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THE EFFECTIVE SIZE OF A HIERARCHICALLY STRUCTURED POPULATION

A knowledge of the effective size of a population (Ne) is important in understanding its current and future evolutionary potential. Unfortunately, the effective size of a hierarchically structured population is not, in general, equal to the sum of its parts. In particular, the inbreeding structure has a major influence on Ne. Here I link Ne to Wright's hierarchical measures of inbreeding, FIS and FST, for an island‐structured population (or metapopulation) of size NT. The influence of FST depends strongly on the degree to which island productivity is regulated. In the absence of local regulation (the interdemic model), interdemic genetic drift reduces Ne. When such drift is combined with local inbreeding under otherwise ideal conditions, the effects of FIS and FST are identical: increasing inbreeding either within or between islands reduces Ne, with Ne = NT/[(1 + FIS)(1 + FST) − 2FISFST]. However, if islands are all equally productive because of local density regulation (the traditional island model), then Ne = NT/[(1 + FIS)(1 –FST)] and the effect of FST is reversed. Under the interdemic model, random variation in the habitat quality (and hence productivity) of islands act to markedly decrease Ne. This variation has no effect under the island model because, by definition, all islands are equally productive. Even when no permanent island structure exists, spatial differences in habitat quality can significantly increase the overall variance in reproductive success of both males and females and hence lower Ne. Each of these basic results holds when other nonideal factors are added to the model. These factors, deviations from a 1:1 sex ratio, greater than Poisson variance in female reproductive success, and variation in male mating success due to polygynous mating systems, all act to lower Ne. The effects of male and female variance on Ne have important differences because only females affect island productivity. Finally, it is noted that to use these relationships, FIS and FST must be estimated according to Wright's definition (and corrected to have a zero expectation under the null model). A commonly used partitioning (θ, θg) can be biased if either island size or the number of islands is small.