Effective size and F-statistics of subdivided populations. II. Dioecious species

For a dioecious diploid population subdivided into an arbitrary number of subpopulations, we have derived recurrence equations for the inbreeding coefficient and coancestries between individuals within and among subpopulations and formulas for effective size and F-statistics. Stable population size and structure, discrete generations, autosomal inheritance, and the island migration model are assumed, and arbitrary distributions of the numbers of male and female progeny per family, different numbers and variable migration rates of males and females are incorporated in our derivation. Some published equations for effective size and F-statistics for a subdivided population are shown to be incorrect because several incorrect probabilities are used in the derivation. A more general equation for effective size is obtained by finding eigenvalue solutions to the recurrence equations for inbreeding coefficient and coancestry in this article, which reduces to the simple and familiar expressions derived by previous authors for the special case of a single unsubdivided population. Our general expressions for F-statistics also reduce to the classical results of WRIGHT's infinite island model and its extensions. It is shown that population structure is important in determining effective size and F-statistics and should be recognized and incorporated into programs for genetic conservation and evolution.