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

Pablo Catalán,Jesús M Seoane,Miguel A.F Sanjuán

doi:10.1016/j.cnsns.2015.01.012

Abstract

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 δ 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 δ 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.

Highlights

Evolutionary game theory models a population of individuals interacting in a game, each playing different strategies
We focus on estimating the abundance of each strategy through time, in order to discover which strategies are being favored by selection
We analyze the effect of selection δ and mutation u on the abundances of the different strategies in the [0, 1] interval playing a Hawk-Dove game

Summary

Introduction

Evolutionary game theory models a population of individuals interacting in a game, each playing different strategies. The payoff of every player will be an average of the payoffs obtained from the games played with every other individual. Payoff is interpreted as fitness, meaning that individuals with higher payoff reproduce faster, and outcompete players of worse strategies. The fitness of an individual depends on the composition of the population at a certain moment of time.

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Conclusion