The Dynamics of Evolutionary Stable Strategies

Abstract

We use the so-called G-function to determine the number of coexisting species with evolutionary stable strategies (ESS). We show that a simple model, with a single resource (carrying capacity) can result in an ESS with more than one (and potentially many) coexisting species. We also show how the adaptive landscape (the shape of the G-function) changes in the pursuit of the evolutionary stable strategy. Next, we use a populations model with a random mating system, and trace the strategy dynamics to ESS from arbitrary initial conditions. We show that with appropriate parameter values, the dynamics lead to chaotic trajectories of the species populations and their evolutionary stable strategies. This indicates that under appropriate conditions, ESS are not necessarily fixed; to be ESS, they must vary (chaotically) with time. The approach we take relies on the fundamental definitions of ESS, and simulation models. This allows applications of ESS analysis to moderately complex models.