PredationPredator-Prey InteractionsSlide 3Strawberry Fields ForeverConsumers can limit resource populationsSlide 6Slide 7Slide 8Predation efficiency is not 100%Effective PredatorsCoupled OscillationsSlide 12Slide 13Modeling Predator-PreySlide 15Slide 16Slide 17Change in Prey PopulationsSlide 19Slide 20Slide 21Slide 22Slide 23Slide 24Realism of the L-V ModelSlide 26Slide 27Predator PopulationsSlide 29Slide 30Slide 31Cycling in Lotka-Volterra EquationsJoint Population GrowthSlide 34Counterclockwise EllipseCounterclockwise Ellipse in Naturebecome OscillationsAre there stable equilibria?Large perturbationsPredator satiationType I Functional ResponseSlide 42Slide 43Type II Functional ResponseSlide 45The Type III ResponseSlide 47Predator switches preyLotka-Volterra PredictionNatural instance of Type II Functional ResponseWolves & CaribouSlide 52Changing the IsoclinesSlide 54Slide 55SummaryPredation1. Top-down Regulation2. OscillationsPredator-Prey InteractionsWhat factors influence the size and stability of populations?Resource availabilityReproductive capacityDisturbanceThreatsPredator-Prey InteractionsDo predators reduce the size of their prey populations below carrying capacity?Hypothesis: Predator regulates the population size of Prey.Experiment: Treatment = exclude the predatorPrediction: Prey population size where the predator is excluded will be greater than prey population size where predators are allowed.Strawberry Fields ForeverCyclamen mites & damaged strawberry fieldTyphlodromus sp.Consumers can limit resource populations•Huffaker’s mite experiment in 1958 (UCLA)•Populations of cyclamen mites, a pest of strawberry crops in California, can be regulated by predatory mite:–cyclamen mites typically invade strawberry crops soon after planting and build to damaging levels in the second year–predatory mites invade these fields in the second year and keep cyclamen mites in check•Experimental plots in which predatory mites were controlled by pesticide had cyclamen mite populations 25 times larger than untreated plots.Strawberry Fields ForeverStrawberry Fields Foreverindiv/leafindiv/36 leafletsStrawberry Fields ForeverPredation efficiency is not 100%Effective Predators High reproductive capacity Strong dispersal Prey switchingCoupled OscillationsRemember the Lynx & the Hare?Persistent cycles are stable interactionsPopulation oscillationsfrom time delaysCoupled OscillationsBean Weevils and Heterospilus wasps Parasitoid wasp lays eggs in weevil larvae living inside a seedModeling Predator-PreyModeling Predator-PreyLotka-Volterra ModelsP = predatorH = prey= f(H, P)dHdtModeling Predator-PreyWhat happens to the prey?= rH – pHP dHdtMortality inflicted by the predatorBut what is pHP really?How could you measure the parts of it?Modeling Predator-Prey= rH – pHP dHdtpHP assumes the law of mass action:predation varies in direct proportion to the product of prey and predator populationsso how do we define p?Change in Prey Populationsr = 1.2, p = 0.01H = 30= rH – pHP dHdtChange in Prey Populationsr = 1.2, p = 0.01H = 30= rH – pHP dHdtr → rate of prey pop. growthp → predation efficiencyH → prey densityChange in Prey Populationsr = 1.2, p = 0.01H = 30= rH – pHP dHdtWhat’s the red star?Maximal prey growth rate (dH/dt = rH – no predators)Slope of the line?Declining growth rate with presence of more predatorsChange in Prey Populationsr = 1.2, p = 0.01H = 30= rH – pHP dHdtWhat’s the blue star? P = r/p^Change in Prey Populationsr = 1.2, p = 0.01H = 10, 30, 50= rH – pHP dHdtWhat’s the blue star? P = r/p^* Higher prey density enables predators to easily find preyChange in Prey PopulationsChange in Prey PopulationsHigher predation efficiency → decreased P where prey growth zero; less prey to convert into predators.Realism of the L-V ModelAs prey population density increases, the “strength” of predation increases (slope is steeper). Is that realistic?Realism of the L-V ModelAs prey population increases, the “strength” of predation increases (slope is steeper). Is that realistic?Size of prey population is importantRealism of the L-V ModelAs prey population increases, the “strength” of predation increases (slope is steeper). Is that realistic?• Predators don’t interfere with each otherPredator Populations= a(pHP) – deaths dPdta = conversion rate of prey energy into predatorsPredator Populations= apHP – dP dPdta = conversion rate of prey energy into predatorsd = predator death rate (let’s assume it’s density independent)Predator PopulationsPredator PopulationsH = d/ap^Cycling in Lotka-Volterra Equations•A graph with axes representing sizes of the predator and prey populations illustrates the cyclic predictions of Lotka-Volterra predator-prey equations:–a population trajectory describes the joint cyclic changes of P and R counterclockwise through the P versus R graphJoint Population GrowthH = d/ap^= 0dPdtThe equilibrium isocline of the preyP = r/p^= 0dHdtThe equilibrium isocline of the predatorJoint Population GrowthSo what would a graph of population size against time look like?Counterclockwise EllipseCounterclockwise Ellipse in NatureNatural cycle from time delay of responsebecome OscillationsAre there stable equilibria?The central equilibrium is unstable; nothing drives the system to the centerDensity-dependence in the predator will dampen the oscillationsTime-lags destabilize the systemPrey refuges increase persistenceLarge perturbationsModel works only near (H,P)Perturbations can permanently disrupt the system^ ^Predator satiationType I Functional ResponsePredicts there is no upper limit to prey consumptionAssumed by Lotka-Volterra modelsmeans that prey consumed = pHPType I Functional ResponsePredicts there is no upper limit to prey consumptionReasonable over some ranges of prey densityMay also be good for filter feedersType I Functional ResponsePredicts there is no upper limit to prey consumptionReasonable over some ranges of prey densityMay also be good for filter feedersGenerally unrealisticsatiationhandling timeType II Functional ResponsePredicts prey consumption per predator levels offType II Functional ResponsePredicts prey consumption per predator levels offAllows for the effects of handling timeThe Type III ResponsePrey consumption starts slow, picks up, then levels offHighest consumption at intermediate prey densitiesAt low density, prey