有限总体演化动力学的平稳稳定性
Stationary Stability for Evolutionary Dynamics in Finite Populations
摘要：
我们证明了一个巨大的扩展进化稳定性理论的有限总体突变，连接的Moran过程的平稳分布理论与进化稳定性的李雅普诺夫理论。我们定义的概念与突变和泛化的莫兰过程的平稳稳定，以及广义的概念，包括突变称为激励稳定状态（ISS）的候选人的进化稳定。对于足够大的人口，极值的平稳分布是ISS候选人，我们给一个家庭的李雅普诺夫量，局部最小化的平稳极值和ISS候选人。在各种示例中，包括Moran和Wright-Fisher过程，我们表明平稳分布的局部最大值捕获了传统定义的进化稳定状态。在大布居极限下恢复了经典的复制子动力学稳定性理论。最后，我们包括描述可能的扩展到人口的可变大小和人口发展的图形。
英文摘要：
We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We define the notion of stationary stability for the Moran process with mutation and generalizations, as well as a generalized notion of evolutionary stability that includes mutation called an incentive stable state (ISS) candidate. For sufficiently large populations, extrema of the stationary distribution are ISS candidates and we give a family of Lyapunov quantities that are locally minimized at the stationary extrema and at ISS candidates. In various examples, including for the Moran and Wright-Fisher processes, we show that the local maxima of the stationary distribution capture the traditionally-defined evolutionarily stable states. The classical stability theory of the replicator dynamic is recovered in the large population limit. Finally we include descriptions of possible extensions to populations of variable size and populations evolving on graphs.
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