PREY ADAPTATION AS A CAUSE OF PREDATOR-PREY CYCLES

We analyze simple models of predator-prey systems in which there is ad aptive change in a trait of the prey that determines the rate at which it is captured by searching predators. Two models of adaptive change are explored: (1) change within a single reproducing prey population t hat has genetic variation for vulnerability to capture by the predator ; and (2) direct competition between two independently reproducing pre y populations that differ in their vulnerability. When an individual p redator's consumption increases at a decreasing rate with prey availab ility, prey adaptation via either of these mechanisms may produce sust ained cycles in both species' population densities and in the prey's m ean trait value. Sufficiently rapid adaptive change (e.g., behavioral adaptation or evolution of traits with a large additive genetic varian ce), or sufficiently low predator birth and death rates will produce s ustained cycles or chaos, even when the predator-prey dynamics with fi xed prey capture rates would have been stable. Adaptive dynamics can a lso stabilize a system that would exhibit limit cycles if traits were fixed at their equilibrium values. When evolution fails to stabilize i nherently unstable population interactions, selection decreases the pr ey's escape ability, which further destabilizes population dynamics. W hen the predator has a linear functional response, evolution of prey v ulnerability always promotes stability. The relevance of these results to observed predator-prey cycles is discussed.