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.