Stochastic dynamics of invasion and fixation

作     者：Arne Traulsen Martin A. Nowak Jorge M. Pacheco 

作者机构：Program for Evolutionary Dynamics Harvard University Cambridge Massachusetts 02138 USA Department of Organismic and Evolutionary Biology and Department of Mathematics Harvard University Cambridge Massachusetts 02138 USA Centro de Física Teórica e Computacional Departamento de Física da Faculdade de Ciências Universidade de Lisboa P-1649-003 Lisboa Codex Portugal 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2006年第74卷第1期

页      面：011909-011909页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

基　　金：NIGMS NIH HHS [R01 GM078986  R01 GM078986-01] Funding Source: Medline 

主　　题：EVOLUTIONARY GAME DYNAMICS PRISONERS-DILEMMA GAME SOCIAL DILEMMAS FINITEPOPULATIONS COOPERATION 

摘      要：We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse temperature in this process controls the intensity of selection, leading to a unified framework for evolutionary dynamics at all intensities of selection, from random drift to imitation dynamics. We derive a simple closed formula that determines the feasibility of cooperation in finite populations, whenever cooperation is modeled in terms of any symmetric two-person game. In contrast with previous results, the present formula is valid at all intensities of selection and for any initial condition. We investigate the evolutionary dynamics of cooperators in finite populations, and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations, as a function of a given initial number of cooperators, showing how this interplay strongly affects the approach to fixation of a given trait in finite populations, leading to counterintuitive results at different intensities of selection.