THE COALESCENT AND THE GENEALOGICAL PROCESS IN GEOGRAPHICALLY STRUCTURED POPULATION
THE COALESCENT AND THE GENEALOGICAL PROCESS IN GEOGRAPHICALLY STRUCTURED POPULATION
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DOI：
10.1007/bf00173909
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发表时间：
1990-01-01
影响因子：
1.9
通讯作者：
NOTOHARA, M
中科院分区：
文献类型：
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作者：
NOTOHARA, M
我们将把Kingman的结合推广到具有种群迁移的地理结构种群模型。用一个连续时间的马尔可夫链来描述它，证明了它是垫脚石模型扩散过程的对偶过程。我们将推导出一个方程组，该方程组描述了从群体中采样的基因的共同祖先的空间分布以及到达一个共同祖先的平均时间。这些方程在三个特定的模型，一个两个人口模型，岛屿模型和一维垫脚石模型与对称最近邻迁移。
We shall extend Kingman''s coalescent to the geographically structured population model with migration among colonies. It is described by a continuous-time Markov chain, which is proved to be a dual process of the diffusion process of stepping-stone model. We shall derive a system of equations for the spatial distribution of a common ancestor of sampled genes from colonies and the mean time to getting to one common ancestor. These equations are solved in three particular models; a two-population model, the island model and the one-dimensional stepping-stone model with symmetric nearest-neighbour migration.