Effective sizes and time to migration-drift equilibrium in geographically subdivided populations.

Many versions of the effective population size (Ne) exist, and they are important in population genetics in order to quantify rates of change of various characteristics, such as inbreeding, heterozygosity, or allele frequencies. Traditionally, Ne was defined for single, isolated populations, but we have recently presented a mathematical framework for subdivided populations. In this paper we focus on diploid populations with geographic subdivision, and present new theoretical results. We compare the haploid and diploid versions of the inbreeding effective size (NeI) with novel expression for the variance effective size (NeV), and conclude that for local populations NeV is often much smaller than both versions of NeI, whenever they exist. Global NeV of the metapopulation, on the other hand, is close to the haploid NeI and much larger than the diploid NeI. We introduce a new effective size, the additive genetic variance effective size NeAV, which is of particular interest for long term protection of species. It quantifies the rate at which additive genetic variance is lost and we show that this effective size is closely related to the haploid version of NeI. Finally, we introduce a new measure of a population's deviation from migration-drift equilibrium, and apply it to quantify the time it takes to reach this equilibrium. Our findings are of importance for understanding the concept of effective population size in substructured populations and many of the results have applications in conservation biology.