Large fluctuations and fixation in evolutionary games
Large fluctuations and fixation in evolutionary games
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DOI：
10.1088/1742-5468/2010/09/p09009
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发表时间：
2010-09-01
影响因子：
2.4
通讯作者：
Mobilia, Mauro
中科院分区：
文献类型：
--
作者：
Assaf, Michael;Mobilia, Mauro
我们研究了属于协调类和反协调类的进化博弈中的大波动。这些模拟合作困境的游戏的动态特征是，两个吸收状态之间存在一个共存固定点。我们对固定问题特别感兴趣它指的是少数突变体占据整个种群的可能性。这里，固定现象是由大波动引起的，并通过推广到处理具有多个吸收态的随机系统的半经典WKB （wentzel - kramer - brillouin）理论进行了研究。重要的是，这种方法使我们能够分析选择和随机波动对进化动力学的综合影响，而不是在以前的工作中经常考虑的弱选择极限。考虑指数前因素，我们精确地计算了反协调对策中长共存状态下的概率分布函数和少数突变体占据整个种群所需的平均固定时间，以及协调类中的固定概率。我们的分析结果与大量的数值模拟结果非常吻合。此外，我们证明了当选择强度有限时，我们的处理优于Fokker-Planck近似。
We study large fluctuations in evolutionary games belonging to the coordination and anti-coordination classes. The dynamics of these games, modeling cooperation dilemmas, is characterized by a coexistence fixed point separating two absorbing states. We are particularly interested in the problem of fixation that refers to the possibility that a few mutants take over the entire population. Here, the fixation phenomenon is induced by large fluctuations and is investigated by a semiclassical WKB (Wentzel-Kramers-Brillouin) theory generalized to treat stochastic systems possessing multiple absorbing states. Importantly, this method allows us to analyze the combined influence of selection and random fluctuations on the evolutionary dynamics beyond the weak selection limit often considered in previous works. We accurately compute, including pre-exponential factors, the probability distribution function in the long-lived coexistence state and the mean fixation time necessary for a few mutants to take over the entire population in anti-coordination games, and also the fixation probability in the coordination class. Our analytical results compare excellently with extensive numerical simulations. Furthermore, we demonstrate that our treatment is superior to the Fokker-Planck approximation when the selection intensity is finite.