In this problem, we will investigate how mutual interference of parasitoids affects

Chapter 10, Problem 50

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In this problem, we will investigate how mutual interference of parasitoids affects their searching efficiency for a host. We assume that N is the host density and P is the parasitoid density. A frequently used model for hostparasitoid interactions is the NicholsonBailey model (Nicholson, 1933; Nicholson and Bailey, 1935), in which it is assumed that the number of parasitized hosts, denoted by Na , is given by Na = N[1 ebP] (10.3) where b is the searching efficiency. (a) Show that b = 1 P ln N N Na by solving (10.3) for b. (b) Consider b = f (P, N, Na) = 1 P ln N N Na as a function of P, N, and Na . How is the searching efficiency b affected when the parasitoid density increases? (c) Assume now that the fraction of parasitized host depends on the host density; that is, assume that Na = g(N) where g(N) is a nonnegative, differentiable function. The searching efficiency b can then be written as follows as a function of P and N: b = h(P, N) = 1 P ln N N g(N) How does the searching efficiency depend on host density when g(N) is a decreasing function of N? (Use the fact that g(N) < N.)