Assessment of the Global Variance Effective Size of Subdivided Populations, and Its Relation to Other Effective Sizes

Abstract

The variance effective population size (\(N_{eV}\)) is frequently used to quantify the expected rate at which a population’s allele frequencies change over time. The purpose of this paper is to find expressions for the global \(N_{eV}\) of a spatially structured population that are of interest for conservation of species. Since \(N_{eV}\) depends on allele frequency change, we start by dividing the cause of allele frequency change into genetic drift within subpopulations (I) and a second component mainly due to migration between subpopulations (II). We investigate in detail how these two components depend on the way in which subpopulations are weighted as well as their dependence on parameters of the model such a migration rates, and local effective and census sizes. It is shown that under certain conditions the impact of II is eliminated, and \(N_{eV}\) of the metapopulation is maximized, when subpopulations are weighted proportionally to their long term reproductive contributions. This maximal \(N_{eV}\) is the sought for global effective size, since it approximates the gene diversity effective size \(N_{eGD}\), a quantifier of the rate of loss of genetic diversity that is relevant for conservation of species and populations. We also propose two novel versions of \(N_{eV}\), one of which (the backward version of \(N_{eV}\)) is most stable, exists for most populations, and is closer to \(N_{eGD}\) than the classical notion of \(N_{eV}\). Expressions for the optimal length of the time interval for measuring genetic change are developed, that make it possible to estimate any version of \(N_{eV}\) with maximal accuracy.