Simplifying size-structure: Stage-structured biomass model€¦ · Simplifying size-structure:...
Transcript of Simplifying size-structure: Stage-structured biomass model€¦ · Simplifying size-structure:...
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?