Adaptive Networks and Control Laboratory, Department of Electronic Engineering, Fudan University, Shanghai 200433, China.
J Theor Biol. 2012 Aug 7;306:1-6. doi: 10.1016/j.jtbi.2012.04.024. Epub 2012 Apr 25.
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 σ 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 σR+S>T+σP. 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 σ 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 σ 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).
有限群体中的进化博弈动力学为理解适应度频率依赖的性状选择提供了一个新的框架。最近，一种简单而基本的进化动力学定律，我们称之为 σ 定律，描述了如何确定两种竞争策略之间的选择：在大多数具有两种策略 A 和 B 的进化过程中，如果且仅当 σR+S>T+σP，则策略 A 在弱选择中优于 B。在某些假设下，该关系适用于具有突变率和弱选择的各种结构种群。在本文中，我们提出了一个基于社区结构种群的博弈模型，并在 Moran 过程下重新考察了这一定律。通过有效居留时间的方法计算 A 和 B 个体的平均收益，我们发现 σ 不仅具有结构种群的特征，还具有个体之间的反应速率。也就是说，两个个体之间的相互作用不是均匀的，我们可以将 σ 视为具有相同策略的任何两个个体之间的反应速率。我们通过在简化的囚徒困境博弈（PDG）中具有非均匀相互作用速率的修正复制者方程验证了这一观点。
