The impact of truncation selection and diffusion on cooperation in spatial games

Natural Selection is frequently modelled via proportional selection where survival is proportional to the average payoff differential. There has been little attention devoted to modelling truncation selection where replicators below a threshold are culled and survivors reproduce. Here, we systematically explore truncation selection for two strategy games in a spatial setting. We employ two variations of truncation selection: independent, where the threshold is fixed; and dependent, where the proportion culled is fixed. Further, we explore the effects of diffusion with the algorithms: contest-diffusion-offspring (CDO), and diffusion-contest-offspring (DCO). CDO and DCO frequently facilitate and diminish cooperation, respectively. For independent truncation, there are three qualitative regimes determined by the payoff threshold: cooperation decreases as the threshold rises; polymorphisms are stable; and extinction is frequent. Further, an intermediate payoff to cooperators playing defectors can maximize cooperation for the DCO algorithm with a high payoff threshold. Dependent truncation affects games differently; lower levels reduce cooperation for the Hawk Dove game and increase it for the Stag Hunt, and higher levels produce the opposite effects. Comparing these truncation methods to proportional selection, we show how they impact the prevalence of cooperation.