Inferring the demographic history of species is one of the greatest challenges in populations genetics. This history is often represented as a history of size changes, ignoring population structure. Alternatively, when structure is assumed, it is defined a priori as a population tree and not inferred. Here we propose a framework based on the IICR (Inverse Instantaneous Coalescence Rate). The IICR can be estimated for a single diploid individual using the PSMC method of Li and Durbin (2011). For an isolated panmictic population, the IICR matches the population size history, and this is how the PSMC outputs are generally interpreted. However, it is increasingly acknowledged that the IICR is a function of the demographic model and sampling scheme with limited connection to population size changes. Our method fits observed IICR curves of diploid individuals with IICR curves obtained under piecewise stationary symmetrical island models. In our models we assume a fixed number of time periods during which gene flow is constant, but gene flow is allowed to change between time periods. We infer the number of islands, their sizes, the periods at which connectivity changes and the corresponding rates of connectivity. Validation with simulated data showed that the method can accurately recover most of the scenario parameters. Our application to a set of five human PSMCs yielded demographic histories that are in agreement with previous studies using similar methods and with recent research suggesting ancient human structure. They are in contrast with the view of human evolution consisting of one ancestral population branching into three large continental and panmictic populations with varying degrees of connectivity and no population structure within each continent.

推断物种的人口历史是种群遗传学中​​最大的挑战之一。这段历史通常被表示为规模变化的历史，而忽略了人口结构。或者，当假设结构时，它先验地定义为种群树而不是推断的。在这里，我们提出了一个基于 IICR（Inverse Instantaneous Coalescence Rate）的框架。可以使用 Li 和 Durbin (2011) 的 PSMC 方法估计单个二倍体个体的 IICR。对于孤立的泛滥人群，IICR 与人口规模历史相匹配，这就是 PSMC 输出的一般解释方式。然而，人们越来越认识到 IICR 是人口模型和抽样方案的函数，与人口规模变化的联系有限。我们的方法将观察到的二倍体个体的 IICR 曲线与在分段静止对称岛模型下获得的 IICR 曲线拟合。在我们的模型中，我们假设固定数量的时间段内基因流量是恒定的，但允许基因流量在时间段之间变化。我们推断岛屿的数量、它们的大小、连通性变化的时期以及相应的连通率。模拟数据验证表明，该方法可以准确地恢复大部分场景参数。我们对一组五个人类 PSMC 的应用产生了人口历史，这些历史与以前使用类似方法的研究和最近的研究表明古代人类结构一致。