L16 predators

L16 predators - BILD 3 LYNX SHOESHOE HARE PREDATION...

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BILD 3 July 19, 2010 Woodruff: predator-prey 1 LYNX SHOESHOE HARE Predation: Accounts for much energy flow through ecosystems Significant source of density-dependent population regulation PREDATION Consider predation as a regulator of prey populations. Lotka-Volterra equations Birth rate of the predator will increase as prey numbers increase Death rate of the prey will increase as predator numbers increase PREDATOR PREY NUMBERS N 1 N 2 BIRTH RATE B 1 B 2 DEATH RATE D 1 D 2 dN/dt = rN = (B – D)N N 1 PREDATOR POPULATION GROWTH dN 1 /dt = (B 1 x N 2 – D 1 )N 1 = B 1 N 2 N 1 – D 1 N 1 N 2 PREY POPULATION GROWTH dN 2 /dt = (B 2 – D 2 x N 1 )N 2 = B 2 N 2 – D 2 N 1 N 2 At what population N will the predator and prey populations be at equilibrium? Setting predator growth rate to zero: dN 1 /dt = B 1 N 2 N 1 – D 1 N 1 = 0 D 1 N 1 = B 1 N 2 N 1 N 2 = D 1 /B 1 N 1 predator N 2 prey Setting predator growth rate to zero: Similarly the prey zero growth curve will be: N 1 = B 2 /D 2 N 1 predator N 2 prey N 2 = D 1 /B 1 N 1 predator

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