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

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.