Evolution in predator-prey systems
Rick Durrett and John Mayberry
Abstract. We study the adaptive dynamics of predator prey systems modeled by a dynamical system in which the characteristics are allowed to evolve by small mutations. When only the prey are allowed to evolve, and the size of the mutational change tends to 0, the system does not exhibit prey coexistence and the parameters of the resident prey type converges to the solution of an ODE. When only the predators are allowed to evolve, coexistence of predators occurs. In this case, depending on the parameters being varied we see (i) the number of coexisting predators remains tight and the differences of the parameters from a reference species converge in distribution to a limit, or (ii) the number of coexisting predators tends to infinity, and we conjecture that the differences converge to a deterministic limit.
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