标题： 关于有限种群的随机演化 显示英文标题

标题： On the stochastic evolution of finite populations

摘要： 这项工作是对用于描述两种类型种群演化的离散马尔可夫链的系统研究。 受众所周知的莫兰（M）过程和弗里希-费舍尔（WF）过程结果的启发，我们定义了一个广义的马尔可夫链模型类，我们称之为基姆拉类。 它涵盖了种群遗传学中使用的大多数模型，并且我们证明了许多适用于M和WF过程的著名结果在该类中仍然有效。 在所有基姆拉过程中，突变基因要么固定，要么消失，我们给出了此类过程的固定概率在突变初始频率上严格递增的必要且充分条件。 这一条件表明存在具有递减固定概率的WF过程——与M过程总是具有严格递增固定概率的情况相反。 作为副产品，我们证明了递增的固定概率唯一地定义了一个实现它的M或WF过程，并且任何没有状态具有平凡固定性的固定概率都可以由至少某个WF过程实现。 这些结果扩展到适合描述时间非齐次动态的过程子类。 我们还讨论了在进化博弈论中广泛使用的频率依赖适应度和收益的传统识别，有限种群下弱选择的作用，以及进化过程中跳跃与频率依赖适应度之间的关系。 显示英文摘要

摘要： This work is a systematic study of discrete Markov chains that are used to describe the evolution of a two-types population. Motivated by results valid for the well-known Moran (M) and Wright-Fisher (WF) processes, we define a general class of Markov chains models which we term the Kimura class. It comprises the majority of the models used in population genetics, and we show that many well-known results valid for M and WF processes are still valid in this class. In all Kimura processes, a mutant gene will either fixate or become extinct, and we present a necessary and sufficient condition for such processes to have the probability of fixation strictly increasing in the initial frequency of mutants. This condition implies that there are WF processes with decreasing fixation probability --- in contradistinction to M processes which always have strictly increasing fixation probability. As a by-product, we show that an increasing fixation probability defines uniquely an M or WF process which realises it, and that any fixation probability with no state having trivial fixation can be realised by at least some WF process. These results are extended to a subclass of processes that are suitable for describing time-inhomogeneous dynamics. We also discuss the traditional identification of frequency dependent fitnesses and pay-offs, extensively used in evolutionary game theory, the role of weak selection when the population is finite, and the relations between jumps in evolutionary processes and frequency dependent fitnesses.