The dynamic effects of an inducible defense in the Nicholson-Bailey model.
We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-prey model. We assume that the defense is of all-or-nothing type but that the probability for a prey individual to express the defended phenotype increases gradually with predator density. Compared to a defense that is independent of predation risk, an inducible defense facilitates persistence of the predator-prey system. In particular, inducibility reduces the minimal strength of the defense required for persistence. It also promotes stability by damping predator-prey cycles, but there are exceptions to this result: first, a strong inducible defense leads to the existence of multiple equilibria, and sometimes, to the destruction of stable equilibria. Second, a fast increase in the proportion of defended prey can create predator-prey cycles as the result of an over-compensating negative feedback. Non-equilibrium dynamics of the model are extremely complex.
Kopp
Michael
M
Department of Physiological Ecology, Max-Planck-Institute of Limnology, P.O. Box 165, 24302 Plön, Germany. kopp@zi.biologie.uni-muenchen.de
Gabriel
Wilfried
W
D000818:Animals; D008954:Models, Biological; D015233:Models, Statistical; D011157:Population Dynamics; D011235:Predatory Behavior