Stochastic Evolutionary Game Dynamics with Environmental Feedback and Selection Heterogeneity

Abstract The interaction between strategy and environment is pervasive in nature and society. Traditional models of finite populations typically assume a uniform intensity of selection. To capture the coupling between individual adaptive differences and environmental dynamics, we develop a stochastic evolutionary game model based on the Moran process that incorporates strategy-dependent environmental feedback and heterogeneous selection intensity. The results reveal a significant synergistic effect between selection heterogeneity and environmental state. In harmony, coordination, coexistence, and prisoner’s dilemma, such heterogeneity leads to diverse evolutionary pathways of cooperation, with stronger selection of cooperators markedly promoting cooperation. Slower environmental change facilitates cooperation when the environment is depleted, while faster feedback strengthens defection in the prisoner’s dilemma. 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Author information Authors and Affiliations Contributions Ting Liu and Jun Jiang performed the data analysis; Yuqiang Feng performed the formal analysis, paper revising; Xianjian Wang performed the validation; Ting Liu wrote the manuscript. All authors reviewed the manuscript. Corresponding author Ethics declarations Conflict of interest No conflict of interest exists in the submission of this manuscript, and manuscript is approved by all authors for publication. Author would like to declare on behalf of his coauthor that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed. Additional information Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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