A clarification of historical concepts of effective population size and their applicability to subdivided populations

The great population geneticist Sewall Wright had a lifelong interest in animal breeding programs. He was concerned that, in these programs, genetic variation would tend to be lost (as measured by him in a tendency for genetic heterozygosity to decrease) when a small number of males is mated to a comparatively large number of females. The calculations in his great 1931 paper were designed to quantify this tendency. Decades later other authors noted further cases when population genetic heterozygosity tended to be lost, a classic example being that of a population whose size changes cyclically with some small population sizes arising during the cycle. These observations led to several definitions of the effective population size. Perhaps the two most frequently discussed in the literature are the inbreeding effective population size and the variance effective population size. The first aim of this note is to show that Wright's (1931) calculations for two-sex populations relate to neither of these, and instead to the far less discussed eigenvalue effective population size. The second aim is to critically assess all three effective population sizes and put two-sex populations into a wider concept of subdivided populations. This analysis reveals some new results, and for two-sex populations without other types of subdivision, we conclude that the eigenvalue effective size is the most relevant type of effective size.