Evolutionary game dynamics in a Wright-Fisher process
Evolutionary game dynamics in a Wright-Fisher process
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DOI：
10.1007/s00285-005-0369-8
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发表时间：
2006-05-01
影响因子：
1.9
通讯作者：
Nowak, MA
中科院分区：
文献类型：
--
作者：
Imhof, LA;Nowak, MA
有限种群中的演化博弈动力学可以用一个依赖于频率的随机Wright-Fisher过程来描述。我们考虑两个策略A和B之间的对称博弈。有离散的世代。在每一代中，个体产生的后代与他们的回报成正比。下一代是从这群后代中随机抽取的。总人口规模是恒定的。由此产生的马尔可夫过程有两个吸收状态对应于所有A或所有B的齐次总体。我们量化的频率依赖的选择，通过比较随机漂移下的吸收概率相应的概率。我们推导出的条件选择，有利于一个战略或其他使用的概念，总积极性。在弱选择的极限下，我们得到了1/3定律：如果A和B是严格纳什均衡，那么选择倾向于用A替换B，如果不稳定均衡发生的频率小于1/3。
Evolutionary game dynamics in finite populations can be described by a frequency dependent, stochastic Wright-Fisher process. We consider a symmetric game between two strategies, A and B. There are discrete generations. In each generation, individuals produce offspring proportional to their payoff. The next generation is sampled randomly from this pool of offspring. The total population size is constant. The resulting Markov process has two absorbing states corresponding to homogeneous populations of all A or all B. We quantify frequency dependent selection by comparing the absorption probabilities to the corresponding probabilities under random drift. We derive conditions for selection to favor one strategy or the other by using the concept of total positivity. In the limit of weak selection, we obtain the 1/3 law: if A and B are strict Nash equilibria then selection favors replacement of B by A, if the unstable equilibrium occurs at a frequency of A which is less than 1/3.