Neutral additive genetic variance in a metapopulation

For neutral, additive quantitative characters, the amount of additive genetic variance within and among populations is predictable from Wright's F-ST, the effective population size and the mutational variance. The structure of quantitative genetic variance in a subdivided metapopulation can be predicted from results from coalescent theory, thereby allowing single-locus results to predict quantitative genetic processes. The expected total amount of additive genetic variance in a metapopulation of diploid individual is given by 2N(e)sigma(m)(2) (1 + F-ST), where F-ST is Wright's among-population fixation index, N-e is the eigenvalue effective size of the metapopulation, and sigma(m)(2) is the mutational variance. The expected additive genetic variance within populations is given by 2N(e) sigma(e)(2)(1 - F-ST), and the variance among demes is given by 4F(ST)N(e)sigma(m)(2). These results are general with respect to the types of population structure involved. Furthermore, the dimensionless measure of the quantitative genetic variance among populations, Q(ST), is shown to be generally equal to F-ST for the neutral additive model. Thus, for all population structures, a value of Q(ST) greater than F-ST for neutral loci is evidence for spatially divergent evolution by natural selection.