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.
Cressman
R
R
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada. rcressman@wlu.ca
Garay
J
J
Hofbauer
J
J
D000818:Animals; D005075:Biological Evolution; D008957:Models, Genetic; D009154:Mutation; D011110:Polymorphism, Genetic; D012641:Selection, Genetic