebstructureinthesenseofCohenetal.(1990). Let Sdenotethe number oftrophic speciesin acommunity. Supposethe trophic species can be ordered from 1 to S (although this ordering is not a priori visible to an observer), and suppose that the ordering specifies a pecking order for feeding, so that any species j in this hierarchy or cascade canfeedonanyspeciesionlyifi<j(whichdoesn’tnecessarilymeanthatj doesfeedoni,onlythatjcanfeedoni).Thus,speciesjcannotfeedonany species with a number k if k (cid:9) j. Second, the cascade model assumes that each species eats any species below it according to this numbering with probability d/S, independently of all else in the web. Thus, the probability that species jdoes not eat species i < jis 1 (cid:1) d/S.These assumptions—that thespeciesareorderedandthattheprobabilityoffeedingisproportionalto 1/S, and that diVerent feeding links are present or absent independently of one another—are all there isto the cascade model. The cascade model has one parameter, d. To compare the model with an individual food web, the parameter d may be estimated from the observed number of species S and the number of links L as d ¼ 2L/(S (cid:1) 1). To comparethemodelwiththepropertiesofacollectionoffoodwebs,assum- ing that the parameter d is the same in all of them, the parameter d may be estimatedfromthetotalnumber ofspeciesandthetotalnumber oflinksin all webs combined or from the set of pairs (S, L) for each web. All predic- tions derive solely from the number of species and the number of links. No otherparameters are free. The cascade model makes a surprising variety of predictions about food webs (Cohen, 1989; Cohen et al., 1990, 1991) such as the number of basal,