A coevolutionary predator-prey model with quantitative characters.

A new model for coevolution in generalized predator-prey systems is presented by incorporating quantitative characters relevant to predation in both prey and predator. Malthusian fitnesses are derived from ecological models, and they include interspecific frequency and density dependence. Both prey and predator characters are under stabilizing selection even without predation, and predation adds an additional linear selection component to both characters. The nonlinear system of differential equations is studied analytically by using local linearization near the equilibrium points. Parameters related to intrinsic growth and death rates and stabilizing selection determine whether there are zero, one, or two equilibria. Additive genetic variances do not have an effect on the equilibrium points, but genetic variability is crucial for determining their stability. Analysis of the linearized model shows that at most one equilibrium can be stable, and stability is achieved when additive genetic variance is high enough in both the prey and predator populations. The stability properties are illustrated by numerical examples of the full dynamics of the original nonlinear model.