Diffusion sustains cooperation via forming diverse spatial patterns in prisoner's dilemma game

How cooperation arouses and maintains in social dilemmas has long been the core problem in evolutionary biology. Assortative interaction has been identified as a fundamental mechanism for cooperation in the social dilemma games. Many studies have shown that spatial limitation can lead to cooperation evolution, but how spatial pattern shape the cooperation is studied rarely. In this paper, using a spatial model of eco-evolutionary prisoner's dilemma game, where the player's diffusion is incorporated definitely, we show that the diffusion can trigger out rich spatial patterns. These self-organized spatial patterns could profoundly affect the cooperation level and system stability. Totally, six types of patterns can be identified according to their influences on cooperation evolution. Cooperation is affected by the spatial configuration of population distributions: spot- or stripe- type pattern promotes the cooperation, but mixed form of them or spatial synchrony suppresses cooperation. In contrast, uniform pattern has no effect on cooperation. Meanwhile, the analysis of spatial autocorrelation about population distributions via local Moran index reveals that the difference of spatial correlations among adjacent sites may be responsible for the functional differentiation of such self-organized structures. Spatial diffusion arouses vastly different spatial patterns, which renders the spatial extension system greatly expands the survival region of cooperators, i.e., the game dynamics continues after the homogeneous system has collapsed. Those results are helpful to understand the function of spatial patterns in supporting cooperation and fostering behavioral diversity.