Predation promotes cooperation in Prisoner's dilemma games

The emergence and maintenance of cooperation among selfish individuals is still a fundamental problem in evolutionary biology and social science, and Prisoner's Dilemma game (PDG) is an important metaphor to study the evolution of cooperation. In this paper, we propose a three-dimensional model based on the PDG in which the harsh ecological environment (indicated by predation stress) is considered. Our results show that proper predation stress is a positive factor for the evolution of cooperation. Moderate predation stress lead to the increase of cooperators, but too large predation stress result in the extinction of cooperators. Moreover, we find that the fraction of cooperators decreases monotonously with the increasing of the cost-to-benefit ratio, but increases monotonously with the increasing of encounter probability. These results indicate that our model represents a step towards understanding how the harsh ecological environment can affect the evolution of cooperation.