EVOLUTIONARY RESPONSES OF FORAGING-RELATED TRAITS IN UNSTABLE PREDATOR-PREY SYSTEMS

The evolutionary responses of predators to prey and of prey to predato rs are analysed using models for the dynamics of a quantitative trait that determines the capture rate of prey by an average searching preda tor. Unlike previous investigations, the analysis centres on models an d/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 ar e a direct consequence of evolutionary response to selection acting on the trait. When the values of predator and prey traits combine multip licatively to determine the capture rate, the predator's trait shows o nly a transient response to changes in the prey's trait in stable syst ems. However, when the population densities exhibit sustained oscillat ions, predators often evolve an increased long-term mean capture rate in response to an increased prey escape ability. Under the multiplicat ive model, prey in stable systems always evolve increased escape abili ty in response to an increased predator capture ability; in unstable s ystems, prey may exhibit the opposite response. Both of these are cons equences of changes in the form of the population cycles that occur wi th changes in capture-related traits. Additional theory is needed to u nderstand evolution and co-evolution of traits related to foraging by species that undergo sustained oscillations in population size.