Stationary frequencies and mixing times for neutral drift processes with spatial structure
Stationary frequencies and mixing times for neutral drift processes with spatial structure
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DOI：
10.1098/rspa.2018.0238
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发表时间：
2018-10-01
影响因子：
3.5
通讯作者：
Nowak, Martin A.
中科院分区：
文献类型：
--
作者：
McAvoy, Alex;Adlam, Ben;Nowak, Martin A.
我们研究了中性进化的一般设置，其中人口是有限的，恒定的大小，可以有空间结构。突变导致不同的遗传类型（性状），可以是离散的或连续的。在最小的假设下，我们证明了进化过程的边际特征分布，它指定了任何给定个体具有某种特征的概率，都收敛到突变过程的平稳分布。特别地，种群中性状的稳态频率与其大小、空间结构和进化更新规则无关，并且这些频率可以通过评估描述大小为1的种群的简单随机过程（即突变过程本身）来计算。我们的结论是通过分析混合时间，其特征在于收敛率的突变过程沿着谱系，在人口变量的进化过程。
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types (traits), which can be discrete or continuous. Under minimal assumptions, we show that the marginal trait distributions of the evolutionary process, which specify the probability that any given individual has a certain trait, all converge to the stationary distribution of the mutation process. In particular, the stationary frequencies of traits in the population are independent of its size, spatial structure and evolutionary update rule, and these frequencies can be calculated by evaluating a simple stochastic process describing a population of size one (i.e. the mutation process itself). We conclude by analysing mixing times, which characterize rates of convergence of the mutation process along the lineages, in terms of demographic variables of the evolutionary process.