Replicators in a Fine-Grained Environment: Adaptation and Polymorphism

Selection in a time-periodic environment is modeled via the two-player replicator dynamics. For sufficiently fast environmental changes, this is reduced to a multiplayer replicator dynamics in a constant environment. The two-player terms correspond to the time-averaged payoffs, while the three- and four-player terms arise from the adaptation of the morphs to their varying environment. Such multiplayer terms can induce a stable polymorphism. The establishment of the polymorphism in partnership games [genetic selection] is accompanied by decreasing mean fitness of the population.