Ross Cressman, József Garay and Josef Hofbauer:
Abstract. 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.