Identity by descent (IBD) sharing is a very important genomic feature in population genetics which can be used to reconstruct recent demographic history. In this paper we provide a framework to estimate IBD sharing for a demographic model called two-population model with migration. We adopt the structured coalescent theory and use a continuous-time Markov jump process { X ( t ), t ≥ 0} to describe the genealogical process in such model. Then we apply Kolmogorov backward equation to calculate the distribution of coalescence time and develop a formula for estimating the IBD sharing. The simulation studies show that our method to estimate IBD sharing for this demographic model is robust and accurate.

中文翻译：

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通过下降估计身份共享的马尔可夫跳跃过程

血统身份 (IBD) 共享是种群遗传学中​​一个非常重要的基因组特征，可用于重建最近的人口统计历史。在本文中，我们提供了一个框架来估计具有迁移的两个人口模型的人口模型的 IBD 共享。我们采用结构化聚结理论并使用连续时间马尔可夫跳跃过程{ X ( t ), t ≥ 0} 来描述该模型中的谱系过程。然后我们应用 Kolmogorov 后向方程来计算聚结时间的分布，并开发出估计 IBD 共享的公式。模拟研究表明，我们为该人口模型估计 IBD 共享的方法是稳健且准确的。