Traulsen Arne, Nowak Martin A, Pacheco Jorge M
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jul;74(1 Pt 1):011909. doi: 10.1103/PhysRevE.74.011909. Epub 2006 Jul 17.
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.
我们研究有限种群中的进化博弈动力学。我们分析了一个进化过程，我们称之为成对比较，为此我们采用了统计力学中普遍存在的费米分布函数。这个过程中的逆温度控制着选择强度，从而为从随机漂移到模仿动力学的所有选择强度下的进化动力学提供了一个统一框架。每当合作是根据任何对称两人博弈来建模时，我们都能推导出一个简单的封闭公式，该公式能确定有限种群中合作的可行性。与之前的结果不同，这个公式在所有选择强度下以及任何初始条件下都是有效的。我们研究了有限种群中合作者的进化动力学，并研究了选择强度与无限种群中内部不动点残余之间的相互作用，将其作为给定初始合作者数量的函数进行分析，展示了这种相互作用如何强烈影响有限种群中给定性状的固定过程，在不同选择强度下导致了违反直觉的结果。
