Notohara Morihiro
Graduate School of Natural Sciences, Nagoya City University, Mizuho, Nagoya, 467-8501, Japan.
J Math Biol. 2010 Nov;61(5):695-714. doi: 10.1007/s00285-009-0318-z. Epub 2009 Dec 24.
The structured coalescent describes the ancestral relationship among sampled genes from a geographically structured population. The aim of this article is to apply the central limit theorem to functionals of the migration process to study coalescence times and population structure. An application of the law of large numbers to the migration process leads to the strong migration limit for the distributions of coalescence times. The central limit theorem enables us to obtain approximate distributions of coalescence times for strong migration. We show that approximate distributions depend on the population structure. If migration is conservative and strong, we can define a kind of effective population size N(e)(*), with which the entire population approximately behaves like a panmictic population. On the other hand, the approximate distributions for nonconservative migration are qualitatively different from those for conservative migration. And the entire population behaves unlike a panmictic population even though migration is strong.
结构化合并描述了来自地理结构化种群的抽样基因之间的祖先关系。本文的目的是将中心极限定理应用于迁移过程的泛函，以研究合并时间和种群结构。大数定律在迁移过程中的应用导致了合并时间分布的强迁移极限。中心极限定理使我们能够获得强迁移情况下合并时间的近似分布。我们表明，近似分布取决于种群结构。如果迁移是保守且强烈的，我们可以定义一种有效种群大小N(e)(*)，在这种情况下，整个种群的行为近似于一个随机交配的种群。另一方面，非保守迁移的近似分布与保守迁移的近似分布在性质上有所不同。即使迁移很强，整个种群的行为也不像随机交配的种群。
