Weak selection and stochastic evolutionary stability in a stochastic replicator dynamics

It is a very challenging problem whether natural selection is able to effectively resist the continuous disturbance of environmental noise such that the direction or outcome of evolution determined by the deterministic selection pressure will not be changed. By analyzing the impact of weak selection on the evolutionary stability of a stochastic replicator dynamics with n possible pure strategies, we found that the weak selection is able to enhance the evolutionary stability, that is, under weak selection, the stochastic evolutionary stability of the system is determined by the mean payoff matrix. This finding strongly implies that the weak selection should be regarded as an important mechanism to ensure evolutionary stability in stochastic environments.

Automated summary

This article examines whether natural selection can effectively resist the continuous disturbance of environmental noise in order to maintain the direction or outcome of evolution determined by deterministic selection pressure. By analyzing the impact of weak selection on stochastic replicator dynamics, it is found that weak selection can enhance evolutionary stability. Under weak selection, the stochastic evolutionary stability of the system is determined by the mean payoff matrix. This finding strongly suggests that weak selection should be regarded as an important mechanism for ensuring evolutionary stability in stochastic environments.