Brown, Marquet, Taper - 1993 - of Body Size Consequences

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Vol.142,No.4TheAmericanNaturalistOctober1993EVOLUTIONOFBODYSIZE:CONSEQUENCESOFANENERGETICDEFINITIONOFFITNESSJAMESH.BROWN,PABLOA.MARQUET,ANDMARKL.TAPER*DepartmentofBiology,UniversityofNewMexico,Albuquerque,NewMexico87131SuibmittedJuly24,1992;RevisedOctober26,1992;AcceptedOctober30,1992Abstract.-Wedevelopageneralmodelfortheeffectofbodysizeonfitness.Wedefinefitnessasreproductivepower,therateofconversionofenergyintooffspring.Reproductivepowerisassumedtobelimitedbyatwo-stepprocess:first,therateofacquisitionofenergyfromtheenvironment,whichscalesallometricallyasbodymassraisedtoapproximatelythe0.75power,andthentherateofconversionofenergyintooffspring,whichscalesasmasstoapproximatelythe-0.25power.Themodelpredicts(1)thedistinctiveright-skewedshapeofthefrequencydistributionoflogarithmsofbodysizesamongspeciesthatisobservedinawidevarietyoforganismsfrombacteriatomammals;(2)ataxon-specificoptimalbodysize,whichformammalsisapproximately100gandissupportedbydataonthebodysizesofmammalsonislands;and(3)thatineachtaxontherelationshipsbetweensuchlife-historyandecologicalcharacteristicsaslongevity,clutchsize,homerangesize,andpopulationdensitywillchangebothslopeandsignoneithersideoftheoptimalsize.Anenergeticdefinitionoffitnesshasthepotentialtounifyareasofecologyandevolutionarybiologythathavepreviouslyusedmodelsbasedondifferentcurrencies.Thermodynamicsandenergeticsprovideaunifyingconceptualbasisformuchofthetheoreticalandempiricalresearchinphysiological,behavioral,andecosys-temsecologybutnotinevolutionarybiologyorpopulationandcommunityecol-ogy.Intheselatterdisciplinestheunifyingconceptisfitness,whichhastradition-allybeendefinedintermsoftherelativerateofincreaseofagenotypeorpopulation.Somenotedphysicistshavesuggestedthatfitnesscouldbecharacter-izedinthermodynamicandenergeticterms.Thus,Boltzmann(1905,citedinOdum1971,p.6)says,"[The]struggleforexistenceisastruggleforfreeenergyavailableforwork,"andLotka(1922,p.147)writes,"Inthestruggleforexis-tence,theadvantagemustgotothoseorganismswhoseenergy-capturingdevicesaremostefficientindirectingavailableenergyintochannelsfavorabletothepreservationofthespecies"(seealsoSchrodinger1947).Inthepresentarticlewerevivethisphysicalperspective,developanenergeticdefinitionoffitness,anduseittomodeltheevolutionofbodysize.Frombacteriatoinsectstomammals,aseeminglyuniversalfeatureoflargetaxonomicgroupsisafrequencydistributionofbodysizesamongspeciesthatishighlyrightskewed,evenonalogarithmicscale(see,e.g.,Stanley1973;May1978,1986;Bonner1988;DialandMarzluff1988;BrownandMaurer1989)(fig.*Presentaddress:DepartmentofBiology,MontanaStateUniversity,Bozeman,Montana59717.Am.Nat.1993.Vol.142,pp.573-584.?)1993byTheUniversityofChicago.0003-0147/93/4204-0001$02.00.Allrightsreserved.Thiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). 0.20.1MAMMALS0.1t10.01.22.43.64.86.0_~~~~~~~TOD0.0.10.2C9o0.01.22.43.64.86.00.0.210.1~~~~FISH0.01.22.43.64.86.0BodyMass,log.0(g)FIG.1.-FrequencydistributionsofnumberofspecieswithrespecttologarithmsofbodymassforNorthAmericanterrestrialmammals,landbirds,andfreshwaterfishes.Notethatthesedistributionsareallverysimilar:rightskewed,withacleardeclineinthenumberofspeciesonbothsidesofthemodalvalue.Thesedatawerecompiledfromavarietyofsources;allometricequationsrelatingbodylengthtobodymasswereusedtoestimatemassforthosespeciesforwhichdirectdatawerenotavailable.Thiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). BODYSIZE,ENERGETICS,ANDFITNESS5751).HutchinsonandMacArthur(1959),whofirstcalledattentiontothispattern,hypothesizedthatitoccursbecausesmallerspeciestendtobemorespecializedandthussubdivideenvironmentsandresourcesmorenarrowlythantheirlargerrelatives.Recentinvestigatorshaveappliedconceptsoffractalgeometrytoac-countforthespecializationandproliferationofspeciesofsmallsize(Morseetal.1985;Lawton1986;May1986).Contrarytothepredictionofthespecializationhypothesis,however,thesmallestsizeclassdoesnotcontainthegreatestnumberofspecies(fig.1).Herewepresentanalternativetothespecializationhypothesis.Wederiveamodelforanoptimalbodymass,basedonenergeticcorrelatesandconsequencesofsizethatappeartobecharacteristicofallorganisms.Webeginwiththewell-establishedempiricalrelationshipsbetweensizeandsuchattributesasmetabolicrateandturnovertime,ontogeneticdevelopmenttime,andlifespan(Peters1983;Calder1984;Schmidt-Nielsen1984).Theseallometricrelationshipssetfundamen-tallimitsonorganicstructureandfunctionanddeterminethetrade-offbetweentherelativeadvantagesofsmallandlargesize.FITNESSREDEFINEDWebeginbydefiningfitnessinenergeticterms.Organismsmustacquireandtransformenergy,nutrients,andsometimesotherlimitedresources,suchaswa-ter,thatmustbeobtainedfromtheenvironmentinordertomaintainhomeostasisandproduceoffspring.Weassumethatevolutionunderfrequency-independentnaturalselectiontendstomaximizethefitnessofindividuals.Fitnessisdefinedhereastheratethatresources,inexcessofthoserequiredforgrowthandmainte-nanceoftheindividual,canbeharvestedfromtheenvironmentandusedforreproduction.Thus,weequatefitnesswithreproductivepower,therateofconversionofenergyintousefulworkforreproduction.ThisisanapplicationofthemaximumpowerprincipleofLotka(1922,1925;Odum1971;seealsoVanValen1976).Traditionally,evolutionarybiologistshavedefinedfitnessintermsoftherateofproductionofoffspring,butsuchdefinitionsarecomplicatedbyvariationinthequalityaswellasthenumberofoffspring(see,e.g.,GadgilandBossert1970;Stearns1976;Endler1986).Becausequalitydependsoncharacteristicsoftheenvironmentaswellasoftheoffspringthemselves,thereisnosingleoptimalnumberofoffspringforagivenamountofreproductivework(Schaffer1974;Slatkin1974;Stearns1976;Gillespie1977).Bydefiningfitnessintermsofpower,weshifttheemphasisfromthetraditionaltrade-offbetweennumberandqualityofoffspringtothemoregeneralcapacitytotransformenergytoreproductivework.THEMODELReproductivepowerismodeledastheconsequenceoftwolimitingrates:therateatwhichanindividualcanacquireresourcesfromitsenvironmentandtherateatwhichitcanconvertthoseresourcesintoreproductivework.WeassumeThiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). 576THEAMERICANNATURALISTthattheprocessisanalogoustoatwo-stepchemicalreactioninwhichtheindivid-ual,I,catalyzestheconversionofresources,R,towork,W:KoR+Io---I,(1)andKiI->Io+W,(2)whereIoandI,representindividualsbeforeandaftertheacquisitionofresourcesfromtheenvironment;IoandI,canbethoughtofeitherastheproportionoftimeasingleindividualspendsinthesetwostatesorastheproportionofthetwokindsofindividualsinthepopulation.Weassumeinthisinitialreportthatreaction1issaturatedwithrespecttoresources.Consequently,theratesofdisappearanceofIoandproductionofI,aredIo=-KoIo+K1(3)dtandd11=KoIo-KIII.(4)dtWediscussbelowsomeofthelikelyresultsofrelaxingthisassumption.Repro-ductivepowerofanindividualisgivenbydWdt=KII.(5)Atsteadystate,dIo/dt=dI/dt=0.RememberingthatIoandIIsumtounity,wehavedWKOK,dtKo+K1(6)IfKoislarge,thenreproductivepowerislimitedbytherateofconversionofresources,anddWK(7)dtOntheotherhand,ifK1islarge,thenresourceacquisitionbecomeslimiting,anddWt-dWKo.(8)WefurtherassumethatthemaximumvaluesofbothKoandK1thatcanbeexpressedbyanindividualareallometricfunctionsofbodymass,M:Ko=CoMbo(9)Thiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). BODYSIZE,ENERGETICS,ANDFITNESS577andK1-CAMbl.(10)Thus,reproductivepowerisgivenbydW_CoMboCMbi(11)dtCoMbo+C1Mb'Finally,maximizingpower,dW/dt,withrespecttobodymassandrearrangingtermsgivethefollowingsimplifiedexpressionfortheoptimalbodymass,M*:11(bo-bi)-CbM*(Cbo)(12)Thebiologicalinterpretationofthismodelisstraightforward.Thesmallestindividualshaveagreatcapacitytoconvertresourcesintoreproductivework,buttheyarelimitedbytherateofacquisitionofresourcesforreproduction.Theymustspendmostoftheirtimeforagingjusttomeettheirhighmass-specificmaintenancemetabolism.Incontrast,largeindividualshaveagreatcapacitytoacquireresources,buttheyareconstrainedbytherateatwhichthesecanbeconvertedintoviableoffspring.Thetrade-offbetweenthesetwolimitingpro-cessesresultsinanoptimalsize.Previousauthors(Case1979;ZiolkoandKoz-lowski1983;Reiss1989)alsouseenergeticconsiderationstoderiveanoptimalbodysize,buttheydonotincorporatetheconstraintonconversionofenergyintooffspringexpressedinourequation(10).IMPLICATIONSThemostdirectapplicationofthemodelisthatitpredictsthevalueoftheoptimalbodysizeifthevaluesoftheallometricconstantsbo,b1,C0,andClareknown.Wesuggestthatthevaluesofboandb,remainvirtuallyconstantamongdifferentkindsoforganisms.Weassumedthatbo,whichscalestherateofenergyacquisitioninexcessofmaintenanceneeds,is0.75,thesameastheallometricexponentforindividualmetabolicrate,productivity,andgrowthrate(Peters1983;Calder1984;Schmidt-Nielsen1984;YodzisandInnes1992).Weassumedthatbl,whichscalestherateoftransformationofenergytoreproductivework,is-0.25,thesameastheallometricexponentforratesofmass-specificmetabo-lismandnearlyallbiologicalconversionprocesses(Peters1983;Calder1984;Schmidt-Nielsen1984;YodzisandInnes1992).Someauthorshavesuggestedontheoreticalorempiricalgroundsthatboandb,mightbe0.67and-0.33,respec-tively.WefollowYodzisandInnes(1992)andothersinusing0.75and-0.25andalsoinnotingthatthemodelisnotsensitivetosmalldifferencesintheexactvaluesofthesegeneralscalingexponents.Incontrast,C0andClaretaxon-specificparameters.WeuseddatafromPeters(1983;dataforpeakmilkproductioninapp.VlIIdandforpopulationproductioninapp.VIIc)toestimateC0andClformammalsas6.0and0.2W,respectively,whenMismeasuredinkilograms.Substitutingthesevaluesintoequation(12)Thiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). 578THEAMERICANNATURALIST000010123456BodySize,(log0g())FIG.2.-Thehump-shapedcurveofreproductivepowerasafunctionofthelogarithmofbodymass(dashedline)predictedbyourmodelwhenreasonablevaluesformammalsweresubstitutedfortheexponentsandconstantsineq.(11).NotethatthemodelpredictsanoptimalbodysizeandadistributionofreproductivepowerthatcloselymatchestheobservedfrequencydistributionofbodymassesamongspeciesofNorthAmericanmammals(histo-gramis;asinfig.1).Thiscorrespondenceisnotexpectedtobeprecise,however,becausethe"Platonic"fitnessfunctionpredictedbythemodeldoesnotincludetheeffectsofre-sourcelimitationandinterspecificinteractions.givesanoptimalbodysizeformammalsof100gandadistributionofreproductivepowerthatisverysimilartotheobservedfrequencydistributionofspecies(fig.2).WhiletheremaybesomeuncertaintyabouttheexactvaluesofC0andCl,substitutingareasonablerangeofempiricalestimatesoftheseparametersformammalsgaveremarkablysimilardistributionsandanoptimalsizethatwasusuallybetween80and250g.Thattheoptimumlieswithinthisrangeissupportedbytwocharacteristicsofinsularandcontinentalmammalfaunas(fig.3):popula-tionsofspeciesthatoncontinentsarelargerthanthissizetendtoevolvedwarfinsularraces,whereaspopulationsofsmallerspeciestendtoevolvegiantinsularraces(Lomolino1985);andastheareaofalandmassandthenumberofspeciespresentdecrease,therangeofsizesrepresentedinthefaunaalsodecreases,sothatwhenthereisonlyasinglespeciespresent,ittendstobeclosetotheoptimalsize(P.A.MarquetandM.L.Taper,unpublishedmanuscript;seealsoMaureretal.1992).Onemayask,Ifthereissuchanoptimum,thenwhyarenotallspeciesattheoptimum?Whyistheresuchawiderangeofsizeswithineachtaxon?OurmodeldevelopsaPlatonicfitnessfunctionthatisbasedongeneralphysiologicalprocessesthatoperateindependentlyofparticularecologicalsettings.Intherealworld,thisfundamentalfitnessfunctioncanbemodifiedbytheinfluenceofabi-Thiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). 60A.!40_.E20aa0Xwen-20t-0--X040-60-101234567MainlandBodySize,1og10(g)108*<^~~~**I.0E-2o-2ISIII..I-101234567BodySize,1og1O(g)FIG.3.-Twoempiricalpatternsinthebodysizesofmammalsonislandsandcontinentsthatsuggesttheexistenceofanoptimalbodysizebetween80and250g.A,Microevolution-arytrendsininsularpopulationsofmammals,whichshowthatpopulationsaboveandbelowtheoptimumtendtoevolvedwarforgiantinsularforms,respectively(datareanalyzedandreplottedfromLomolino1985).B,Maximum(squares)andminimum(stars)bodysizesofterrestrialmammalsinhabitingalargesampleofislandsandcontinents.Notethat,asthesizeofthelandmassandthenumberofspeciespresentdecreases,therangeofbodysizestendstoconvergetowardtheoptimalbodymass(fromP.A.MarquetandM.L.Taper,unpublishedmanuscript).Thiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). 580THEAMERICANNATURALISToticenvironmentalconditionsandthepresenceofotherorganisms.Thus,con-trarytotheassumptionofequation(3),thesupplyofresourcesoftendoeslimittherateofacquisition.Thecapacityofindividualstousethespectrumofavailableresourcesvarieswithbodysize.Forexample,inmammalianherbivorestheca-pacitytoextractusableenergyandnutrientsfromdifferentkindsoffooddependsonallometricanatomicalandphysiologicalconstraintsondigestion(DemmentandVanSoest1985;JusticeandSmith1992).Theresultisthat,whenaspeciesoftheoptimalsizeispresentandusingonepartoftheresourcespectrum,otherspeciesaremorelikelytoinvadeandpersistiftheyareofdifferentsizesandusedifferentresources(RummelandRoughgarden1985;TaperandCase1992).Thedifferentiationinsizeobservedwithinataxonofrelatedorganismsistheresultoffrequency-dependentprocesses:bothmicroevolutionarychangeswithinspeciesandmacroevolutionaryprocessesoforiginationandextinction.Ourmodelpredictsthat,whenonlyasinglespeciesispresent,itshouldbeclosetotheoptimalsize.Asthenumberofspeciesincreasesasaresultofspeciationorcolonization,othersizeswilltendtobecomeestablished,usingmorecompletelythedistributionofreproductivepowerdiagramedinfigure2.Thus,theintraspe-cificevolutionarysizetrendsinmammalsonislands(fig.3A)arelargelytheresultofmicroevolutionaryprocesses,whereasthediversityofsizesofspeciesoncontinentsandislands(fig.3B)islargelyaconsequenceofmacroevolutionaryprocesses.Both,however,appeartoreflecttheinfluenceofthesametaxon-specificfitnessfunction(Stanley1973;Maureretal.1992;P.A.MarquetandM.L.Taper,unpublishedmanuscript).Theevolutionarydiversificationoflineagesinvolvesthemakingandbreakingofconstraints.Constraintsareexpressedinthewaythatevolutionaryhistoryandphylogeneticrelationshipslimitvariationinthestructureandfunctionofcontemporaryorganisms(see,e.g.,BrooksandMcLennan1991;HarveyandPagel1991).Intermsofthemodel,constraintsareexpressedastaxon-specific(ormorerigorouslyasclade-specific)valuesoftheconstantsC0-andC1.Theselimitboththerangeofbodysizesandthedistributionofbodysizesofthespecieswithinalineage.Thus,thedistributionsofsizesformammals,birds,andfishes(fig.1)arequantitativelydifferentbecauseoftaxon-specificvaluesoftheC's,buttheyarequalitativelyofnearlyidenticalshapebecauseofidenticalvaluesoftheb's.Thesamepatternholdsfordifferentlevelsofphylogeneticdifferentiationwithinthesetaxa.Forexample,withinbirds,constraintsowingtodiet,digestivephysiology,andotherfactorscauseowls(orderStrigiformes)tobelargerontheaveragethanflycatchers(familyTyrannidae),buteachofthesetaxonomicgroupsexhibitsitsownuniqueright-skeweddistribution(fig.4).Auniquefeatureofourmodelisthatitpredictsthatmanyecologicalandsomephysiologicalallometricrelationshipsshouldchangeslopeandsignatapproxi-matelytheoptimalsize,astherate-limitingprocessshiftsfromresourceacquisi-tiontoresourceconversion.Thisisahard,aprioripredictionthatisreadilysubjecttoempiricaltest.Infact,thereisalreadysomeevidencetosupportthisprediction.Forexample,homerangesizesofmammalsareinverselyrelatedtobodymassinspeciessmallerthanapproximately100gandpositivelycorrelatedwithbodysizeinspecieslargerthanthisthresholdvalue(BrownandMaurerThiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). BODYSIZE,ENERGETICS,ANDFITNESS581STRIGIFORMES0.21(00.?0.11ffi0.01.42.84.200O0.4TYRANNIDAE0?.0.3-0.2-0.1i0.01.42.84.2BodyMass,1og1,(g)FIG.4.-Frequencydistributionsforthenumberofspeciesasafunctionofbodysize(onalogarithmicaxis)fortwolineagesofNorthAmericanlandbirds:top,theowls,orderStrigiformes;andbottom,theflycatchers,familyTyrannidae,orderPasseriformes.1989;BrownandZeng1989);maximumpopulationdensitiesofmammalsandbirdsexhibittheoppositepattern(BrownandMaurer1987,1989;seealsoDamuth1981;Lawton1990;Marquetetal.1990).Somelife-historyattributesandforagingcharacteristicsshowsimilarpatterns.Forexample,hummingbirdsandinsectivo-rousbats,amongthesmallestbirdsandmammals,respectively,havelifespanslongerthantheirsomewhatlargerrelativesandmuchlongerthanpredictedfortheirsizesfromtheallometricequationsderivedfromdataforbirdsandmammalsofawiderangeofsizes(Calder1989;Findley1993).Sofarasweareaware,oursistheonlymodelthatpredictsnonlinearallometricrelationshipsformanylife-historyandecologicalcharacteristicsofspecieswithinlargetaxonomicgroups.Inevaluatingthisprediction,itmustbeborneinmindthattheallometricequationsreportedintheliteraturearealmostalwaysderivedfromlinearregressionsfittedtolog-transformeddataforallspeciesinataxonforwhichmeasurementsareavailable.Nonlinearitiesinallometricrelationshipshaveoftennotbeendetected,becausethemajorityofspeciesarelargerthantheThiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). 582THEAMERICANNATURALISToptimalsize(fig.1),andtheybiasthedatatowhichlinearallometricequationsarefitted.Iftheslopesandsignsofallometricrelationshipsdoindeedchangeoneithersideoftheoptimalsize,thiswilloftenbeapparentonlyinthesubstantialdeviationsofvaluesforthesmallestorganismsfromthosepredictedfromthepublishedallometricequations.Withthiscaveat,ourmodeloffersasingleparsimoniousexplanationformanyallometricpatternsinecologyandevolution.Thefactthatthemaximumrateofpopulationgrowth,rmax,scalesasmassraisedtothe-0.25power(Peters1983),followsdirectlyfromequations(7)and(10)butonlyforthelargemajorityofspeciesthatareabovetheoptimalbodysize.Themodelcomplementstreatmentsoflife-historyevolution(see,e.g.,Harveyetal.1989;Reiss1989;Charnov1991),whichexplicitlyconsidertherelationshipbetweenbodysizeandallocationofenergytoreproduction.Theseothertreatmentsassumethatwhenindividualgrowth,whoseratescalesasM0.75,ceases,resourcescanthenbedevotedentirelytoreproduction.Theythenconsidertheeffectofsizeonthetrade-offbetweentherateofresourceacquisitionandthetimingofreproductivematuration.Thistrade-offisimportant,especiallyinadjustingspecificsuitesoflife-historytraitstoparticularenvironmentalconditions.Thesemodelsassume,however,thatfit-nessislimitedbyresourceacquisition,whereasoursassumesthattherearealsophysiologicalconstraintsonenergyconversion.Thesetwoconstraintsofenergyacquisitionandconversion,bythemselves,aresufficienttoproduceahump-shapeddistributionofreproductivepower(fig.2),whichinturnpredictsboththeoptimalbodysizeandtheallometryofmanycorrelatedlife-historytraits.Wedefinereproductivepower,dW/dt,astheinstantaneousrateofconversionofenergyintooffspringinamatureorganism.Actually,dW/dtreflectstheener-geticlimitsonthecapacitytoproduceoffspring.Wehavedeliberatelynotspeci-fiedhowthisenergyisreflectedinthequantityandqualityoftheseoffspring.Theoptimalallocationofthisenergywilldependontheparticularenvironmentexperiencedbyeachpopulationandtheeffectoftheseconditionsongrowth,survival,andreproduction.Futureelaborationsofourmodelcouldincorporatethesedetailsofecology,specifyinghowenergyisallocatedtosurvivalandpro-ductionofoffspringoverthelifetime.Thiswouldreconcileourtreatmentwiththeoriesoflifehistorythatarebasedontraditionaldefinitionsoffitnessintermsofageoffirstreproduction,survival,andfecundity(see,e.g.,Roff1981;Harveyetal.1989;Charnov1991).SYNTHESISTheconceptofreproductivepowerintegratescertainaspectsofthephysiologi-calandbehavioralecologyofindividualswiththeevolutionaryecologyofpopula-tionsandcommunities.Itprovidesanenergeticandthermodynamicbasisforfitness.Ourmodeldevelopsanexplicitrelationshipbetweenthefundamentalenergeticcharacteristicsofindividualsembodiedinequations(1)and(2)andtheallocationofenergytoproducenewindividuals.Heretofore,ecologistswhohavestudiedinteractionswiththeabioticenvironment,foraging,andreproductionofindividualshaveusedenergyasanexplicitcurrencyinboththeoreticalmodelsThiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). BODYSIZE,ENERGETICS,ANDFITNESS583andempiricalstudies.Incontrast,ecologistsandevolutionarybiologistswhohavestudiedstructureanddynamicsofpopulationsandcommunitiesandthegeneticsofevolutionarychangehaveusedtherateofchangeinpopulationsizeorallelefrequencyasthecurrencyofinterest.Recently,however,YodzisandInnes(1992;seealsoPeters1983;Calder1984)havedemonstratedtheutilityofmodelingpopulationdynamicsfromtheperspectiveofenergeticsandallometry.Byextendingthisapproachtoincludeamuchwiderrangeofecologicalandevolutionaryprocesses,ourmodeloffersaunifiedthermodynamicbasisforun-derstandingpopulationdynamics,communityorganization,evolutionarygeneticchange,andorganism-mediatedecosystemprocesses.ItrepresentsthekindofphysicalbiologyenvisagedbyBoltzmann(1905)andLotka(1922)inthequotesabove(seealsoSchrodinger1947).ACKNOWLEDGMENTSWethankW.A.CalderIII,T.J.Case,E.L.Charnov,P.H.Harvey,A.Kodric-Brown,J.H.Lawton,B.A.Maurer,F.A.Smith,andE.ToolsonforcommentsandtheNationalScienceFoundationforsupport(grantBSR-8807792).LITERATURECITEDBoltzmann,L.1905.PopulareSchriften.Barth,Leipzig.Bonner,J.T.1988.Theevolutionofcomplexitybymeansofnaturalselection.PrincetonUniversityPress,Princeton,N.J.Brooks,D.R.,andD.A.McLennan.1991.Phylogeny,ecology,andbehavior.UniversityofChicagoPress,Chicago.Brown,J.H.,andB.A.Maurer.1987.Evolutionofspeciesassemblages:effectsofenergeticcon-straintsandspeciesdynamicsonthediversificationoftheNorthAmericanavifauna.Ameri-canNaturalist130:1-17.1989.Macroecology:thedivisionoffoodandspaceamongspeciesoncontinents.Science(Washington,D.C.)243:1145-1150.Brown,J.H.,andZ.Zeng.1989.ComparativepopulationecologyofelevenspeciesofrodentsintheChihuahuandesert.Ecology70:1507-1525.Calder,W.A.,III.1984.Size,function,andlifehistory.HarvardUniversityPress,Cambridge,Mass.1989.Avianlongevityandaging.Pages185-204inD.E.Harrison,ed.Geneticeffectsonaging.Vol.2.Telford,Caldwell,N.J.Case,T.J.1979.Optimalbodysizeandananimalsdiet.ActaBiotheoretica28:54-69.Charnov,E.L.1991.Evolutionoflifehistoryvariationamongfemalemammals.ProceedingsoftheNationalAcademyofSciencesoftheUSA88:1134-1137.Damuth,J.1981.Populationdensityandbodysizeinmammals.Nature(London)290:699-700.Demment,M.W.,andP.J.VanSoest.1985.Anutritionalexplanationforbody-sizepatternsofruminantandnonruminantherbivores.AmericanNaturalist125:641-672.Dial,K.P.,andJ.M.Marzluff.1988.Arethesmallestorganismsthemostdiverse?Ecology69:1620-1624.Endler,J.A.1986.Naturalselectioninthewild.PrincetonUniversityPress,Princeton,N.J.Findley,J.S.1993.Bats.CambridgeUniversityPress,Cambridge.Gadgil,M.,andW.H.Bossert.1970.Lifehistoricalconsequencesofnaturalselection.AmericanNaturalist104:1-24.Gillespie,J.H.1977.Naturalselectionforvariancesinoffspringnumber:anewevolutionaryprinci-ple.AmericanNaturalist111:1010-1014.Thiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c). 584THEAMERICANNATURALISTHarvey,P.H.,andM.D.Pagel.1991.I'hecomparativemethodinevolutionarybiology.OxfordUniversityPress,Oxford.Harvey,P.H.,A.F.Read,andD.E.L.Promislow.1989.Lifehistoryvariationinplacentalmam-mals:unifyingthedatawiththetheory.OxfordSurveysinEvolutionaryBiology6:13-31.Hutchinson,G.E.,andR.H.MacArthur.1959.Atheoreticalmodelofsizedistributionsamongspeciesofanimals.AmericanNaturalist93:117-125.Justice,K.E.,andF.A.Smith.1992.Amodelofdietaryfiberusebysmallmammalianherbivores,withempiricalresultsforNeotomna.AmericanNaturalist128:398-416.Lawton,J.H.1986.Surfaceavailabilityandinsectcommunitystructureandfractaldimensionofplants.Pages317-331inB.E.JuniperandT.R.E.Southwood,eds.Insectsandtheplantsurface.Arnold,London.1990.Speciesrichnessandpopulationdynamicsofanimalassemblages-patternsinbodysize:abundanceandspace.PhilosophicalTransactionsoftheRoyalSocietyofLondonB,BiologicalSciences330:283-291.Lomolino,M.V.1985.Bodysizesofmammalsonislands:theislandrulereexamined.AmericanNaturalist125:310-316.Lotka,A.J.1922.Contributiontotheenergeticsofevolution.ProceedingsoftheNationalAcademyofSciencesoftheUSA8:147-155.1925.Principlesofphysicalbiology.Williams&Wilkins,Baltimore.Marquet,P.A.,S.N.Navarrete,andJ.C.Castilla.1990.Scalingpopulationdensitytobodysizeinrockyintertidalcommunities.Science(Washington,D.C.)250:1125-1127.Maurer,B.A.,J.H.Brown,andR.D.Rusler.1992.Themicroandmacroinbodysizeevolution.Evolution46:939-953.May,R.M.1978.Thedynamicsanddiversityofinsectfaunas.Pages188-204inL.A.MoundandN.Waloff,eds.Diversityofinsectfaunas.BlackwellScientific,Oxford.1986.Thesearchforpatternsinthebalanceofnature:advancesandretreats.Ecology67:1115-1126.Morse,D.R.,J.H.Lawton,M.M.Dodson,andM.H.Williamson.1985.Fractaldimensionofvegetationandthedistributionofarthropodbodylengths.Nature(London)314:731-732.Odum,H.T.1971.Environment,power,andsociety.Wiley,NewYork.Peters,R.H.1983.Theecologicalimplicationsofbodysize.CambridgeUniversityPress,Cambridge.Reiss,M.J.1989.Theallometryofgrowthandreproduction.CambridgeUniversityPress,Cam-bridge.Roff,D.1981.Onbeingtherightsize.AmericanNaturalist118:405-422.Rummel,J.D.,andJ.Roughgarden.1985.Atheoryoffaunalbuildupforcompetitioncommunities.Evolution39:1009-1033.Schaffer,W.M.1974.Selectionforoptimallifehistories:theeffectsofagestructure.Ecology55:291-303.Schmidt-Nielsen,K.1984.Scaling:whyisbodysizesoimportant?CambridgeUniversityPress,Cambridge.Schrodinger,E.1947.Whatislife?thephysicalaspectofthelivingcell,andMindandmatter.CambridgeUniversityPress,Cambridge.Slatkin,M.1974.Hedgingone'sevolutionarybets.Nature(London)250:704-705.Stanley,S.M.1973.AnexplanationforCope'srule.Evolution27:1-26.Stearns,S.C.1976.Life-historytactics:areviewoftheideas.QuarterlyReviewofBiology51:3-47.Taper,M.L.,andT.J.Case.1992.Modelsofcharacterdisplacementandthetheoreticalrobustnessoftaxoncycles.Evolution46:317-333.VanValen,L.1976.Energyandevolution.EvolutionaryTheory1:179-229.Yodzis,P.,andS.Innes.1992.Bodysizeandresource-consumerdynamics.AmericanNaturalist139:1151-1175.Ziolko,M.,andJ.Kozlowski.1983.Evolutionofbodysize:anoptimizationmodel.MathematicalBioscience64:127.Editor:MarkD.RausherThiscontentdownloadedfrom141.225.112.053onSeptember12,201612:02:17PMAllusesubjecttoUniversityofChicagoPressTermsandConditions(http://www.journals.uchicago.edu/t-and-c).