In this paper we develop a general framework for how the genetic composition of a structured population with strong migration between its subunits, evolves over time. The dynamics is described in terms of a vector-valued Markov process of allele, genotype or haplotype frequencies that varies on two time scales. The more rapid changes are random fluctuations in terms of a multivariate autoregressive process, around a quasi equilibrium fix point, whereas the fix point itself varies more slowly according to a diffusion process, along a lower-dimensional subspace. Under mild regularity conditions, the fluctuations have a magnitude inversely proportional to the square root of the population size N, and hence can be used to estimate a broad class of genetically effective population sizes Ne, with genetic data from one time point only. In this way we are able to unify a number of existing notions of effective size, as well as proposing new ones, for instance one that quantifies the extent to which genotype frequencies fluctuate around Hardy-Weinberg equilibrium.

中文翻译：

---

在两个时间尺度上定义的遗传过程的局部波动，并应用于有效的大小估计。

在本文中，我们建立了一个总体框架，以了解随着时间的流逝，结构化种群的遗传组成如何在其亚基之间发生强烈迁移。根据在两个时间尺度上变化的等位基因，基因型或单倍型频率的向量值马尔可夫过程来描述动力学。更快的变化是围绕准平衡固定点的多元自回归过程的随机波动，而固定点本身根据扩散过程沿着较低维子空间的变化更慢。在适度的规律性条件下，波动的大小与人口规模N的平方根成反比，因此可以用于仅从一个时间点获取遗传数据来估计广泛的遗传有效人口规模Ne。