Evolutionary Stability Concepts for N–species Frequency-dependent Interactions

The classical static concept of an evolutionarily stable strategy (ESS) for a single species gives rise to two new notions when there are more than two species (called an N–species ESS and RL-stability). The paper relates these to the dynamic stability of monomorphic and polymorphic evolutionary systems. It is shown that RL-stability implies the global asymptotic stability of either system with or without mutations. However, the N–species ESS only implies stability of the monomorphic system.