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Evolutionary game dynamics in finite populations provides a new framework tounderstand the selection of traits with frequency-dependent fitness. Recently,a simple but fundamental law of evolutionary dynamics, which we call {\sigma}law, describes how to determine the selection between two competing strategies:in most evolutionary processes with two strategies, A and B, strategy A isfavored over B in weak selection if and only if {\sigma}R + S > T + {\sigma}P.This relationship holds for a wide variety of structured populations withmutation rate and weak selection under certain assumptions. In this paper, wepropose a model of games based on a community-structured population and revisitthis law under the Moran process. By calculating the average payoffs of A and Bindividuals with the method of effective sojourn time, we find that {\sigma}features not only the structured population characteristics but also thereaction rate between individuals. That's to say, an interaction between twoindividuals are not uniform, and we can take {\sigma} as a reaction ratebetween any two individuals with the same strategy. We verify this viewpoint bythe modified replicator equation with non-uniform interaction rates in asimplified version of the prisoner's dilemma game (PDG).

The \sigma law of evolutionary dynamics in community-structured populations