ExtinctionPopulationextinctionprocess Fourgeneralcausesofextinction1.Environmentalstochasticity2.Demographicstochasticity3.Abioticcatastrophes4.LackgeneticvariationExtinctionEnvironmentalstochasticityRandom,temporalvariation:exogenousfactor(s)Individuals’experiencesamebirth,deathrates Temporalfluctuations,Between-generationscale Good,BadYears=Generations:foodabundance

Smallpopulation&badyear Extinction

ExtinctionDemographicstochasticityRandomvariationamongindividuals,

Within-generationscale

Numberoffspring,survivalIndividuals’birthanddeathratesindependent,

hencecandifferImportantsmallpopulations:chanceextinction ExtinctionDemographicstochasticityFixtime;ExtinctionPr declineswithInitial populationize

FixPopsize;ExtinctionPr increaseswithtimeMTE=(ExtinctionPr)-1ExtinctionAbiotic(Physical)CatastrophesLarge,suddendensityreduction Environmental,anthropogenic Climatechange

TimescalerelativetogenerationtimeExtinctionGeneticLackvariation,populationfailstoadaptRarest,but[again]globalclimatechangeBehaviorPopulationDynamicsVucetichetal.2019.Effectsofsocialstructureand preydynamicsonextinctionriskingray wolves.ConservationBiology11:957.1.Wolves:socialbehavior-group,pack 1litter/year,dominantfemale amplifydemographicstochasticity2.Preyavailability:fluctuate,sourceof

environmentalstochasticityBehaviorPopulationDynamicsGraywolf(Canislupus)IsleRoyale,MI;islandinLakeSuperior NationalPark,>500mi2Wolvesfeedonmoose Abundanceofoldmoose(>9yrs)key

BehaviorPopulationDynamicsObjective:Simulatewolfpopulationdynamics Predictmeantimetoextinction(MTE)1.Age-dependentmortalityinwolves 1/3pupsdiefirstyear Nowolvesolderthan11yrs2.Randomlittersizeinwolves,Mean=1BehaviorPopulationDynamics3.Wolfpacks: Somerestructuringbetweenyears Whenpreyabundancefalls, smallestpackdisperses,mortalitycost Survivorsjoinanotherpack Numberpacksproportionaltono.old-moose

Wolf/PackCountvsMooseWolf,Pack,MooseDynamicsBehaviorPopulationDynamicsMeanTimetoExtinction,WolfPopulation Weakdependence,initialpopulationsize Standardresultnotobserved Strongeffect,initialnumberofpacks

SimulationresultsBehaviorPopulationDynamicsReproductiveunitispack

Numberpacks,notpopulationsizecritical extinctionprocessSocialorganization,withdominance-based breeding,amplifieseffectsof

demographicstochasticityonextinction

BehaviorPopulationDynamicsNo.oldmooseconstant=305 Wolves:MTE=155yrsNo.oldmoosecycles,mean=305 Wolves:MTE=105yrsEnvironmentalstochasticity

StandardresultBehaviorPopulationDynamicsSocialgroupsize

IndividualdemographicperformanceHowmightgroupsizeGinfluencepopulationdynamics?Trainor,K.E.&T.Caraco.2019.Groupsize,energybudgetsandpopulationdynamiccomplexity.EvolutionaryEcologyResearch8:1173-1192.

ModelAssumptions(1)Foragerssearchingroups,GindividualsRatefood-clumpdiscovery1/(populationdensity)

Densitydependence

G;interference,mutualismEnergyconsumptionrandomNumberclumps,clumpsizeModelAssumptions(2)StarvationConsumptionenergyrequirementVariationbetweengroupsPredationwhileforagingRandomindependentattacksIncreaseswithconsumerdensitySurvival&ReproductionSurvivingnon-breedingseasonAvertstarvationAvoidpredationReproduction:RfixedSurvivor+(R-1)offspringReturnMap(1)nt+1=F(nt)ntF(nt):Density-dependentreproductionF=Rxp(avertstarvation|G,n)xp(avoidpredation|n)

Stabledynamics:stablenodeForα>1,Q=8,Vc=1.0;G=28tntStabledynamics:stablenodeα>1(mutualism?)IndividualencountersclumpsfasterasGincreasesMeanenergyintakemayIncreaseEnergyintakevariancedeclinesStableCycleForα=1.0,Q=10,Vc=0.5;G=32StableCycleα=1.0IndividualencountersclumpsindependentlyofGMeanenergyintakeindependentofGEnergyintakevariancedeclinesComplexdynamicsForα=0.8,Q=12,Vc=0.5;G=20Complexdynamicsα<1(interference)IndividualencountersclumpsslowerasGincreasesMeanenergyintakedeclineswithGChaoticdynamics;oftennearextinct