Estimating F-statistics

A moment estimator of theta, the coancestry coefficient for alleles within a population, was described by Weir & Cockerham in 1984 (100) and is still widely cited. The estimate is used by population geneticists to characterize population structure, by ecologists to estimate migration rates, by animal breeders to describe genetic variation, and by forensic scientists to quantify the strength of matching DNA profiles. This review extends the work of Weir & Cockerham by allowing different levels of coancestry for different populations, and by allowing non-zero coancestries between pairs of populations. All estimates are relative to the average value of theta between pairs of populations. Moment estimates for within- and between-population theta values are likely to have large sampling variances, although these may be reduced by combining information over loci. Variances also decrease with the numbers of alleles at a locus, and with the numbers of populations sampled. This review also extends the work of Weir & Cockerham by employing maximum likelihood methods under the assumption that allele frequencies follow the normal distribution over populations. For the case of equal theta values within populations and zero theta values between populations, the maximum likelihood estimate is the same as that given by Robertson & Hill in 1984 (70). The review concludes by relating functions of theta values to times of population divergence under a pure drift model.