Mutation-selection equilibrium in finite populations playing a Hawk–Dove game

• The evolution of a finite population playing a Hawk–Dove game with mixed strategies is analyzed.
• The effect of selection on the abundances of favored strategies is nonlinear.
• The mutation rate has an opposite and stronger effect to that of selection.
• We provide some heuristic arguments to theoretically justify the nonlinear relationship between selection and mutation.

We study the evolution of a finite population playing a Hawk–Dove game with mixed strategies. Players have a fixed strategy and their offspring inherit the parental strategy, with a probability u   of mutating to another strategy. Payoff in the game is the only variation in fitness among individuals, and a selection coefficient δδ measures the importance of the game in the overall fitness. Population evolution is carried out through a Moran process. We compare our numerical simulations with theoretical predictions in earlier work by Tarnita et al. (2009). Our results show that the effect of selection on the abundances of favored strategies is nonlinear, being less intense as δδ increases. The mutation rate u has an opposite and stronger effect to that of selection. Heuristic theoretical arguments are given in order to explain this nonlinear relationship.