Notohara Morihiro, Umeda Takayoshi
Graduate School of Natural Sciences, Nagoya City University, Mizuho, Nagoya 467-8501, Japan.
Theor Popul Biol. 2006 Nov;70(3):289-99. doi: 10.1016/j.tpb.2006.05.005. Epub 2006 May 26.
The aim of this article is to investigate the distribution of the coalescence time (T) for sampled genes in the structured coalescent. We obtain some exact solutions for small samples and approximate distributions for n sampled genes in strong and weak migration. We also conduct computer simulation to evaluate efficiencies of these approximations and show the dependency of the distribution of the coalescence time on the geographical structure and the intensity of migration. In a panmictic population, we prove that the conditional distribution of the coalescence time given the number of segregating sites (S) among sampled genes is given by the weighted mean of the convolution of gamma distributions. We also study the joint distribution of T and S in the structured coalescent model and show some exact solutions.
本文旨在研究结构化合并模型中抽样基因的合并时间（T）的分布。我们得到了小样本的一些精确解以及强迁移和弱迁移情况下n个抽样基因的近似分布。我们还进行了计算机模拟，以评估这些近似方法的效率，并展示合并时间分布对地理结构和迁移强度的依赖性。在一个随机交配的群体中，我们证明了给定抽样基因中分离位点数量（S）时合并时间的条件分布由伽马分布卷积的加权均值给出。我们还研究了结构化合并模型中T和S的联合分布，并给出了一些精确解。
