Frequency‐dependent evolution in a predator–prey system

Abstract

We present a discrete‐time predator–prey model in which the prey population is assumed to evolve in response to a toxicant. We incorporate frequency‐dependent selection into the prey evolution, assuming that an individual's susceptibility to predation depends on both the trait it possesses and the traits of others in the population. When frequency‐dependent selection is symmetric, we show that the trait equation is unable to track changes in the fitness landscape, that is, the fitness landscape may change while the trait continues to evolve to the same trait value. As a result, evolution may produce unfit prey populations. Meanwhile, we show that asymmetric frequency‐dependence may have a destabilizing effect on the system, resulting in a closed invariant curve via a Neimark–Sacker bifurcation.