We introduce a modified spatial -Fleming–Viot process to model the ancestry of individuals in a population occupying a continuous spatial habitat divided into two areas by a sharp discontinuity of the dispersal rate and effective population density. We derive an analytical formula for the expected number of shared haplotype segments between two individuals depending on their sampling locations. This formula involves the transition density of a skew diffusion which appears as a scaling limit of the ancestral lineages of individuals in this model. We then show that this formula can be used to infer the dispersal parameters and the effective population density of both regions, using a composite likelihood approach, and we demonstrate the efficiency of this method on a range of simulated data sets.

中文翻译：

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使用长共享单倍型对空间异质人群进行人口统计推断

我们引入了一种改进的空间-Fleming-Viot过程来模拟占据连续空间栖息地的种群中个体的祖先，该栖息地通过分散率和有效种群密度的急剧不连续性分为两个区域。我们根据采样位置推导出两个个体之间共享单倍型片段的预期数量的分析公式。该公式涉及偏斜扩散的转变密度，该密度在该模型中表现为个体祖先谱系的缩放限制。然后，我们证明该公式可用于使用复合似然方法推断两个区域的扩散参数和有效人口密度，并且我们在一系列模拟数据集上证明了该方法的效率。