10-1-09 - Biology 330 Class Notes You need lx*dx and ex...

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Biology 330 – Class Notes – 10/1/09 You need lx*dx and ex columns for your life table H: # of prey P: # of predators The intensity of the interaction between predators and prey depends on the size of the population Both populations are high very intense Both populations are low very low intensity few predators, rare prey dH/dt = r*H – (rho)*(H)*(P) dP/dt = -d*P + (alpha)*(rho)*(H)*(P) (rho) = Proportionality constant – “rho” – just a measure of foraging efficiency This is used to convert the intensity of the interaction into the predator and prey population count (alpha) = biomass conversion efficiency o This is a constant used to account for the fact that it may take many kills by a fox before it reproduces It takes many more chipmunks to be killed and consumed by the fox before the fox reproduces 1 more individual So there is a disproportionate number of consumed prey to cause the creation of 1 more predator Is it possible for a population to be in equilibrium? If equilibrium populations are possible (dH/dt = 0 and dP/dt = 0) o This means the populations of predators and prey are IN BALANCE, not that there are no births and deaths there ARE births and deaths, but the net addition and loss of individuals is zero. r*H = (rho)*(H)*(P) and P = (r / rho) and dH/dt = 0 dP = (alpha)*(rho)*(H)*(P) and H = (d / alpha*rho) and dP/dt = 0 (SEE GRAPH ON PAGE 1 OF PAPER)
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Is this model of predator and prey populations realistic? NO. WHY? THE ASSUMPTIONS ARE NOT ALWAYS TRUE. ASSUMPTIONS OF Latger Predator-Prey MODEL: 1. Rho is constant foraging efficiency is constant 2. There is no carrying capacity in this model (no limits to population sizes) TRAJECTORY OF PREDATOR AND PREY POPULATIONS Type II Functional Response The prey population density was kept constant The number of flies consumed is a function of the number of flies in the feeding arena What about the efficiency at which the predator eats the prey? o The praying mantis is constantly eating more flies, but its proportionally less o The slope is getting more shallow, suggesting that the praying mantis
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