On the concept of the effective population size

The concept of the effective population size is discussed. It is shown that the “eigenvalue” and the “inbreeding” effective population sizes are in principle different, even though they have been sometimes identified in the literature. On the other hand the “eigenvalue” and “variance” effective sizes are usually both close when the latter exists. Since, however, there are many models for which a variance effective size cannot in principle exist, it seems useful to introduce the eigenvalue effective size and to examine some of its properties.