The Distribution of F_st for the Island Model in the Large Population, Weak Mutation Limit

Abstract

Populations are often divided into subpopulations. Biologists use the statistic F _st to perform hypothesis tests for the existence of population subdivision and to estimate migration rates between different subpopulations. The distribution of F _st is not known. In this article, we use coalescent theory methods to find the limiting distribution of F _st in the large population, weak mutation limit under the island model of migration. Our analysis uses the scattering-collection decomposition of the island model coalescent introduced by Wakeley.

Keywords:

• Coalescent
• Ewens' sampling formula
• F _st
• Island model

Mathematics Subject Classification:

• 92D10
• 60K35
• 62E20