Variance and covariance of homozygosity in a structured population

The variance of homozygosity for a K-allele model with n partially isolated subpopulations is derived numerically using identity coefficients. The variance of homozygosity within a subpopulation is shown to depend strongly upon the migration rates between subpopulations but is not strongly influenced by the number of alleles possible at a locus. The variance of homozygosity within a subpopulation, given the value of expected homozygosity, is approximately equal to the value of the variance of homozygosity given by Stewart's formula for a single population. If the population is presumed to be panmictic, but is actually subdivided, and the gametes are sampled at random from the total population, the apparent variance of homozygosity depends on the number of alleles possible. With small migration rates and K large, the apparent variance of homozygosity is much smaller than in a single population with the same expected homozygosity. However, when K is small, the variance of homozygosity is approximately given by Stewart's formula. The transient behavior of the variance of homozygosity shows that a large number of generations may be required to approach equilibrium values.