Evolution of size‐dependent intraspecific competition predicts … · 2019-03-07 · 480 | Functional Ecology HI A N D DE OOS but not from other small larvae (Gribbin & Thompson,

Functional Ecology 201933479ndash490 emsp|emsp479wileyonlinelibrarycomjournalfec

Received2August2018emsp |emsp Accepted21November2018DOI 1011111365-243513253

R E S E A R C H A R T I C L E

Evolution of size‐dependent intraspecific competition predicts body size scaling of metabolic rate

Vincent Hin emsp|emspAndreacute M de Roos

ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicensewhichpermitsusedistributionandreproductioninanymediumprovidedtheoriginalworkisproperlycitedcopy 2018 The Authors Functional EcologypublishedbyJohnWileyampSonsLtdonbehalfofBritishEcologicalSociety

InstituteforBiodiversityandEcosystemDynamicsUniversityofAmsterdamAmsterdamTheNetherlands

CorrespondenceVincent HinEmailvhinuvanl

Funding informationEuropeanResearchCouncilEuropeanUnionsSeventhFrameworkProgramme(FP2007‐2013)GrantAwardNumber322814

HandlingEditorYngvildVindenes

Abstract1 GrowthinbodysizeisaccompaniedbychangesinforagingcapacityandmetaboliccostswhichleadtochangesincompetitiveabilityduringontogenyTheresultingsize‐dependentcompetitiveasymmetryinfluencespopulationdynamicsandcommunitystructurebutitisnotclearwhethernaturalselectionleadstoasymmetryinintraspe-cificcompetition

2 Weaddress thisquestionbyusinga size‐structuredconsumerndashresourcemodel inwhichthestrengthanddirectionofcompetitiveasymmetrybetweendifferentcon-sumer individualsdependson the scalingofmaximum ingestionandmaintenancemetabolismwithconsumerbodysizeWeuseadaptivedynamicstostudyselectiononthescalingexponentsoftheseprocesses

3 Selectionleadstoanidenticalscalingofmaximumingestionandmaintenanceme-tabolismwithconsumerbodysizeEqualscalingexponentsneutralizestrongcom-petitive differences within the consumer population because all consumerindividualsrequirethesameamountofresourcestocovermaintenancerequire-mentsFurthermorethescalingexponentsrespondadaptivelytochangesinmor-talitysuchthatbiomassproductionthroughgrowthorreproductionincreasesinthelifestagethatissubjecttoincreasedmortalityAlsodecreasingsizeatbirthleadstoincreasedinvestmentinjuvenilegrowthwhileincreasingmaximumsizeleadstoincreasedinvestmentinpost‐maturationgrowthandreproduction

4 TheseresultsprovideanexplanationforobservedvariationintheontogeneticscalingofmetabolicratewithbodysizeDataofteleostfisharepresentedthatsupportthesepredictionsHoweverselectiontowardsequalscalingexponentsiscontradictedbyempiricalfindingswhichsuggeststhatadditionalecologicalcomplexitybeyondthisbasicconsumerndashresourceinteractionisrequiredtounderstandtheevolutionofsize‐dependentasymmetryinintraspecificcompetition

K E Y W O R D S

asymmetricintraspecificcompetitionbodysizedynamicenergybudgetsmetabolicscaling

1emsp |emspINTRODUC TION

Intraspecificcompetitionisoftenasymmetricsuchthatsomemem-bers of a population have a large negative effect on others but

suffer littlefromcompetitionthemselvesFurthermorethisasym-metryoftendependsonindividualbodysizeForexamplesmalllar-vae of the damselfly Ischnuru elegans suffer from reduced growth andlongerdevelopmenttimesduetointerferencefromlargelarvae

480emsp |emsp emspenspFunctional Ecology HIN aNd de ROOS

but not from other small larvae (Gribbin amp Thompson 1990) Incase of resource (or exploitative) competition competitive abilityof individuals increases with energy assimilation rate and decreases withmetabolicmaintenancecosts(PerssonLeonardssonDeRoosGyllenbergampChristensen1998Werner1994)Energyassimilationhasvariousbehaviouralandphysiologicalcomponentssuchasat-tackratehandlingtimeandassimilationefficiencywhichcanscalewithbodysizeindifferentways(Perssonetal1998Peters1983)The nature of the scaling relationships of energy assimilation andmetabolicmaintenance costswith body size ultimately determinewhether large or small individuals are competitively superior andtherefore able to growor reproducewith the available resourcesInfishforexamplemetaboliccostsgenerally increasefasterwithbodysizethanenergyassimilationrates(Persson1985PerssonampDeRoos2006)whichmeans that larger individuals requiremoreresourcestocovermaintenancerequirementsThiscanleadtostar-vationof large individualswhenmanysmall conspecifics suppressresourcedensityTheseconsequencesofasymmetric intraspecificcompetition are often found in freshwater fish species that pre-dominantly feed on the same resource (Edeline Terao ampNaruse2016 Hjelmamp Persson 2001 Persson 1985 Sanderson HrabikMagnusonampPost1999WardWebsterampHart2006)

Size‐dependentasymmetryinintraspecificcompetitionhaslargeconsequences for population dynamics species coexistence andcommunitystructure(DeRoosampPersson2013DeRoosPerssonampMcCauley2003)Concerningpopulationdynamicstheoccurrenceandtypeofpopulationcycleshasbeenlinkedtothebody‐sizescal-ingofcompetitiveabilityasmeasuredbythemaintenanceresourcedensity(MRDPerssonetal1998)Sometimesreferredtoascriticalresourcedensity(BystroumlmampAndersson2005PerssonampDeRoos2006)theMRDistheresourcedensitythatanindividualrequirestocoveritsmaintenancemetabolismwithsuperiorcompetitorshavingalowerMRDAnincreaseintheMRDwithbodysizeleadstopopu-lationcyclesinducedbycompetitivesuperiorityofsmallindividuals(juvenile‐drivencyclesDeRoosampPersson2013)whileadecreaseoftheMRDwithbodysizeimpliesthatlargeindividualsarecompet-itivelysuperiorandthiscausesadult‐drivencycles

Consequences of size‐dependent competitive asymmetry forspeciescoexistenceandcommunitystructurearemediatedthroughchanges in thepopulationsizedistributionWhencompetitiveabil-itychangeswithbodysizeeitherlargeorsmall individualsproducemore biomass per unit of existing biomass (ie they have a highermass‐specific biomass production rate) Generally newly producedbiomassisallocatedtoreproductionbyadultsandtosomaticgrowthby juveniles Stage‐specific differences in mass‐specific biomassproductionleadtodifferencesinratesofbiomasstransferbetweenthesedifferentlifestageswithbiomassmaturationratesbeinghigher(lower)thanbiomassreproductionrateswhenjuveniles(adults)haveahighermass‐specificbiomassproductionrateThiscreatesanener-geticbottleneckintheflowofbiomassacrossthelifecycleasbiomassaccumulatesinthelifestagewiththelowestmass‐specificproductionrate (DeRoos etal 2007) Increasing (size‐ or stage‐specific)mor-talityalleviatessuchabottleneckandcausesanovercompensatory

increaseofbiomassintheotherlifestage(DeRoosetal2007)Thisphenomenonofbiomassovercompensationisshowntooccurinbothexperimental (Cameron amp Benton 2004 Schroumlder Persson amp DeRoos2009)andnaturalsystems(Ohlbergeretal2011)andcanleadtocommunitywideeffectssuchasemergentAlleeeffects(DeRoosPerssonampThieme2003) emergent facilitationbetween twosize‐selective predators (DeRoos SchellekensVanKootenampPersson2008)andalternativestablestates(Guill2009)

Besides its impact on population dynamics and communitystructureasymmetriccompetitioncanconsiderablyinfluenceindi-viduallifehistorywithpotentialevolutionaryconsequencesAmod-ellingstudybasedonTrinidadianguppiesrevealedthatthedegreeof asymmetry in competition changedbothmean and varianceofgenerationtimeand lifeexpectancyatbirthandalsothevarianceoflifetimereproductivesuccess(Bassaretal2016)Thisstudysug-geststhatasymmetriccompetitioncaninfluencethedirectionandspeedofevolutionary life‐historychanges throughchanges in thenature of density dependence although explicit predictions werenot discussed Evolutionary consequences of intraspecific compe-tition have mainly been studied in the light of ecological character displacementwhereincreasedcompetitionleadstodiversificationin diet andmorphology between individuals (SvanbaumlckampBolnick2007) It remains unclear how the degree and direction of asym-metryincompetitionaffectseco‐evolutionarydynamicsandunderwhich conditions natural selection would lead to symmetry or asym-metryinintraspecificcompetition

The scaling of energy assimilation and maintenance metabolism withbodymassisoftenallometricandcanbedescribedbyapowerfunctionthatcontainsaproportionalityconstantandascalingexpo-nent (Glazier2005Peters1983)Twoframeworksprovideavaluefor the scalingexponentsof assimilation andmaintenancemetabo-lism the ontogenetic growth model of West Brown and Enquist(OGM‐modelHouZuoMosesampWoodruff2008WestBrownampEnquist2001)anddynamicenergybudget (DEB)theory(Kooijman2010)Inbothframeworksontogeneticgrowthresultsfromthedif-ferencebetweenresourceorenergysupplyandmaintenancecostsofexistingcellsorstructure (KearneyampWhite2012MainoKearneyNisbetampKooijman2014VanderMeer2006)IntheOGM‐modelenergysupplyisproportionaltotherestingmetabolicratewhichisassumedtoscalewiththree‐quarterspowerofbodymass(Houetal2008Westetal2001)Thisthree‐quartersscalingfollowsfromanindependentmodelofadistributionnetworkthatdeliversresourcesto terminalunits (capillaries)Minimizationof theenergetic costs insuchanetwork leads toa fractal‐likedistributionnetwork inwhichthenumberofterminalunitsscaleswiththree‐quarterspowertobodymass (West1997WestBrownampEnquist1999)DEB theoryde-scribes an individual in terms of structural body volume and reserve densityResourcesupplyisassumedproportionaltostructuralsurfaceareaandthereforescaleswithatwo‐thirdspowerofstructuralvol-umefor isomorphicallygrowingorganismswhilemaintenancecostsincreaseisometricallywithvolume(Kooijman19862010)

Recently data are accumulating that indicate substantial varia-tion in thevalueof thescalingexponentofmetabolic rateand this

emspensp emsp | emsp481Functional EcologyHIN aNd de ROOS

variationhasbeenrelatedtotaxonomicdiversitylifestyleinaquaticorganisms (pelagic vs non‐pelagic) temperature life stage activitylevel physiological state predation and body shape (Glazier 20052006 2009 Glazier Hirst amp Atkinson 2015 Glazier etal 2011Hirst Glazier amp Atkinson 2014 Killen Atkinson amp Glazier 2010)Glazier(2005)arguesthatthediversescalingrelationshipsobservedinnatureresultfromdiverseadaptationsincombinationwithecologi-calphysico‐chemicalconstraintsThissuggeststhatscalingexponentscanchangeadaptively forexample throughchanges inbodyshapeduring ontogeny (Hirst etal 2014 Killen etal 2010Okie 2013)Suchchangeswouldalterthedegreeofcompetitiveasymmetrywithinthepopulationandhavesubstantialconsequencesforpopulationandcommunitydynamicsaswellas individual lifehistoryHoweverex-plicit predictions about the evolutionary dynamics of competitiveasymmetryarelackingThereforethemainpurposeofthisstudyistounderstandtheselectionpressuresthatactonthescalingofcompet-itiveabilitywithbodysizeasdeterminedbythebody‐sizescalingsofenergy assimilation and maintenance metabolism

To this aim we formulate a size‐structured consumerndashresourcemodel inwhich ingestionmaintenancegrowthand reproductionofconsumerindividualsaredescribedbyaDEBmodelEnergyassimila-tionisproportionaltoresourceingestionandbothmaximumingestionandmaintenanceratesfollowpowerfunctionsofbodymassTheindi-vidual‐levelDEBmodelistranslatedtothepopulationlevelbyconsid-eringthedensitydistributionofindividualsalongthebodymassaxisas in theframeworkofphysiologicallystructuredpopulationmodels(MetzampDiekmann1986)Weexplorehowthescalingexponentsofmaximumingestionandmaintenanceaffectpopulationdynamicsandsubsequentlystudytheevolutionarydynamicsthatresultfromselec-tionpressuresonthesescalingexponentsFitnessandthedirectionandstrengthofselectionarisethroughthefeedbackbetweenanindi-vidualanditsenvironmentThereforeweusetheframeworkofadap-tivedynamics(GeritzKisdiMeszenaampMetz1998Metz2012)tostudyevolutionarychangeandidentifyevolutionaryendpointsofthescalingexponentsofingestionandmaintenancerates

2emsp |emspMODEL DESCRIPTION

21emsp|emspDEB model

TheDEBmodel(Table1)specifiesratesofresourceingestionmain-tenancegrowthreproductionandmortalityofaconsumerindividualas a function of its body mass s and resource density R Resource competitionbetweenindividualsisexplicitlyincorporatedbyconsid-eringaself‐replenishingdynamicresourcefromwhichallconsumerindividualsfeedandbymodellinggrowthandreproductionasfood‐dependentprocessesAllocationofassimilatedenergyfromresourcefeedingfollowsanet‐productionallocationschemeinwhichmainte-nancetakesprecedenceovergrowthandreproduction(LikaampNisbet2000)Thereforegrowthandreproductiononlyoccurwhenresourcedensityismorethansufficienttocovermaintenancerequirements

Maintenanceandmaximumingestionratesfollowpowerfunc-tions of bodymass given byT(s∕sr)P and M(s∕sr)

Q respectively

In these functionsbodymasss isdividedbyparametersr This parameteractsastherotationpointforthepowerfunctionsofmaintenance and maximum ingestion and is referred to as thereference body mass The scaling constants T and M respec-tively indicate themaintenanceandmaximum ingestionrateofan individual with reference body mass srTheexponentsP and Q determine the body mass scalings An increase in P and Q im-pliesanincreaseinrespectivelymaintenanceandmaximumin-gestion for individuals with s gt sr and a decrease for individuals with s lt srIndividualsarebornwithsizesbmatureatsizesj and canreachamaximumsizeofsmiffooddensityissufficientForsb lt sr lt smthereisatrade‐offbetweenindividualswithslt sr and conspecificswiths gt sr forbothmaintenanceandmaximum in-gestionratesBydefaultajuvenilendashadulttrade‐offisassumedbysetting sr = sjbutdeviationsfromthisassumptionareexploredThe rate of food ingestion (I(R s))furthermorefollowsaHollingtype‐II functional responseof resourcebiomasswithhalf‐satu-ration constant H(seeTable1)Ingestedfoodisassimilatedwithefficiency σ which also includes overhead costs for somaticgrowth and reproduction The biomass production rate (Ω(R s))istheamountofbiomassthatcanbeusedforgrowthandrepro-ductionperunitoftimeandisequaltoassimilatedbiomassminusmaintenancecosts(Table1)

Topreventindividualsfromgrowingtoverylargebodysizesincasemaximumingestionincreasesfasterwithbodysizethanmaintenance(ieQgtP)wemodeladultallocationtowardsgrowthwithasigmoidfunction (s)thatdecreasesfromoneatmaturationsizesjtowardszeroatthemaximumindividualbodysizesm(Table1)Consequentlyasymp-toticsize is limitedtosm ifresourcedensity issufficientbutthissizemightnotbereachedifresourcesarelimitedInadultsthefractionof

TA B L E 1 emspModelequations

Equation Description

I(Rs) = M(

s

sr

)QR

R+H

Resource ingestion

Ω(R s) = I(Rs) minus T(

s

sr

)P Biomassproduction

ds(R a)da

= g(R s) = (s)Ω+(R s) with s(R 0) = sbGrowthrate

b(R s) =(1minus(s))Ω+ (R s)

sb

Fecundityrate

120581(s) =

⎧⎪⎨⎪⎩

1 for slt sj

1 minus 3L(s)2 + 2L(s)3 for sjle slt sm0 for s = sm

with L(s) = sminus sj

sm minus sj

Allocation function

120583(R s) =

120583c + 120583j minus

Ωminus (R s)

sfor slt sj

120583c + 120583a minusΩminus (R s)

sfor sge sj

Mortality rate

G(R) = (Rmax minus R) Resource growth rate

Note We use Ω + (R s) to denote max(Ω(R s)0) and Ωminus(R s) means min(Ω(R s)0)


biomassproductionnotspendongrowth(1minus(s))isallocatedtorepro-ductionThereforeadultindividualsallocateanincreasingfractionoftheir biomass production towards reproduction Juveniles (sble slt sj)spendallbiomassproductionongrowthGrowthinmasswithagea oc-cursonlyifthebiomassproductionrateΩ(R s)ispositiveandisgivenbythedifferentialequationds(R a)

dainTable1Thesizeatbirthsb is used

asinitialconditionofthisdifferentialequationReproductionalsoonlyoccursforpositivevaluesofΩ(R s) and individual fecundity is denoted by b(R s)(rateofoffspringproductionperadultTable1)

Mortality ((R s)) is composed of background mortality for all individuals (c) andadditional size‐dependentmortality for juveniles(j) and adults (a Table1) Furthermore mortality increases whenfoodconditionsare insufficient tocovermaintenancerequirementsThisstarvationmortalityisequaltothemagnitudeofthemass‐spe-cificbiomassproductionwhennegativeStarvationishandledasanin-creaseinmortalityinsteadofareductioninbodymass(DeRoosetal2007)Theseparticularstarvationdynamicswillnotinfluencetheevo-lutionarypredictionsofthemodelsincetheseassumethepopulationtobeatequilibriumunderwhichstarvationdoesnotoccurResourcegrowth (G(R))followssemi‐chemostatdynamics(Table1)

Model parameters and their default values are summarized inTable2andamoredetaileddescriptionoftheparameterderivationisavailableinSupportingInformationAppendixS1(seealsoDeRoosampPersson2013)

22emsp|emspModel analysis

We used PSPManalysis (De Roos 2018) a software packagefor the analysis of physiologically structured populationmodelsto calculatemodel equilibria as a functionofmodelparametersPSPManalysis solves for the resourcedensity (R) andpopulationbirth rate (b)atequilibriumbyintegratingrepeatedlyacoupledsetof ordinary differential equations that describe the growth sur-vivalcumulativeresourceingestionandcumulativereproductionuntiltheequilibriumconditionR0(R) = 1issatisfiedHereR0rep-resentstheexpectedlifetimereproductivesuccessofasinglein-dividual(seeDeRoos2018formoredetails)EquilibriumanalysiswascomplementedwiththeEscalatorBoxcarTrain(EBT)methodtostudytransientandnon‐equilibriumdynamics(DeRoos1988)TheEBTmethodcalculatespopulationdynamicsasafunctionoftimebydividingthesizedistributionintocohortsofsimilarly‐sizedindividualsandforeverytimestepcalculatingthegrowthmortal-ity and reproduction for each cohort as a functionof the bodymass of individuals within that cohort and resource density

To study evolutionary dynamics we used the framework ofadaptive dynamics (Geritz etal 1998Metz 2012Metz GeritzMeszeacutena JacobsampVanHeerwaarden1995)whichassumes thatmutation limitedevolutionproceedsaccordingtosubsequent traitsubstitutions in the direction of the selection gradient This can result in an evolutionary singular strategy (ESS) if the selectiongradientbecomeszeroPSPManalysiscalculatestheselectiongra-dient and detects and classifies ESSs according to their stabilitypropertiesasdiscussedinGeritzetal (1998)Sinceourmodelhas

aone‐dimensionalenvironmentallESSsareconvergenceandevo-lutionarystable(CSSscontinuouslystablestrategies)FurthermorePSPManalysisisusedtocalculateevolutionaryisoclineswhichde-notetheESS‐valueofonemodelparameterasafunctionofasecondmodelparameter

3emsp |emspRESULTS

31emsp|emspEcological dynamics as function of Q and P

The model dynamics as a function of Q and PshowasimilarpatternForP gt Q themaintenancerate increasesfasterwithbodymasss thanthemaximumingestionrate(Qlt1 inFigure1andashdandPgt1 in Figure1endashh)inwhichcasesmallindividualsproducemorebiomassperunitofexistingbiomassandrequirelessresourcestocovertheirmaintenance requirements than large individualsAstableequilib-rium results inwhich the asymptotic bodymass is determined bythesizeatwhichadultindividualsspendallassimilatedbiomassonmaintenance Consequently when PgtQ the resource density at equilibriumcoincideswiththeMRDofthelargestindividualsinthepopulation(Figure1ae)whicharewellbelowthemaximumpossiblebody mass of sm = 10(Figure1dh)

The lowmass‐specific biomass production of adults is insuffi-cient to compensate for adult biomass loss throughmortality andthere is a net biomass loss in the adult stage This net loss is com-pensatedforbyanetbiomassgaininthejuvenilestagewherethebiomass production exceeds the biomass loss through mortalityThediscrepancyinbiomassproductionbetweenthetwolifestagestranslatestoadiscrepancyintotalbiomassreproductionandmat-urationrateswherematurationexceedsreproductionbecausethenetproductionofbiomassoccursinthejuvenilestage(Figure1cg)Juveniles therefore grow rapidly but growth and reproduction of

TA B L E 2 emspModelparameters

Symbol Unit Value Description

Rmax mgL 30 Maximumresourcedensity

δ perday 001 Resource renewal rate

Q mdash 1 Maximumingestionexponent

P mdash 1 Maintenanceexponent

M gday 01 Maximumingestionconstant

T gday 001 Maintenance constant

μc perday 00015 Backgroundmortality

μj perday 00 Additional juvenile mortality

μa perday 00 Additional adult mortality

σ mdash 05 Assimilation efficiency

H mgL 3 Half-saturation density

sb g 01 Bodymassatbirth

sj g 1 Bodymassatmaturation

sr g 1 Reference body mass

sm g 10 Maximumbodymass


adultsisslowAsaresultthepopulationisdominatedbyadultbio-mass(Figure1bf)

Ifthemaximumingestionrateincreasesfasterwithbodymassthan the maintenance rate (QgtP) larger individualsbothhaveahighermass‐specific biomassproduction rate and a lowerMRD(Qgt1inFigure1andashdandPlt1inFigure1endashh)Thisinducespopu-lationcyclesdrivenbyadultsthatareclosetothemaximumsizeandhindergrowthofnewborn individuals (Figure1dh)Growthofnewbornsoccursonlywhenbackgroundmortalityhasdimin-ished adult density to allow the resource to increase above the MRDofnewbornindividualsThisexplainsthecoincidenceoftheresource density with the MRD of newborn individuals (thin solid linesinFigure1ae)Becauseingestionincreasesfasterwithsizethanmaintenance the growing juveniles decrease the resourcedensityandinhibitgrowthof latercohorts Ifabundantenoughtheselatercohortswilleithercatchupwiththeearlierproduced

individuals when the resource density increases or die due tobackground and starvation mortality Adult‐driven cycles existfor P = 1 and Qgt1 and forQ = 1 and Plt1TheiramplitudeandperiodincreaseswithincreasingdifferencebetweenQ and P

32emsp|emspEvolutionary dynamics converge towards Q = P

An ESS exists for values ofQ and P where the equilibrium re-source density reaches a minimum (dashed vertical lines in Figure1) These ESSs are convergent and evolutionarily stableendpoints of evolution (continuously stable strategies CSSs)BothCSSs arewithin the parameter region of stable ecologicaldynamics Convergence stabilitywithin the parameter range ofpopulationcycleswasconfirmedbyexplicitlyassessingthefateofmutantphenotypesinthecyclicattractoroftheresidentOnlymutantswithatraitvalueclosertotheCSSwereabletoinvade

F I G U R E 1 emsp Model dynamics as a functionofthemaximumingestionscalingexponentQ(leftpanelswithP=1)andthemaintenanceratescalingexponentP(rightpanelswithQ=1)Thicklinesindicatestablemodelequilibriawhilethe solid-filled and dashed areas show therangeandextentofpopulationcycles(ae)Resourcebiomass(greythicklinesandshading)andthemaintenanceresource density for the smallest (solid blacklines)andlargestindividuals(dottedblacklines)occurringinthepopulation(bf)Adults(black)andjuvenile(grey)consumerbiomass(cg)Totalpopulationreproduction(black)andmaturation(grey)ratesinbiomass(dh)Bodymassoflargestindividualsinthepopulation(asymptoticbodysize)Theverticaldashedlinesshowthepositionofthecontinuouslystablestrategies(CSS)ofQ inpanelsadandtheCSSofP in eh All otherparametersasinTable2

0

1

2

3

4

5

Res

ourc

e bi

omas

s (a)

0

5

10

15

20

Con

sum

er b

iom

ass

(b)

0

002

004

006

008

Mat

amp r

ep r

ate (c)

04 06 08 1 12

4

6

8

10

Asy

mpt

otic

mas

s

Max ingestion exp (Q)

(d)

0

1

2

3

4

5(e)

0

5

10

15

20(f)

0

002

004

006

008(g)

04 06 08 1 12

4

6

8

10

Maintenance exp (P)

(h)


andreplacetheresidentpopulationInthefollowingwerefertotheCSSofQ as QandtotheCSSofP as P

The value of Q as a function of PaswellasthevalueofP as a func-tion of Q is shown in theQminusP‐parameter space in Figure2 Theseevolutionaryisoclinesappeartobeontopofeachotherbutcloserin-spectionrevealsthattheycrossexactlyatQ = P (insetFigure2)ThesmalldifferencebetweenbothisoclinesmeansthattheCSS‐valueofoneexponent isapproximatelyequal to thevalueof theothernon‐evolvingexponentThereforetheevolvingexponentwillapproximatethevalueofthenon‐evolvingexponentBecausetheevolutionaryiso-clinescrossexactlyatzerodifferencethetwo‐dimensionalCSSofQ and PhasthepropertythatQ = PForthedefaultparameters(Table2)thecommonCSS‐valueisQ = Pasymp119BecauseQ = PtheMRDintheCSSdoesnotchangewithbodymassHoweversinceQ = Pgt10 the mass‐specificbiomassproductionrateincreaseswithbodymassIntheSupportingInformationFigureS1weshowthattheresultofQ = P is independentofthescalingreferencesizesrwhilethejoinedvalueofQ and Pdoesdependonsr Increasing sr leads to a decrease of Q = P Thisresultstillholdsifweapplyseparatescalingreferencemassesformaximum ingestionandmaintenance (Supporting InformationFigureS1)InadditionweexploretheeffectonQ and PofparametersRmaxM TcH and inSupportingInformationFigureS2Noneofthesepa-rametersleadstoadifferencebetweentheevolvedscalingexponentsMoreovertheonlyparametersthatslightlyaffectthevaluesofQ and P are the maintenance constant (T)andthebackgroundmortalityrate(c

)TheeffectoftheremainingmodelparametersonQ and P is described below

33emsp|emspEffect of juvenile and adult size ranges

Theevolutionaryconvergenceof the scalingexponents toacom-monCSS‐valueisrobustagainstchangesinsizeatbirthsb and the maximumbodysizesmalthoughthevalueofthecommonCSS‐pointisinfluencedbythesesizeparametersFigure3showsthatincreas-ingthesizerangeofalifestagechangesQ and P such that the mass-specificbiomassproductionofthislifestageincreasesAdecreaseinsbleadstoalargerjuvenilesizerangeandtriggersanevolutionaryre-sponseofadecreaseinQ and PThisincreasesmass‐specificbiomassproductionforjuvenilesincreasesgrowthandmaturationratesandleadstoalowerjuvenilebiomassdensity(Figure3bc)Alternativelya larger adult size range (increase inmaximum size sm) triggers anevolutionary responseof increasing valuesofQ and P (Figure3d)Consequentlytheincreasedbiomassproductionofadultsincreasesreproductionandleadstoloweradultbiomassdensity(Figure3ef)Foronespecificcombinationofsb and sm does selection on Q and P lead to Q = P = 1 (dashedverticallinesinFigure3)Onlyforthiscombinationof sizeparametersdoes themodelpredict themass‐specificbiomassproductiontobeindependentofbodysize

34emsp|emspEffect of stage‐specific mortality

Theresponsetoincreasingstage‐specificmortalityisshowninFigure4TheevolutionaryresponseofQ and P(Figure4dndashfandjndashl)iscomparedwiththepopulationresponsetoincreasingmortalityincasethescalingexponentsdonotevolve(Figure4andashcandgndashi)butareinsteadfixedattheirCSS‐valuefornoadditionalstage‐specificmortalityAtj = 0thiscausesahighermass‐specificbiomassproductionforadultscomparedtojuvenilesandconsequentlythepopulation‐levelreproductionrateexceeds the population‐level maturation rate (Figure4cf) For addi-tional adult mortality (a)thesizeatbirthparameterissettosb = 005 and this leads to Q = Pasymp0872 for a = 0 (Figure4gj)Consequentlythemass‐specificbiomassproduction ishigher for juveniles and thisleadstoalargerpopulation‐levelmaturationratecomparedtothepop-ulation‐levelreproductionrate(Figure4il)Whenscalingexponentsdonotevolveadditionalstage‐specificmortalityleadstoadecreaseintherate of the most-limiting life-history transition (maturation for increas-ingjuvenilemortality[Figure4c]andreproductionforincreasingadultmortality[Figure4i])andanincreaseintherateoftheothernon‐lim-iting life‐history transition However there is no overcompensatoryresponseof(stage‐specific)biomassdensitywithincreasingmortality(Figure4bh)

Forevolvingscalingexponentsadditionalstage‐specificmortalitydoes not change the evolutionary convergence of Q and P towards a commonvaluebutdoesinfluencethiscommonCSS‐valueIncreasingjuvenile mortality decreases Q = P(Figure4d)Theresponseofdecreas-ing Qincreasesenergyassimilationforjuvenilesbutsimultaneouslyju-venilesexperiencehighermaintenancecostsdue toadecrease inP

F I G U R E 2 emspEvolutionaryisoclinesshowingthevalueofQ (thecontinuouslystablestrategies[CSS]ofQ)asafunctionofP (greyline)andP(theCSSofP)asafunctionofQ(blackdashedline)intheQminus PmdashplaneThindashedlinesrepresentQ = P The intersection of both isoclines with the line Q = P is indicated with asolidpointTheinsetshowsthedifferencebetweeneachofthetwo evolutionary isoclines and the line Q = PasafunctionofQ (horizontalaxisrangeisidenticaltothatofmainfigure)IsoclinescrossexactlywhenthisdifferenceiszeroAllotherparametersasin Table 2

04 06 08 1 12 14

06

08

1

12

14

Maximum ingestion exponent (Q)

Mai

nten

ance

exp

onen

t (P

)

minus002

0

001

PminusQ


Nonethelessthenetresultisanincreaseinthemass‐specificbiomassproductionrateforjuvenilesAccordinglythepopulation‐levelmatura-tionrateincreaseswithincreasingjuvenilemortality(Figure4f)whichleadstoan increase inadultandtotalconsumerbiomass (Figure4e)Insteadtheresponsetoincreasingadultmortalityleadstohigherval-ues of Q and P and an increase in juvenile biomass through an increase inthepopulation‐levelreproductionrateConsequentlyanovercom-pensatoryresponseof(stage‐specific)biomassdensityoccurswithin-creasingmortalitywhenthescalingexponentsformaximumingestionandmaintenancerespondadaptivelytosuchmortalitychanges

4emsp |emspDISCUSSION

Recent studies show considerable variation in the intraspecific scal-ing ofmetabolismwith body size (Glazier 2005)Metabolic rate af-fectscompetitiveabilityandthereforechanges incompetitiveabilityduring ontogeny can arise through changes in the scaling of metabolic ratewithbodymassThepopulationandcommunityeffectsofsuch

size‐dependentchangesincompetitionarewelldocumented(DeRoosampPersson2013)Herewereportthefirstresultsontheevolutionarydynamicsofthescalingofcompetitiveabilitywithbodysize Incaseofatrade‐offintheenergeticsbetweenjuvenileandadultindividualsthescalingexponentsofmaximumingestionandmaintenanceevolvetominimizethecompetitiveasymmetrywithinthepopulationThisisachieved when maintenance and ingestion scale in the same way with bodysizeOnlyinthiscaseareallthedifferently‐sizedindividualsequalwithrespecttotheresourcedensitytheyrequiretocovertheirmain-tenance costs (maintenance resource densityMRD)We show thatthis result is robust against changes in anyof themodelparameters(Figures3and4SupportingInformationFiguresS1andS2)

Wehypothesizethattheinabilityofthecurrentmodeltoproduceanevolutionarystableoutcomeinwhichthescalingexponentsofmain-tenanceandmaximumingestiondifferisrelatedtothenegativeeffectsofsize‐dependentchangesintheMRDontheresourceuseefficiencyofasingleindividualAtpopulationequilibriumasingleindividualhastoreplaceitselfandthiscanonlyhappeniftheresourcedensity(R)ex-ceedstheMRDofallconsumerindividualsConsequentlyiftheMRDisasize‐dependentfunctionofconsumerbodysizeR has to increase be-yondthemaximumofthisfunctionLetsconsiderthecasethatmainte-nanceincreasesfasterwithbodysizecomparedtomaximumingestion(PgtQ)TheMRDisanincreasingfunctionofbodysizeandRexceedstheMRDofthelargestconsumerindividuals(Figure1)Comparedtothe smallest individuals the largest individuals suffermost from re-sourcelimitationastheirbiomassproductionis justabovezeroThisallowsfortheinvasionofamutanttypewithalowermaximumMRDForthismutanttypetherelativeincreaseinbiomassproductionduringthephaseofstrongresourcelimitation(whenlarge)willoutweightherelative decrease in biomass production when small Consequentlythismutantwillousttheresidentsinceitisabletoreplaceitselfwithalower R-value Individual resource use efficiency will therefore be most efficientwhentheMRDisaconstantfunctionofbodysizeAlthoughwedidnotprovethisdirectlywesuspectthatthismechanism isre-sponsibleforthestrongselectiontowardsequalscalingexponentsofmaintenanceandmaximumingestion

Obviouslyatrade‐offisrequiredtoconstraintheevolutionofthescalingexponentsofmaintenanceandmaximumingestionBydefaultwe have adopted a juvenilendashadult trade‐off by setting the point ofrotationofthepower‐lawfunctionsthatdescribethesescalingexpo-nentstothesizeatmaturationIfwewoulduseforexamplethesizeatbirth insteadan increase inQ and a decrease in Pwould lead torespectivelyanincreaseinmaximumingestionandadecreaseinthemaintenance rate for all consumer individuals This would inevitably cause runaway selection towards higher Q and lower PwhichisclearlyunrealisticAlthoughthereisnogoodempiricaljustificationforajuve-nilendashadulttrade‐off itdoesallowustostudytheselectionpressuresthatarise fromunequalscalingexponentsofmaintenanceandmaxi-mum ingestion

The evolutionary prediction of equal scaling exponents of main-tenance andmaximum ingestion is at oddswith the existing theoriesabout ontogenetic growth These theories assume an isometric increase of maintenance costs (P = 1) and a sublinear allometry of maximum

F I G U R E 3 emspContinuouslystablestrategies‐valuesofscalingexponentsofmaximumingestionQ(greysolidline)andmaintenance rate P(blackdashedline)inpanels(aandd)asafunctionofthejuvenilesizerangeparameterizedbysminus1

b(andashc)and

theadultsizerangeparameterizedbysm(dndashf)(be)Adult(black)andjuvenile(grey)consumerbiomass(cf)Population‐levelreproduction(black)andmaturation(grey)ratesinbiomassThevertical dashed lines indicate the value of sminus1

b(andashc)andsm(dndashf)

where Q and P evolve to 1

04

06

08

1

12C

SS

of Q

amp P

(a)

4

5

6

7

8

(b)Con

sum

er b

iom

ass

10 20 50 1000

0002

0004

0006

Mat

amp r

ep r

ate

Juvenile size range sbminus1

(c)

(d)

(e)

35 5 7 10

Adult size range sm

(f)


ingestion rates (Q = 3∕4 or Q = 2∕3 Kooijman 2010 Van derMeer2006Westetal2001)SuchacombinationofscalingexponentsleadstoadecreaseintheMRDwithindividualbodysizeWeshowthatthisleadstonegativeselectiononthemaintenanceexponentandpositiveselectiononthemaximum ingestionexponentAlsoour resultsshowthat when either Q or Pisfixedtheotherexponentstillevolvestoavalueclose to theevolutionarilyconstrainedscalingexponentTherefore inthismodeltherecanonlybeadifferencebetweenbothexponentswhentheyarebothconstrainedandnon‐evolvableSelectivechangeinoneorbothexponentswilleventuallybringthemtogether

Despitethedifficultiesofmeasuringmaintenanceandingestionratesmostdatasuggestthatmaintenanceratesindeedscalefasterwith body size than ingestion rates although considerable varia-tionexists (Glazier 2005MainoampKearney2015)Onedifficultyin measuring maintenance metabolic rate is that resting individu-alscanstill invest ingrowthorreproductionThereforemeasureslikerestingorbasalmetabolicratestillincludeoverheadscostsfortheseinvestments(Kooijman1986McCauleyMurdochNisbetamp

Gurney1990)Evenifmaintenanceratewouldbemeasuredreliablytheresultingmaintenancerateexponentoftenshowsconsiderablevariation (Glazier 2005) Likewise scaling of ingestion also variesbetween groups The two‐thirds scaling predicted byDEB theoryappearstoholdfornon‐volantmammalsbutthepooledmassex-ponentforbothnon‐volantmammalsandbirdsis073andforbirdsalone it is evenhigher (KearneyampWhite2012) Significantvaria-tion in the scaling of ingestion was also observed for insects (Maino ampKearney2015)Duetothisvariationacomparisonbetweenthetwo can only be informative when measurements are performedunder identical conditions and for the same species or even thesamepopulationSuchacomparisonexistsforDaphniaspinwhichmaintenanceratesincreasesuperlinearwithbodymass(gt1)duetocontributionstocarapaceformationandingestionfollowsanover-allexponentof073(GurneyMcCauleyNisbetampMurdoch1990McCauleyetal1990)

Also ontogenetic growth data suggest that the maintenance rate scalingexceedstheingestionratescalingasthisleadstotheoften

F I G U R E 4 emspEquilibriaasafunctionofincreasingstage‐specificmortalityforjuveniles(jleftsixpanels)andadults(arightsixpanels)Eachsetofsixpanelscomparesthepopulationresponsefornon‐evolvingscalingexponents(Q and Pfixedattheircontinuouslystablestrategies‐valuesfornoadditionalmortality)withthecaseinwhichthescalingexponentsrespondadaptivelytoincreasingstage‐specificmortality (Q and P)Toppanelsvaluesofmaximumingestion(Qgreysolidline)andmaintenancescalingexponent(Pblackdashedline)middlepanelsadult(solidblacklines)juvenile(greylines)andtotal(dashedblacklines)consumerbiomassbottompanelspopulation‐levelratesofreproduction(blacklines)andmaturation(greylines)intermsofbiomassLeftsixpanelsdefaultparameters(Table2)whereQ = Pasymp1193 at j = 00Rightpanelsdefaultparameters(Table2)inadditiontosb = 005forwhichQ = P = 0872 at a = 00

04

06

08

1

12

Q amp

P

(a)

Nonminusevolving Q amp P

0

3

6

9

12

15

Con

sum

er b

iom

ass

(b)

0 0006 0012

0

001

002

003

004

Mat

amp r

ep r

ate

Juvenile mortality

(c)

04

06

08

1

12(d)

Evolving Q amp P

0

3

6

9

12

15(e)

0 0006 0012

0

001

002

003

004

Juvenile mortality

(f)

04

06

08

1

12(g)


0

3

6

9

12

15 (h)

0 0002 0004

0

0005

001

0015

Adult mortality

(i)

04

06

08

1

12

Q amp

P

(j)

Evolving Q amp P

0

3

6

9

12

15

Con

sum

er b

iom

ass

(k)

0002 0004

0

0005

001

0015

Mat

amp r

ep r

ate

Adult mortality

(l)


observedpatternofdecreasingontogenetic growth rateswith in-creasingsize(Peters1983Ricklefs2003)Equalscalingexponentswould leadtoanexponentialgrowthpatternwhichare lessoftenobserved (Kooijman 2010) However a decreasing ontogeneticgrowthratewithbodysizecanalsoarisefromanincreasingenergyallocation towards reproduction (Barneche Robertson White ampMarshall 2018) and does not necessarily imply a lower ingestionrate scaling Another way to assess the scalings of maintenance and ingestion rates isbyusing thescalingof theMRDwithbodysizeSeveral empirical studies indicate that the MRD is an increasingfunctionofbodysizewhichimpliesasteeperscalingofmaintenancecomparedtoingestionandleadstoacompetitiveadvantageofsmallindividuals (AljetlawiampLeonardsson2002BystroumlmampAndersson2005HjelmampPersson2001) Inconclusionbothdataandtheo-reticalmodelsonontogeneticgrowth indicateasteeperbody‐sizescalingofmaintenancecomparedto ingestionandthiscontradictstheevolutionarypredictionofequalscalingexponents

Onesimpleexplanation for thisdiscrepancy is that thescalingexponentsareconstrainedandthereforecannotevolvebutthereis at least someevidence against this explanation First of all therange of observed intraspecific scaling exponents does suggestthereisvariationforselectiontoacton(Glazier2005)Thisvaria-tionhasbeenrelatedtolifestyleactivitygrowthformtemperatureandpredation(Glazier20052006Glazieretal2015Hirstetal2014Killenetal2010)Forexamplebodyshapechangescanin-fluencethe intraspecificscalingofmetabolic rate (Okie2013)AsshownbyHirstetal(2014)growthinthreedimensions(isomorphicgrowth)isrelatedtolowscalingexponentswhileone‐dimensionalgrowth(elongation)relatestoexponentsaroundoneThesefindingsfavour theories that assume that metabolic scaling is determined by transportofmaterialsacrosssurfacemembranesandindicatethatchangesingrowthformcaninfluencethescalingofresourcesupplyratesSelectionwouldhencebeabletochangethescalingofmaxi-mumingestionwithbodysizebyalteringthedimensionofontoge-netic growth

SecondlyGlazieretal (2011) illustrate thatadaptationstodif-ferentenvironmentscanleadtodifferentscalingexponentsTheseauthors show how the scaling of resting metabolic rate in the am-phipodGammarus minusdependsonthepresenceoffishpredatorsIndividuals from three populations that naturally co‐occur with apredatoryfishhavealowerscalingexponentthanindividualsfromtwo populations in which these predators are absent The lowerscalingexponents resulted in ahighermetabolic rate for small in-dividuals and a lower metabolic rate for large individuals This led tofastergrowthtolowerasymptoticsizesofindividualsinfish‐ex-posedpopulations(Glazieretal2011)Theseresultscorrespondtoourevolutionarypredictionsincaseofincreasingjuvenilemortalitywhichlowerstheevolutionaryequilibriumofthescalingexponentsofmaintenanceandmaximumingestionandleadstoahighergrowthpotentialofjuvenilesattheexpenseofadultgrowthpotential

The inability of the current model to reproduce evolutionarystable scaling exponents that match empirical observations sug-gests that our model misses a crucial aspect of biological reality

Indeed we have used a basic size‐structured consumerndashresourcemodelwith a single typeof resource anda simpleDEBmodel todescribeconsumerenergeticsAlthoughsimilarDEBmodelsareableto reproduce empirical patterns of ontogenetic growth reproduc-tion andmetabolism from theprinciplesof energy andmass con-servation (Kooijman 2010) ourmodel appears less successful forexplainingtheevolutionofmetabolismandlifehistoriesLikelythisrequiresincorporatingadditionalecologicalcomplexitybesidestheelementaryconsumerndashresourceinteractionstudiedhereForexam-ple additional ecological interactionsmight change theevolution-arypredictionsInmanyempiricalsystemsontogeneticdietshiftspreypredator size ratios and interference competition reduce thesize dependencyof themaintenance resourcedensity and in thisway counteract the negative competitive effect of small individu-alsonlargeconspecifics(AljetlawiampLeonardsson2002BystroumlmampAndersson2005HjelmampPersson2001)Similarlycannibalismoradditional resources typesmight stabilize size‐dependent changesinthemaintenanceresourcedensitybyreducingthestrengthofin-traspecificcompetitionFuture researchshouldpointoutwhetheradditionalecologicalcomplexitycanallowforanevolutionarystableoutcomeinwhichthevaluesofthescalingexponentsdiffer

Othertypesofstructuredpopulationmodelshaveprovensuc-cessfulinprovidingevolutionarypredictionsofobservedlife‐historystrategiesForexampleevolutionarypredictionsfromintegralpro-jectionmodels (IPMs) closelymatch observed flowering decisionsofmonocarpicperennialplants(ChildsReesRoseGrubbampEllner2004 Metcalf Rose amp Rees 2003 Metcalf etal 2008) Thesemodels differ from our approach as they are parameterizedwithfunctionsfittedongrowthreproductionandmortalitydata(Metcalfetal2003)andarenotbasedonenergybudgetdynamicsTheworkonmonocarpic perennials has revealedwhichmodel componentsarerequiredtosuccessfullypredictevolutionarystablestrategiesofnaturalpopulationsOnesuchcomponent isvariation inbody‐sizegrowth(Metcalfetal2003)whichisabsentintheframeworkweuseTheseandotherinsightsfromdemographicevolutionarymod-elscouldbeusedtoimproveevolutionarypredictionsofstructuredpopulationmodelsthatarebasedonexplicitenergydynamics

InarecentstudyBarnecheetal(2018)foundthatinmarinefishesreproductionscaleswithbodysizewithapowerlargerthan1(hyper-allometrically) Inourmodelthescalingofreproductiveoutputwithbodysizedependson(a)theevolvedscalingexponentsofmaintenanceandmaximum ingestion that govern the scaling of biomass produc-tion (b)thesigmoidal(s)-function that models allocation of biomass production to growth vs reproduction As we show in SupportingInformationFigureS3thesetwocomponentsresultinascalingofreal-izedreproductionratewithbodysizethatcloselyresemblesahyperal-lometricscalingaswasfoundbyBarnecheetal(2018)

AsasecondresultweshowhowthecommonCSS‐valueofthescalingexponentsdependsonmortalityratesandsizerangesofju-venileandadultlifestages(Figures3and4)Basedonthiswepre-dictthatmetabolicscalingexponentsdecreasewiththesizerangeandmortalityrateofjuvenilelifestagewhiletheyincreasewiththesizerangeandmortalityrateoftheadultlifestageWetestedthis


predictionbyusingdataonscalingexponentsofstandardorroutinemetabolicrateforteleostfishaspublishedbyClarkeandJohnston(1999)andKillenetal(2010)andcombiningthesewithestimatesoflength at maturation (lmat)andeggdiameter(legg as length estimates aremostreadilyavailableforfish)Intotalweobtainedlengthesti-matesfor41ofthe89speciesintheoriginaldatasetofKillenetal(2010)InFigure5thetemperature‐correctedscalingexponentsofmetabolismareplottedagainstthelogarithmsoflmat∕legg In agree-mentwithourevolutionarypredictionthescalingexponentofstan-dard metabolic rate decreases significantly with an increase in the juvenilesizerangedespitethesmallsamplesizeandtheconsider-ablevariationthatisnormallyassociatedwithmetabolicscalingex-ponentseggdiametersandmaturationsizes(Bagenal1971Kamler2005Killenetal2010)

Inthisstudyweignoretheproximatecausesthatleadtotheallometric scaling of maintenance metabolism and ingestion and insteadfocusontheultimateevolutionarycausesthatareshapedby how individuals interact with each other through their inter-action with a shared environment Such interactions ultimatelydetermine fitness and drive evolutionary change Although this model describes a basic consumerndashresource interaction it pro-videsapowerfulandrobustnullmodelagainstwhichtoevaluateevolutionaryconsiderationsregardingtheintraspecificscalingofingestionandmaintenancewithbodysizeWhilethemodelpro-videsanexplanation for theobservedvariation in thescalingofbasalmetabolismwithbody size (Figure5) thepredictedevolu-tionary convergence of ingestion and maintenance exponents

contrastwith a substantial amount of empirical findings Futurestudies should focus on how energeticmodels such as the onedescribed here can be extended with more ecological realismsuch that their evolutionary predictions are better in line withreal-world observations

ACKNOWLEDG EMENTS

This research was supported by funding from the EuropeanResearchCouncilundertheEuropeanUnionsSeventhFrameworkProgramme (FP2007‐2013)ERC Grant Agreement No 322814LennartPerssonRomainRichardandtworeviewersprovidedusefulcommentsthatconsiderablyimprovedthemanuscript

AUTHOR S CONTRIBUTIONS

VH and AMdR designed the research and contributed to later versionsofthemanuscriptVHanalysedthemodelandwrotefirstversionofmanuscriptAllauthorsgavefinalapprovalforpublication

DATA ACCE SSIBILIT Y

Data in Figure5 are deposited in the Dryad Digital Repositoryhttpsdoiorg105061dryad2fc6677 (Hin amp De Roos 2018a)Code to run the model is available via Zenodo httpsdoiorg105281zenodo1494830(HinampDeRoos2018b)

ORCID

Vincent Hin httpsorcidorg0000‐0002‐9497‐1224

Andreacute M de Roos httpsorcidorg0000‐0002‐6944‐2048

R E FE R E N C E S

AljetlawiAAampLeonardssonK (2002)Size‐dependentcompetitiveability inadeposit‐feedingamphipodMonoporeia affinis Oikos9731ndash44httpsdoiorg101034j1600‐07062002970103x

BagenalTB(1971)TheinterrelationofthesizeoffisheggsthedateofspawningandtheproductioncycleJournal of Fish Biology3207ndash219httpsdoiorg101111j1095‐86491971tb03665x

BarnecheDRRobertsonDRWhiteCRampMarshallDJ(2018)Fish reproductive‐energyoutput increasesdisproportionatelywithbody size Science360 642ndash645 httpsdoiorg101126scienceaao6868

Bassar RDChildsD Z ReesM Tuljapurkar S ReznickDNampCoulsonT(2016)TheeffectsofasymmetriccompetitiononthelifehistoryofTrinidadianguppiesEcology Letters19268ndash278httpsdoiorg101111ele12563

Bystroumlm P amp Andersson J (2005) Size‐dependent forag-ing capacities and intercohort competition in an ontoge-netic omnivore (Arctic char) Oikos 110 523ndash536 httpsdoiorg101111j0030‐1299200513543x

Cameron T C amp Benton T G (2004) Stage‐structured har-vesting and its effects An empirical investigation using soilmites Journal of Animal Ecology 73 996ndash1006 httpsdoiorg101111j0021‐8790200400886x

F I G U R E 5 emspThescalingexponentofstandardorroutinemetabolismwithbodysizeof41teleostfishspeciesplottedagainstthelogarithmoftheratiooflengthatmaturationandeggdiameterasameasureforthejuvenilesizerangeDataonscalingexponentsarefromKillenetal(2010)ThelinesshowaRMAregressionwith95confidenceintervalsThepointindicatedbytheopencirclewith the cross is the eel Anguilla anguillaandwasnotpartoftheregressionequationSeeSupportingInformationAppendixS2foradetaileddescriptionofdatacollectionandanalysisDataaredepositedinDryadDigitalRepository(HinampDeRoos2018a)

3 4 5 6 7 8

04

06

08

1

12

14 y = minus019(minus033 minus013)x + 172(141 239)r 2 = 0357 P perm(one tailed) lt 001

log(Juvenile size range)

Sca

ling

of s

tand

ard

met

abol

ism


ChildsD Z ReesM RoseK EGrubb P JampEllner S P (2004)Evolution of sizendashdependent flowering in a variable environmentConstructionandanalysisofastochasticintegralprojectionmodelProceedings of the Royal Society of London B Biological Sciences271425ndash434httpsdoiorg101098rspb20032597

ClarkeAampJohnstonNM(1999)Scalingofmetabolicratewithbodymassandtemperature inteleostfishJournal of Animal Ecology68893ndash905httpsdoiorg101046j1365‐2656199900337x

De Roos AM (1988) Numerical methods for structured populationmodels The escalator boxcar train Numerical Methods for Partial Differential Equations4173ndash195

DeRoosAM(2018)PspmanalysisAnalysisofphysiologicallystructuredpopulation models Retrieved from httpsbitbucketorgamderoospspmanalysis

DeRoosAMampPerssonL(2013)Population and community ecology of ontogenetic developmentPrincetonNJPrincetonUniversityPresshttpsdoiorg1015159781400845613

De Roos AM Persson L ampMcCauley E (2003) The influence ofsize‐dependent life‐historytraitsonthestructureanddynamicsofpopulations and communitiesEcology Letters6 473ndash487 httpsdoiorg101046j1461‐0248200300458x

De Roos AM Persson L amp Thieme H R (2003) Emergent Alleeeffects in top predators feeding on structured prey populationsProceedings of the Royal Society of London B Biological Sciences270611ndash618httpsdoiorg101098rspb20022286

DeRoosAM Schellekens T VanKooten TampPersson L (2008)Stage‐specific predator species help each other to persist whilecompetingforasinglepreyProceedings of the National Academy of Sciences of the United States of America10513930ndash13935httpsdoiorg101073pnas0803834105

De Roos A M Schellekens T van Kooten T van de Wolfshaar KClaessenD amp Persson L (2007) Food‐dependent growth leads toovercompensationinstage‐specificbiomasswhenmortalityincreasesThe influence of maturation versus reproduction regulation The American Naturalist170E59ndashE76httpsdoiorg101086520119

EdelineETeraoOampNaruseK(2016)Empiricalevidenceforcom-petition‐driven semelparity inwildmedakaPopulation Ecology58371ndash383httpsdoiorg101007s10144‐016‐0551‐4

GeritzSAHKisdiEMeszenaGampMetzJAJ(1998)Evolutionarilysingular strategies and the adaptive growth and branching of theevolutionary tree Evolutionary Ecology 12 35ndash57 httpsdoiorg101023A1006554906681

GlazierDS(2005)Beyondthelsquo34‐powerlawrsquoVariationintheintra‐and interspecific scalingofmetabolic rate in animalsBiological re-views of the Cambridge Philosophical Society80611ndash662httpsdoiorg101017S1464793105006834

Glazier D S (2006) The 34‐power law is not universal Evolutionof isometric ontogenetic metabolic scaling in pelagic animalsBioScience 56 325ndash332 httpsdoiorg1016410006‐3568(2006)56[325TPLINU]20CO2

GlazierDS(2009)Activityaffectsintraspecificbody‐sizescalingofmet-abolic rate in ectothermic animals Journal of Comparative Physiology B179821ndash828httpsdoiorg101007s00360‐009‐0363‐3

GlazierDSButlerEMLombardiSADeptolaTJReeseAJampSatterthwaiteEV (2011)EcologicaleffectsonmetabolicscalingAmphipodresponsestofishpredatorsinfreshwaterspringsEcological Monographs81599ndash618httpsdoiorg10189011‐02641

GlazierDSHirstAGampAtkinsonD(2015)Shapeshiftingpredictsontogenetic changes inmetabolic scaling in diverse aquatic inver-tebrates Proceedings of the Royal Society B Biological Sciences28220142302httpsdoiorg101098rspb20142302

GribbinSDampThompsonDJ(1990)Asymmetricintraspecificcom-petitionamonglarvaeofthedamselflyIschnura elegans(ZygopteraCoenagrionidae) Ecological Entomology 15 37ndash42 httpsdoiorg101111j1365‐23111990tb00781x

Guill C (2009) Alternative dynamical states in stage‐structured con-sumer populations Theoretical Population Biology 76 168ndash178httpsdoiorg101016jtpb200906002

GurneyWMcCauleyENisbetRampMurdochW(1990)Thephysi-ologicalecologyofDaphniaAdynamicmodelofgrowthandrepro-duction Ecology71716ndash732httpsdoiorg1023071940325

HinVampDeRoosAM(2018a)DatafromEvolutionofsize‐dependentintraspecificcompetitionpredictsbodysizescalingofmetabolicrateDryad Digital Repositoryhttpsdoiorg105061dryad2fc6677

HinVampDeRoosAM(2018b)CodefromEvolutionofsize‐depen-dent intraspecific competition predicts body size scaling ofmeta-bolic rate Zenodohttpsdoiorg105281zenodo1494830

Hirst AGGlazierD S ampAtkinsonD (2014) Body shape shiftingduring growth permits tests that distinguish between competinggeometric theories of metabolic scaling Ecology Letters17 1274ndash1281httpsdoiorg101111ele12334

HjelmJampPerssonL(2001)Size‐dependentattackrateandhandlingcapacityInter‐cohortcompetitioninazooplanktivorousfishOikos95520ndash532httpsdoiorg101034j1600‐07062001950317x

Hou C ZuoWMosesM ampWoodruffW (2008) Energy uptakeand allocation during ontogeny Science322 736ndash739httpsdoiorg101126science1162302

Kamler E (2005) Parent‐egg‐progeny relationships in teleost fishesAnenergeticsperspectiveReviews in Fish Biology and Fisheries15399ndash421httpsdoiorg101007s11160‐006‐0002‐y

KearneyMRampWhiteCR (2012)Testingmetabolic theoriesThe American Naturalist180546ndash565httpsdoiorg101086667860

KillenSSAtkinsonDampGlazierDS(2010)Theintraspecificscal-ing of metabolic rate with body mass in fishes depends on life-style and temperature Ecology Letters 13 184ndash193 httpsdoiorg101111j1461‐0248200901415x

KooijmanSALM (1986)Energybudgetscanexplainbodysizere-lations Journal of Theoretical Biology 121 269ndash282 httpsdoiorg101016S0022‐5193(86)80107‐2

KooijmanS(2010)Dynamic energy budget theory for metabolic organisa-tion(3rded)CambridgeUKCambridgeUniversityPress

LikaKampNisbetR(2000)AdynamicenergybudgetmodelbasedonpartitioningofnetproductionJournal of Mathematical Biology386361ndash386httpsdoiorg101007s002850000049

MainoJLampKearneyMR(2015)Ontogeneticandinterspecificscal-ing of consumption in insectsOikos124 1564ndash1570 httpsdoiorg101111oik02341

MainoJLKearneyMRNisbetRMampKooijmanSALM(2014)Reconciling theories for metabolic scaling Journal of Animal Ecology8320ndash29httpsdoiorg1011111365‐265612085

McCauleyEMurdochWNisbetRampGurneyW(1990)Thephysio-logicalecologyofDaphniaDevelopmentofamodelofgrowthandre-productionEcology71703ndash715httpsdoiorg1023071940324

MetcalfCJERoseKEChildsDZSheppardAWGrubbPJampReesM(2008)Evolutionoffloweringdecisionsinastochasticden-sity‐dependentenvironmentProceedings of the National Academy of Sciences of the United States of America10510466ndash10470httpsdoiorg101073pnas0800777105

MetcalfJCRoseKEampReesM(2003)EvolutionarydemographyofmonocarpicperennialsTrends in Ecology and Evolution18471ndash480httpsdoiorg101016S0169‐5347(03)00162‐9

Metz J A J (2012) Adaptive dynamics In AHastingsamp L J Gross(Eds) Encyclopedia of theoretical ecology (pp 7ndash17) Berkeley CACaliforniaUniversityPress

MetzJAJampDiekmannO(1986)The dynamics of physiologically struc-tured populationsLecturenotesinbiomathematicsBerlinGermanySpringer‐Verlag

Metz J A J Geritz S A H Meszeacutena G Jacobs F J A amp VanHeerwaardenJS(1995)AdaptivedynamicsAgeometricalstudyoftheconsequencesofnearlyfaithfulreproductionWorkingpaper


International Institute for Applied Systems Analysis LaxenburgAustria

Ohlberger J Langangen Oslash Edeline E Claessen D Winfield I JStenseth N C amp Voslashllestad L A (2011) Stage‐specific biomassovercompensationbyjuvenilesinresponsetoincreasedadultmor-tality inawildfishpopulationEcology922175ndash2182httpsdoiorg10189011-04101

OkieJG(2013)GeneralmodelsforthespectraofsurfaceareascalingstrategiesofcellsandorganismsFractalitygeometricdissimilitudeand internalizationThe American Naturalist181421ndash439httpsdoiorg101086669150

PerssonL (1985)AsymmetricalcompetitionAre largeranimalscom-petitively superiorThe American Naturalist126261ndash266httpsdoiorg101086284413

PerssonLampDeRoosAM(2006)Food‐dependentindividualgrowthandpopulationdynamics infishesJournal of Fish Biology691ndash20httpsdoiorg101111j1095‐8649200601269x

Persson L Leonardsson K De Roos A M Gyllenberg M ampChristensen B (1998) Ontogenetic scaling of foraging rates andthe dynamics of a size‐structured consumer‐resource modelTheoretical Population Biology54270ndash293httpsdoiorg101006tpbi19981380

PetersRH (1983)The ecological implications of body sizeCambridgeUK Cambridge University Press httpsdoiorg101017CBO9780511608551

Ricklefs R (2003) Is rate of ontogenetic growth constrained by re-source supply or tissue growth potential A comment on Westet als model Functional Ecology 17 384ndash393 httpsdoiorg101046j1365‐2435200300745x

Sanderson B L Hrabik T RMagnuson J J amp Post DM (1999)Cyclicdynamicsofayellowperch(Perca flavescens)populationinanoligotrophiclakeEvidencefortheroleofintraspecificinteractionsCanadian Journal of Fisheries and Aquatic Sciences56 1534ndash1542httpsdoiorg101139f99‐077

Schroumlder A Persson L amp De Roos A M (2009) Culling experi-ments demonstrate size‐class specific biomass increases withmortality Proceedings of the National Academy of Sciences of the United States of America106 2671ndash2676 httpsdoiorg101073pnas0808279106

Svanbaumlck R amp Bolnick D I (2007) Intraspecific competition drivesincreased resource use diversity within a natural populationProceedings of the Royal Society B Biological Sciences274839ndash844httpsdoiorg101098rspb20060198

Van der Meer J (2006) Metabolic theories in ecology Trends in Ecology and Evolution 21 136ndash140 httpsdoiorg101016jtree200511004

WardAJWWebsterMMampHartPJB(2006)Intraspecificfoodcompetition in fishes Fish and Fisheries 7 231ndash261 httpsdoiorg101111j1467‐2979200600224x

Werner E (1994) Ontogenetic scaling of competitive relations Size‐dependenteffectsandresponsesintwoanuranlarvaeEcology75197ndash213httpsdoiorg1023071939394

WestGB (1997)Ageneralmodelfortheoriginofallometricscalinglaws in biology Science 276 122ndash126 httpsdoiorg101126science2765309122

WestGBBrownJHampEnquistBJ(1999)ThefourthdimensionoflifeFractalGeometryandallometricscalingoforganismsScience2841677ndash1679httpsdoiorg101126science28454201677

West G B Brown J H amp Enquist B J (2001) A general modelfor ontogenetic growth Nature 413 628ndash631 httpsdoiorg10103835098076

SUPPORTING INFORMATION

Additional supporting information may be found online in theSupportingInformationsectionattheendofthearticle

How to cite this articleHinVdeRoosAMEvolutionofsize‐dependentintraspecificcompetitionpredictsbodysizescalingof metabolic rate Funct Ecol 201933479ndash490 httpsdoiorg1011111365-243513253


but not from other small larvae (Gribbin amp Thompson 1990) Incase of resource (or exploitative) competition competitive abilityof individuals increases with energy assimilation rate and decreases withmetabolicmaintenancecosts(PerssonLeonardssonDeRoosGyllenbergampChristensen1998Werner1994)Energyassimilationhasvariousbehaviouralandphysiologicalcomponentssuchasat-tackratehandlingtimeandassimilationefficiencywhichcanscalewithbodysizeindifferentways(Perssonetal1998Peters1983)The nature of the scaling relationships of energy assimilation andmetabolicmaintenance costswith body size ultimately determinewhether large or small individuals are competitively superior andtherefore able to growor reproducewith the available resourcesInfishforexamplemetaboliccostsgenerally increasefasterwithbodysizethanenergyassimilationrates(Persson1985PerssonampDeRoos2006)whichmeans that larger individuals requiremoreresourcestocovermaintenancerequirementsThiscanleadtostar-vationof large individualswhenmanysmall conspecifics suppressresourcedensityTheseconsequencesofasymmetric intraspecificcompetition are often found in freshwater fish species that pre-dominantly feed on the same resource (Edeline Terao ampNaruse2016 Hjelmamp Persson 2001 Persson 1985 Sanderson HrabikMagnusonampPost1999WardWebsterampHart2006)

Size‐dependentasymmetryinintraspecificcompetitionhaslargeconsequences for population dynamics species coexistence andcommunitystructure(DeRoosampPersson2013DeRoosPerssonampMcCauley2003)Concerningpopulationdynamicstheoccurrenceandtypeofpopulationcycleshasbeenlinkedtothebody‐sizescal-ingofcompetitiveabilityasmeasuredbythemaintenanceresourcedensity(MRDPerssonetal1998)Sometimesreferredtoascriticalresourcedensity(BystroumlmampAndersson2005PerssonampDeRoos2006)theMRDistheresourcedensitythatanindividualrequirestocoveritsmaintenancemetabolismwithsuperiorcompetitorshavingalowerMRDAnincreaseintheMRDwithbodysizeleadstopopu-lationcyclesinducedbycompetitivesuperiorityofsmallindividuals(juvenile‐drivencyclesDeRoosampPersson2013)whileadecreaseoftheMRDwithbodysizeimpliesthatlargeindividualsarecompet-itivelysuperiorandthiscausesadult‐drivencycles

Consequences of size‐dependent competitive asymmetry forspeciescoexistenceandcommunitystructurearemediatedthroughchanges in thepopulationsizedistributionWhencompetitiveabil-itychangeswithbodysizeeitherlargeorsmall individualsproducemore biomass per unit of existing biomass (ie they have a highermass‐specific biomass production rate) Generally newly producedbiomassisallocatedtoreproductionbyadultsandtosomaticgrowthby juveniles Stage‐specific differences in mass‐specific biomassproductionleadtodifferencesinratesofbiomasstransferbetweenthesedifferentlifestageswithbiomassmaturationratesbeinghigher(lower)thanbiomassreproductionrateswhenjuveniles(adults)haveahighermass‐specificbiomassproductionrateThiscreatesanener-geticbottleneckintheflowofbiomassacrossthelifecycleasbiomassaccumulatesinthelifestagewiththelowestmass‐specificproductionrate (DeRoos etal 2007) Increasing (size‐ or stage‐specific)mor-talityalleviatessuchabottleneckandcausesanovercompensatory

increaseofbiomassintheotherlifestage(DeRoosetal2007)Thisphenomenonofbiomassovercompensationisshowntooccurinbothexperimental (Cameron amp Benton 2004 Schroumlder Persson amp DeRoos2009)andnaturalsystems(Ohlbergeretal2011)andcanleadtocommunitywideeffectssuchasemergentAlleeeffects(DeRoosPerssonampThieme2003) emergent facilitationbetween twosize‐selective predators (DeRoos SchellekensVanKootenampPersson2008)andalternativestablestates(Guill2009)

Besides its impact on population dynamics and communitystructureasymmetriccompetitioncanconsiderablyinfluenceindi-viduallifehistorywithpotentialevolutionaryconsequencesAmod-ellingstudybasedonTrinidadianguppiesrevealedthatthedegreeof asymmetry in competition changedbothmean and varianceofgenerationtimeand lifeexpectancyatbirthandalsothevarianceoflifetimereproductivesuccess(Bassaretal2016)Thisstudysug-geststhatasymmetriccompetitioncaninfluencethedirectionandspeedofevolutionary life‐historychanges throughchanges in thenature of density dependence although explicit predictions werenot discussed Evolutionary consequences of intraspecific compe-tition have mainly been studied in the light of ecological character displacementwhereincreasedcompetitionleadstodiversificationin diet andmorphology between individuals (SvanbaumlckampBolnick2007) It remains unclear how the degree and direction of asym-metryincompetitionaffectseco‐evolutionarydynamicsandunderwhich conditions natural selection would lead to symmetry or asym-metryinintraspecificcompetition

The scaling of energy assimilation and maintenance metabolism withbodymassisoftenallometricandcanbedescribedbyapowerfunctionthatcontainsaproportionalityconstantandascalingexpo-nent (Glazier2005Peters1983)Twoframeworksprovideavaluefor the scalingexponentsof assimilation andmaintenancemetabo-lism the ontogenetic growth model of West Brown and Enquist(OGM‐modelHouZuoMosesampWoodruff2008WestBrownampEnquist2001)anddynamicenergybudget (DEB)theory(Kooijman2010)Inbothframeworksontogeneticgrowthresultsfromthedif-ferencebetweenresourceorenergysupplyandmaintenancecostsofexistingcellsorstructure (KearneyampWhite2012MainoKearneyNisbetampKooijman2014VanderMeer2006)IntheOGM‐modelenergysupplyisproportionaltotherestingmetabolicratewhichisassumedtoscalewiththree‐quarterspowerofbodymass(Houetal2008Westetal2001)Thisthree‐quartersscalingfollowsfromanindependentmodelofadistributionnetworkthatdeliversresourcesto terminalunits (capillaries)Minimizationof theenergetic costs insuchanetwork leads toa fractal‐likedistributionnetwork inwhichthenumberofterminalunitsscaleswiththree‐quarterspowertobodymass (West1997WestBrownampEnquist1999)DEB theoryde-scribes an individual in terms of structural body volume and reserve densityResourcesupplyisassumedproportionaltostructuralsurfaceareaandthereforescaleswithatwo‐thirdspowerofstructuralvol-umefor isomorphicallygrowingorganismswhilemaintenancecostsincreaseisometricallywithvolume(Kooijman19862010)

Recently data are accumulating that indicate substantial varia-tion in thevalueof thescalingexponentofmetabolic rateand this








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Evolution of size‐dependent intraspecific competition predicts … · 2019-03-07 · 480 | Functional Ecology HI A N D DE OOS but not from other small larvae (Gribbin & Thompson,