ModuleSTRU,Master2EBE

Simplifyingsize-structure:Stage-structuredbiomassmodel

DavidClaessenInsDtutdeBiologiedel’EcoleNormaleSupérieureCentredeformaDonsurl’environnementetlasociété

Size-structuredmodel

•  Themodelincorporatesinasimplemannerthethreemostbasicaspectsofsize-dependentlifehistories:–  bothforagingrateandmetabolicrequirementsincreasewithbodysize

–  growthinbodysizedependsonfoodavailability–  small,juvenileindividualsdonotreproducebutusetheirenergyforgrowthanddevelopment,whilelarger,adultindividualsusetheirenergyforreproducDon.

•  Basicdynamicenergybudgetmodels–  (Gurneyetal.,1990;Perssonetal.,1998;Kooijman,2000).

SimplifyingassumpDons

•  Bodymass,s– Birthsizesb,maturaDonsizesm– AllindividualsconsumersharedresourceR– Type2funcDonalresponse–  JuvenilemaxingesDonratescales Imax*s– AdultmaxingesDonratescales Imax*s*q–  Juvenilesallocate100%togrowth– Adultsallocate100%toreproducDon– Maintenancecostsequal T*s

Individualgrowth&reproducDon

•  NetbiomassproducDonperunitofbiomass:

•  Juvenilegrowthrate:

•  AdultreproducDonrate:

Forjuveniles

Foradults

Mortality:starvaDon

•  Iftheintakerateistoolow,individualsstarveandsufferaddiDonalmortality

•  StarvaDonmortalityequaltoenergydeficit

Thefullsize-structuredmodel

G(R)istheresourceregrowthdynamics(ie.,logisDcorsemi-chemostat)

SimplificaDontostagestructure

•  Theidea:– Aggregatethesize-structureintostages– Forexample:juveniles&adults– Butnotinatrivialway,butinamathemaDcallycorrectway!

•  Newvariables:

Thefinal,stage-structuredmodel

WiththematuraDonterm:

Comparisonofsize-structuredandstage-structuredmodels

Genera&oncyclesappearinthesizestructuredmodelwhenjuvenilesarecompeDDvelysuperior(q<1)

Small-amplitudecyclesappearinthesizestructuredmodelwhenjuvenilesarecompeDDvelyinferior(q>1)

Comparison(2)•  Theequilibriumiscorrectlypredicted:–  Thestage-structuredbiomassmodelisanexactrepresentaDonofasize-structuredpopulaDonmodel

–  consistentlytranslatesassumpDonsaboutconsump-Don,growthandbioenergeDcsofindividualconsumersintoaresource-dependent,populaDon-levelmaturaDonrate,

–  ratherthanthemoreintuiDveapproachofassuminganad-hoc,phenomenologicaldependenceofmaturaDononresourcedensity.

•  WhenpopulaDoncycles,thecorrespondencebreaksdown–  Exceptwhenq>1(adultssuperiorcompeDtors)

Whatcanwedowiththismodel

•  Stage-structuredbiomassmodel:– MuchmoresimplethanKMmodel– Numericallytractable(bifurcaDonanalysis)– Moreeasilyextendable:

•  Foodwebstructure?•  MulDplepredators?•  MulDplecompeDtors?

– Thesimplicityallowscomplexityelsewhere

Firstresults

•  DeRoosetal2007AmericanNaturalist•  Whatistheconsequenceofresource-dependentmaturaDon?

•  PredicttheresponseofastructuredpopulaDontoincreasedmortality– Dynamicsinequilibrium!

•  Comparecasesq<1andq>1

JuvenilessuperiorcompeDtors(q=0.5)

AdultssuperiorcompeDtors(q=2)

•  Whydoesstagebiomassincreasewithmortality?•  CompeDDonforfoodinfleuncesboth–  ReproducDon–  Juvenilegrowth(andhencematuraDon)

•  WhichprocessismorestronglyaffectedbycompeDDon?– DependsontheequilibriumstateofthepopulaDon– DependsonthecompeDDvesuperiorityofjuvenilesvsadults

PopulaDonregulaDon

•  Inequilibrium,thepopulaDoncanberegulatedbymaturaDonorbyreproducDon– WhichprocessismorelimiDngforbiomassturnover?

•  Inequilibrium,thiscondiDonmusthold:

– Onestageisanetproducer,theotherstageanetsinkofbiomass

MaturaDonlimitaDon

•  WhenadultsaresuperiorcompeDtors(q>1ormuA<muJ)–  theadultsareanetproducers–  juvenilesareanetsink

•  PopulaDonismatura&onlimited–  JuvenilegrowthisthelimiDngfactor– ReproducDonisabundant

ReproducDonlimitaDon

•  WhenjuvenilesaresuperiorcompeDtors(q<1ormuA>muJ)–  theadultsareanetsink–  juvenilesareanetbiomassproducDonstage

•  PopulaDonisreproduc&onlimited–  Juvenilegrowthisfast(andhencematuraDon)– ReproducDonisstronglylimitedbycompeDDon

Conclusions•  Whenincreasingmortality,thisrelievescompeDDonforfood

•  ThisinfluencesmoststronglyonthemostlimiDngprocess–  Henceifreproduc&onregulated,increasingmortalitywillincreasereproducDon,whichwillincreasejuvenilebiomass!

–  HenceifmaturaDonregulated,increasingmortalitywillincreasematuraDon,whichwillincreaseadultbiomass!

•  ImplicaDons:predors,foodwebstructure…

Overview•  Includesize-structureinpopulaDonmodels–  KMmodel–  PLdRGCmodel–  Stage-structuredbiomassmodel

•  Generalconclusions:–  SizestructurecausespopulaDoncyclesduetoasymmetriccompeDDon(GeneraDoncycles)

–  OtherecologicalinteracDonsinterfere?–  Sizestructure&fooddependentgrowthimplyamorecomplexregulaDonofpopulaDons:•  Fecundity,mortality,growth,maturaDon

–  ImplicaDonsforspeciescoexistence?Foodwebstructure?