The hierarchical island model revisited

Formulae were derived for the genetic differentiation between populations within a metapopulation (F(SM)), and between metapopulations (F(MT)) as functions of migration and mutation rates, size and number of populations and metapopulations. We show that F(MT )= 1/(1 + 4N(e)m), where N(e )is the effective size of a metapopulation, and where the migration rate between metapopulations is m. The formulae for F(MT )and F(SM )were more general than previously proposed since we have relaxed some previously made hypotheses and we included the effect of the mutation rate. Using our formula, some unexpected result of estimation of gene flow, previously obtained, can be explained readily.