The Effective Size of a Subdivided Population

Abstract

This paper derives the long-term effective size, Ne, for a general model of population subdivision, allowing for differential deme fitness, variable emigration and immigration rates, extinction, colonization, and correlations across generations in these processes. We show that various long-term measures of Ne, are equivalent. The effective size of a metapopulation can be expressed in a variety of ways. At a demographic equilibrium, Ne, can be derived from the demography by combining information about the ultimate contribution of each deme to the future genetic make-up of the population and Wright's FST's. The effective size is given by Ne = 1/(1 + var (ϑ))〈(1 – fSTi)/Nin〉, where n is the number of demes, ϑi is the eventual contribution of individuals in deme i to the whole population (scaled such that Σiϑi = n), and 〈 〉 denotes an average weighted by ϑi2. This formula is applied to a catastrophic extinction model (where sites are either empty or at carrying capacity) and to a metapopulation model with explicit dynamics, where extinction is caused by demographic stochasticity and by chaos. Contrary to the expectation from the standard island model, the usual effect of population subdivision is to decrease the effective size relative to a panmictic population living on the same resource.