Evolutionary responses of foraging-related traits in unstable predator-prey systems

The evolutionary responses of predators to prey and of prey to predators are analysed using models for the dynamics of a quantitative trait that determines the capture rate of prey by an average searching predator. Unlike previous investigations, the analysis centres on models and/or parameter values for which the two-species equilibrium is locally unstable. The instability in some models is driven by the predator's non-linear functional response to prey; in other models, the cycles are a direct consequence of evolutionary response to selection acting on the trait. When the values of predator and prey traits combine multiplicatively to determine the capture rate, the predator's trait shows only a transient response to changes in the prey's trait in stable systems. However, when the population densities exhibit sustained oscillations, predators often evolve an increased long-term mean capture rate in response to an increased prey escape ability. Under the multiplicative model, prey in stable systems always evolve increased escape ability in response to an increased predator capture ability; in unstable systems, prey may exhibit the opposite response. Both of these are consequences of changes in the form of the population cycles that occur with changes in capture-related traits. Additional theory is needed to understand evolution and co-evolution of traits related to foraging by species that undergo sustained oscillations in population size.