6A verbal model of predator-prey cycles: Predators eat prey and reduce their numbersPredators go hungry and decline in numberWith fewer predators, prey survive better and increaseIncreasing prey populations allow predators to increaseAnd repeat…
7Why don’t predators increase at the same time as the prey?
8The Lotka-Volterra Model: Assumptions Prey grow exponentially in the absence of predators.Predation is directly proportional to the product of prey and predator abundances (random encounters).Predator populations grow based on the number of prey. Death rates are independent of prey abundance.
9R = prey population size (“resource”) P = predator population sizer = exponential growth rate of the preyc = capture efficiency of the predators
10rate of change inthe prey populationintrinsic growthrate of the preyremoval of preyby predators
11a = efficiency with which prey are converted into predators For the predators:a = efficiency with which prey are converted into predatorsd = death rate of predatorsdeath rate of predatorsrate of change in thepredator populationconversion of preyinto new predators
12Prey population reaches equilibrium when dR/dt = 0 equilibrium – state of balance between opposing forcespopulations at equilibrium do not changePrey population stabilizes based on the size of the predator population
13Predator population reaches equilibrium when dP/dt = 0 Predator population stabilizes based on the size of the prey population
14Isocline – a line along which populations will not change over time. Predator numbers will stay constant if R = d/acPrey numbers will stay constant if P = r/c.
15Number of Predators (P) Number of prey (R) Predators are stable when: Prey are stable when:Number ofPredators (P)Number of prey (R)
16Number of Predators (P) Number of prey (R) Prey are stable when: Prey IsoclineNumber ofPredators (P)r/cd/acNumber of prey (R)
17Number of Predators (P) Number of prey (R) Predators are stable when: isoclineNumber ofPredators (P)d/acNumber of prey (R)
18equilibriumNumber ofPredators (P)r/cd/acNumber of prey (R)
19Predation (Chapter 18) Finish Lotka-Volterra model Functional vs. numeric responsesStability in predator-prey cycles
20Number of predators depends on the prey population. isoclineNumber ofPredators (P)PredatorsdecreasePredatorsincreased/acNumber of prey (R)
21Number of prey depends on the predator population. Prey decreasePreyIsoclineNumber ofPredators (P)r/cPrey increased/acNumber of prey (R)
24Changing the number of prey can cause 2 types of responses: Functional response – relationship between an individual predator’s food consumption and the density of preyNumeric response – change in the population of predators in response to prey availability
25Lotka-Volterra: prey are consumed in direct proportion to their availability (cRP term) known as Type I functional responsepredators never satiate!no limit on the growth rate of predators!
26Type II functional response – consumption rate increases at first, but eventually predators satiate (upper limit on consumption rate)
27Type III functional response – consumption rate is low at low prey densities, increases, and then reaches an upper limit
28Why type III functional response? at low densities, prey may be able to hide, but at higher densities hiding spaces fill uppredators may be more efficient at capturing more common preypredators may switch prey species as they become more/less abundant
33Predator-prey cycles can be unstable efficient predators can drive prey to extinctionif the population moves away from the equilibrium, there is no force pulling the populations back to equilibriumeventually random oscillations will drive one or both species to extinction
35Factors promoting stability in predator-prey relationships Inefficient predators (prey escaping)less efficient predators (lower c) allow more prey to survivemore living prey support more predatorsOutside factors limit populationshigher d for predatorslower r for prey
36Alternative food sources for the predator less pressure on prey populationsRefuges from predation at low prey densitiesprevents prey populations from falling too lowRapid numeric response of predators to changes in prey population
37Huffaker’s experiment on predator-prey coexistence 2 mite species, predator and prey
38Initial experiments – predators drove prey extinct then went extinct themselves Adding barriers to dispersal allowed predators and prey to coexist.
39Refuges from predation allow predator and prey to coexist.
40Prey population outbreaks Population growth curve for logistic population growthPer capita population growth rateroKDensity of prey population
41Density of prey population Type III functional response curve for predatorsPer capita death rateKDensity of prey population