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The dynamic effects of an inducible defense in the Nicholson-Bailey model

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Kopp,  Michael
Department Ecophysiology, Max Planck Institute for Limnology, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Gabriel,  Wilfried
Department Ecophysiology, Max Planck Institute for Limnology, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Citation

Kopp, M., & Gabriel, W. (2006). The dynamic effects of an inducible defense in the Nicholson-Bailey model. Theoretical Population Biology, 70(1), 43-55. doi:10.1016/j.tpb.2005.11.002.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-D893-3
Abstract
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.