Notohara M
Department of Biology, Faculty of Science, Kyushu University, Fukuoka, Japan.
J Math Biol. 1990;29(1):59-75. doi: 10.1007/BF00173909.
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.
我们将把金曼合并模型扩展到具有殖民地间迁移的地理结构种群模型。它由一个连续时间马尔可夫链描述，该链被证明是踏脚石模型扩散过程的对偶过程。我们将推导关于来自殖民地的抽样基因共同祖先的空间分布以及达到一个共同祖先的平均时间的方程组。这些方程在三个特定模型中求解：双种群模型、岛屿模型和具有对称最近邻迁移的一维踏脚石模型。
