The law of evolutionary dynamics in community-structured population

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• 作者：Changbing Tang^a ; Xiang Li^a ; ^{lix@fudan.edu.cn} ; Lang Cao^b ; Jingyuan Zhan^a
• 关键词：Evolutionary game theory ; Sojourn time ; Non-uniform interaction rate ; Simplified PDG
• 刊名：Journal of Theoretical Biology
• 出版年：2012
• 期刊代码：79_00225193
• 类别：mt
• 出版时间：7 August, 2012
• 卷：306
• 期：Complete
• 页码：1-6
• 文件大小：540 K

摘要

Evolutionary game dynamics in finite populations provide a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call law, describes how to determine the selection between two competing strategies: in most evolutionary processes with two strategies, A and B, strategy A is favored over B in weak selection if and only if . This relationship holds for a wide variety of structured populations with mutation rate and weak selection under certain assumptions. In this paper, we propose a model of games based on a community-structured population and revisit this law under the Moran process. By calculating the average payoffs of A and B individuals with the method of effective sojourn time, we find that features not only the structured population characteristics, but also the reaction rate between individuals. That is to say, an interaction between two individuals are not uniform, and we can take as a reaction rate between any two individuals with the same strategy. We verify this viewpoint by the modified replicator equation with non-uniform interaction rates in a simplified version of the prisoner's dilemma game (PDG).