Predator-Prey Cycles PDF

Ecology Week 10 Lecture 16 – Predation 16b: Predator-Prey Cycles  Predator-Prey Cycles Classic example is North American lynx (Lynx canadensis) which preys almost exclusively on snow-shoe hare (Lepus americanus). 2 3  Predator-...

Ecology Week 10 Lecture 16 – Predation 16b: Predator-Prey Cycles  Predator-Prey Cycles Classic example is North American lynx (Lynx canadensis) which preys almost exclusively on snow-shoe hare (Lepus americanus). 2 3  Predator-Prey Cycles In Arctic tundra regions: 9-year cycles in large animals – Hare, muskrat, ruffed grouse – Lynx, red fox 4-year cycles in small animals – Voles, mice, lemmings – Hawks, owls  Predator-Prey cycle – Prey population (snowshoe hare) increases, more food for the predator (lynx) and predator population increases (after time delay). – Increase predator population means more predation leading to a decline in the prey population size. 5  Theoretical Model: Period of a cycle is time between peaks (10yrs here) 6 Theoretical Model: 7 Lotka-Volterra Predation Model For the prey population is: dR = rR – cRP dt – R (Resource) = size of prey population – r (rate) = growth rate of prey population – c (capture efficiency) = ability of predators to capture prey – P (Predator) = size of predator population. Continuous-time or Discrete-time model? Lotka-Volterra Predation Model dR = rR - cRP dt The rate The growth rate The removal of of change = - of the prey prey individuals in the prey population by predators population  Lotka-Volterra Predation Model The equation for predator population is: dP = acRP - dP dt a (assimilation efficiency) = efficiency with which food is converted to population growth d (death rate) = constant rate of predator death 10 Lotka-Volterra Predation Model When will populations increase? For prey, when: rR>cRP Rearranging: P