Frequency-Dependent Stability for Two-Species Interactions

Evolutionary game theory is extended to models of two-species interactions where fitnesses are based on individual characteristics (strategies) rather than on a population dynamic that assumes homogeneous species. It is shown that the coevolutionary theories in the literature that combine ecology with genetic viability selection are part of this extended theory and that the dynamic stability resulting from a separation of ecological and evolutionary processes actually follows from game-theoretic solution concepts. The main focus of the paper is to investigate the application of the ESS (evolutionarily stable strategy) solution concept to dynamic stability when fitnesses are given by random interactions between individuals as opposed to viability selection. For two-species frequency-dependent interactions, the ESS criterion that implies stability asserts that, in any system near the ESS, at least one of the species is better off (i.e., more fit) if it evolves towards the ESS. The global stability of a polymorphic two-species ESS that is shown for two-species matrix games gives a powerful tool to predict the course of evolution through static fitness comparisons.