An application of the central limit theorem to coalescence times in the structured coalescent model with strong migration.

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.