Strategy abundance in 2x2 games for arbitrary mutation rates

TL;DR

This paper demonstrates that a known condition for strategy abundance in 2x2 evolutionary games remains valid across a broad class of stochastic processes, regardless of mutation rate or selection strength.

Contribution

It generalizes previous results by proving the strategy abundance condition holds for arbitrary mutation rates and various stochastic birth-death processes.

Findings

The abundance condition is valid for a wide class of stochastic processes.

The result holds for any mutation rate and intensity of selection.

Previous limits of weak mutation or weak selection are extended to general cases.

Abstract

We study evolutionary game dynamics in a well-mixed populations of finite size, N. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the average abundances of two strategies, A and B, under mutation and selection. The game dynamical interaction between the two strategies is given by the 2x2 payoff matrix [(a,b), (c,d)]. It has previously been shown that A is more abundant than B, if (N-2)a+Nb>Nc+(N-2)d. This result has been derived for particular stochastic processes that operate either in the limit of asymptotically small mutation rates or in the limit of weak selection. Here we show that this result holds in fact for a wide class of stochastic birth-death processes for arbitrary mutation rate and for any intensity of selection.