Estimates of inbreeding in a natural population: a comparison of sampling properties

The average inbreeding coefficient f of a population can be estimated in several different ways based solely on the genotypic frequencies at a single locus. The means and variances of four different estimates have been compared. While the four estimates are equivalent when there are two alleles, the best estimates when there are three or more alleles are based upon total heterozygosity (Formula: see text) where x and y are the expected and observed number of heterozygotes) and the proportion of alleles that are homozygous (Formula: see text) where k = the number of alleles, aii = the number of AiAi homozygotes, and 2aij = the number of AiAj heterozygotes). Both are minimally based estimates of f and have identical sampling variances when all alleles are equally frequent. However, when alleles have different frequencies, the choice between these two estimates depends on the gene frequencies and the true inbreeding coefficient of a population; f2 is the best estimate when the true average inbreeding coefficient is suspected to be low or f = 0, while f1 is best in populations with large average inbreeding coefficients. Approximate sampling variances of these two estimates are given for any f and any number of alleles with arbitrary gene frequencies; these approximations are accurate for samples as small as n = 100. The chi-square and maximum likelihood estimates of f are not as good for realistic sample sizes.