Consider the following general model, where N is the prey density, P is the predator density, x is the prey defense, r(x) is the prey growth rate, k is the prey density-dependence parameter, f(x) is the attack rate, c is the conversion efficiency, d is the predator mortality rate, and Gx is the prey additive genetic variance. Because x is the defense trait, we assume∂f (x) ∂x < 0. In addition, we assume ∂r(x) ∂x < 0 due to the cost of defense.
(a) What is an internal equilibrium of N and P?
(b) Consider a situation where we increase the predator mortality rate, d. When does the predator go extinct?
(c) How does increasing d affect prey defense trait evolution?
(d) How does prey defense trait evolution affect the mortality rate at which the predator goes extinct?
