Diffusion sustains cooperation via forming diverse spatial patterns in prisoners dilemma game Abstract   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 ecoevolutionary prisoneru0027s dilemma game, where the playeru0027s diffusion is incorporated definitely, we show that the diffusion can trigger out rich spatial patterns. These selforganized 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 selforganized 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.

The effects of heterogeneity of updating rules on cooperation in spatial network Abstract   The emergence and maintenance of cooperation remains to be one of the overreaching problems and a number of scholars have devoted endless efforts to resolve such problems. To further explore this issue, we focus on the impact of heterogeneity of updating rules on cooperative behavior in voluntary prisoneru0027s dilemma; here, two types of strategy updating rules are considered to mimic social facts which are listed as strategy learning mechanism and strategy teaching mechanism. The stability of different mechanisms on promoting cooperation is thoroughly investigated in this manuscript. Numerical simulations are conducted while corresponding results are presented with sufficient clarifications. We find that the strategy learning mechanism can promote cooperation steadily. However, with the variance in the proportion of the two update rules in the investigated community, the strategy teaching mechanism seems to be more sensitive. Moreover, compared with strategy learning mechanism, strategy teaching mechanism plays a more important and apparent role in promoting cooperation. We also find that personal strategy is sensitive to the varying of Loneru0027s payoff xcfx83, especially when xcfx83 is close to 1. We hope our findings will shed some lights on resolving the social dilemmas.