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