FITNESS MINIMIZATION AND DYNAMIC INSTABILITY AS A CONSEQUENCE OF PREDATOR-PREY COEVOLUTION

We analyse dynamic models of the coevolution of continuous traits that determine the capture rate of a prey species by a predator. The goal of the analysis is to determine conditions when the coevolutionary dyn amics will be unstable and will generate population cycles. We use a s implified model of the evolutionary dynamics of quantitative traits in which the rate of change bf the mean trait Value is proportional to t he rate of increase of individual fitness with trait value. Traits tha t increase ability in the predatory interaction are assumed to have ne gative effects on another component of fitness. We concentrate on the role of equilibrial fitness minima in producing cycles. In this case, the mean trait of a rapidly evolving species minimizes its fitness and it is 'chased' around this equilibrium by adaptive evolution in the o ther species. Such cases appear to be most likely if the capture rate of prey by predators is maximal when predator and prey phenotypes matc h each other. They are possible, but less likely when traits in each s pecies determine a one-dimensional axis of ability related to the inte raction. Population dynamics often increase the range of parameter val ues for which cycles occur, relative to purely evolutionary models, al though strong prey self-regulation may stabilize an evolutionarily uns table subsystem.