Behavior Behavior Population Population DynamicsDynamics

Behavior Behavior Directly Governs Individual Demographic PerformanceDirectly Governs Individual Demographic Performance

Indirectly Effects Population DynamicsIndirectly Effects Population Dynamics

Population Growth Implies Chance of ExtinctionPopulation Growth Implies Chance of Extinction

Here, Take Behavior = Social OrganizationHere, Take Behavior = Social Organization

ExtinctionExtinction

Population extinction processPopulation extinction process

Four general causes of extinctionFour general causes of extinction

1. Environmental stochasticity1. Environmental stochasticity

2. Demographic stochasticity2. Demographic stochasticity

3. Abiotic catastrophes3. Abiotic catastrophes

4. Lack genetic variation4. Lack genetic variation

ExtinctionExtinction

Environmental stochasticityEnvironmental stochasticity

Random, temporal variation: Random, temporal variation: exogenousexogenous factor (s) factor (s)

Individuals’ experience Individuals’ experience samesame birth, death rates birth, death rates Temporal fluctuations, Temporal fluctuations, Between-generationBetween-generation scale scale

Good, Bad Years = Generations: food abundanceGood, Bad Years = Generations: food abundance

Small population & bad year Small population & bad year ExtinctionExtinction

ExtinctionExtinction

Demographic stochasticityDemographic stochasticity

Random variation among individuals, Random variation among individuals,

Within-generationWithin-generation scale scale

Number offspring, survivalNumber offspring, survival

Individuals’ birth and death rates Individuals’ birth and death rates independentindependent,,

hence can differhence can differ

Important small populations: chance extinctionImportant small populations: chance extinction

ExtinctionExtinction

Demographic stochasticityDemographic stochasticity

Fix time; Extinction PrFix time; Extinction Pr

declines with Initialdeclines with Initial

population izepopulation ize

Fix Pop size; Extinction PrFix Pop size; Extinction Pr

increases with timeincreases with time

MTE = (Extinction Pr)MTE = (Extinction Pr)-1-1

ExtinctionExtinction

Abiotic (Physical) CatastrophesAbiotic (Physical) Catastrophes

Large, sudden density reductionLarge, sudden density reduction

Environmental, anthropogenicEnvironmental, anthropogenic

Climate changeClimate change

Time scale relative to generation timeTime scale relative to generation time

ExtinctionExtinction

GeneticGenetic

Lack variation, Lack variation, populationpopulation fails to fails to adaptadapt

Rarest, but [again] global climate changeRarest, but [again] global climate change

Behavior Behavior Population Population DynamicsDynamicsVucetich Vucetich et alet al. 1997. Effects of social structure and . 1997. Effects of social structure and

prey dynamics on extinction risk in gray prey dynamics on extinction risk in gray wolves. Conservation Biology 11:957.wolves. Conservation Biology 11:957.

1. Wolves: social behavior - group, pack1. Wolves: social behavior - group, pack

1 litter/year, dominant female1 litter/year, dominant female

amplify amplify demographic stochasticitydemographic stochasticity

2. Prey availability: fluctuate, source of 2. Prey availability: fluctuate, source of

environmental stochasticityenvironmental stochasticity

Behavior Behavior Population Population DynamicsDynamics

Gray wolf (Gray wolf (Canis lupus)Canis lupus)

Isle Royale, MI; island in Lake SuperiorIsle Royale, MI; island in Lake Superior

National Park, > 500 miNational Park, > 500 mi22

Wolves feed on mooseWolves feed on moose

Abundance of old moose (> 9 yrs) keyAbundance of old moose (> 9 yrs) key

Behavior Behavior Population Population DynamicsDynamics

Objective: Simulate wolf population dynamicsObjective: Simulate wolf population dynamics

Predict mean time to extinction (MTE)Predict mean time to extinction (MTE)

1. Age-dependent mortality in wolves1. Age-dependent mortality in wolves

1/3 pups die first year1/3 pups die first year

No wolves older than 11 yrsNo wolves older than 11 yrs

2. Random litter size in wolves, Mean = 12. Random litter size in wolves, Mean = 1

Behavior Behavior Population Population DynamicsDynamics

3. Wolf packs:3. Wolf packs:

Some restructuring between yearsSome restructuring between years

When prey abundance falls,When prey abundance falls,

smallest pack disperses, mortality costsmallest pack disperses, mortality cost

Survivors join another packSurvivors join another pack

Number packs proportional to no. old-moose Number packs proportional to no. old-moose

Wolf/Pack Count vs MooseWolf/Pack Count vs Moose

Wolf, Pack, Moose DynamicsWolf, Pack, Moose Dynamics

Behavior Behavior Population Population DynamicsDynamics

Mean Time to Extinction, Wolf PopulationMean Time to Extinction, Wolf Population

Weak dependence, initial Weak dependence, initial population sizepopulation size

Standard result not observedStandard result not observed

Strong effect, initial Strong effect, initial number of packsnumber of packs

Simulation resultsSimulation results

Behavior Behavior Population Population DynamicsDynamics

Reproductive unit is packReproductive unit is pack

Number packs, not population size criticalNumber packs, not population size critical

extinction processextinction process

Social organization, with dominance-based Social organization, with dominance-based breeding, amplifies effects of breeding, amplifies effects of

demographic stochasticitydemographic stochasticity on extinction on extinction

Behavior Behavior Population Population DynamicsDynamics

No. old moose constant = 305No. old moose constant = 305

Wolves: MTE = 155 yrsWolves: MTE = 155 yrs

No. old moose cycles, mean = 305No. old moose cycles, mean = 305

Wolves: MTE = 105 yrsWolves: MTE = 105 yrs

Environmental stochasticityEnvironmental stochasticity

Standard resultStandard result

Behavior Behavior Population Dynamics Population Dynamics

Social Social group sizegroup size Individual demographic performance Individual demographic performance

How might group size How might group size GG influence population dynamics? influence population dynamics?

Trainor, K.E. & T. Caraco. 2006. Group size, energy Trainor, K.E. & T. Caraco. 2006. Group size, energy budgets and population dynamic complexity. budgets and population dynamic complexity.

Evolutionary Ecology ResearchEvolutionary Ecology Research 8:1173-1192. 8:1173-1192.

Model Assumptions (1)Model Assumptions (1)

Foragers search in groups, Foragers search in groups, GG individuals individuals Rate food-clump discoveryRate food-clump discovery

1/(population density)1/(population density)

Density dependenceDensity dependence GG; interference, mutualism; interference, mutualism

Energy consumption randomEnergy consumption random Number clumps, clump sizeNumber clumps, clump size

Model Assumptions (2)Model Assumptions (2)

StarvationStarvation Consumption Consumption energy requirement energy requirement Variation between groupsVariation between groups

Predation while foragingPredation while foraging Random independent attacksRandom independent attacks Increases with consumer densityIncreases with consumer density

Survival & Survival & ReproductionReproduction Surviving non-breeding seasonSurviving non-breeding season

Avert starvationAvert starvation Avoid predationAvoid predation

Reproduction: Reproduction: RR fixed fixed Survivor + (Survivor + (RR-1) offspring-1) offspring

Return Map (1)Return Map (1)

nnt+t+11 = F(n = F(ntt) n) ntt

F(nF(ntt)): Density-dependent reproduction: Density-dependent reproduction

FF = = R R x x pp(avert starvation |(avert starvation |GG,,nn) )

x x pp(avoid predation |(avoid predation |nn))

Stable dynamics: stable Stable dynamics: stable nodenode

For For αα > 1, > 1, QQ = 8, = 8, VcVc = 1.0; = 1.0; GG = 28 = 28

t

nt

Stable dynamics: stable nodeStable dynamics: stable node

αα > 1 (mutualism ?) > 1 (mutualism ?)

Individual encounters clumps faster as Individual encounters clumps faster as GG increases increases

Mean energy intake may IncreaseMean energy intake may Increase

Energy intake variance declinesEnergy intake variance declines

Stable CycleStable Cycle

For For αα = 1.0, = 1.0, QQ = 10, = 10, VcVc = 0.5; = 0.5; GG = 32 = 32

Stable CycleStable Cycle

αα = 1.0 = 1.0

Individual encounters clumps independently of Individual encounters clumps independently of GG

Mean energy intake independent of Mean energy intake independent of GG

Energy intake variance declinesEnergy intake variance declines

Complex dynamicsComplex dynamics

For For αα = 0.8, = 0.8, QQ = 12, = 12, VcVc = 0.5; = 0.5; GG = 20 = 20

Complex dynamicsComplex dynamics

αα < 1 (interference) < 1 (interference)

Individual encounters clumps slower as Individual encounters clumps slower as G increasesG increases

Mean energy intake declines with Mean energy intake declines with GG

Chaotic dynamics; often near extinctionChaotic dynamics; often near extinction

Behavior Behavior Population Population DynamicsDynamics

Interactions among individual group membersInteractions among individual group members

Interference, independence, mutualismInterference, independence, mutualism

Survival through non-breeding seasonSurvival through non-breeding season

Complexity of population dynamicsComplexity of population dynamics

Likelihood of extinctionLikelihood of extinction