DEVIATIONS FROM HARDY-WEINBERG PROPORTIONS: SAMPLING VARIANCES AND USE IN ESTIMATION OF INBREEDING COEFFICIENTS

[摘要] An analysis is made of the distribution of deviations from Hardy-Weinberg proportions with k alleles and of estimates of inbreeding coefficients ( f ) obtained from these deviations.—If f is small, the best estimate of f in large samples is shown to be 2∑ i ( Tii/Ni )/( k - 1), where Tii is an unbiased measure of the excess of the i th homozygote and Ni the number of the i th allele in the sample [frequency = Ni /(2 N )]. No extra information is obtained from the Tij , where these are departures of numbers of heterozygotes from expectation. Alternatively, the best estimator can be computed from the Tij , ignoring the Tii . Also (1) the variance of the estimate of f equals 1/( N ( k - 1)) when all individuals in the sample are unrelated, and the test for f = 0 with 1 d.f. is given by the ratio of the estimate to its standard error; (2) the variance is reduced if some alleles are rare; and (3) if the sample consists of full-sib families of size n , the variance is increased by a proportion ( n - 1)/4 but is not increased by a half-sib relationship.—If f is not small, the structure of the population is of critical importance. (1) If the inbreeding is due to a proportion of inbred matings in an otherwise random-breeding population, f as determined from homozygote excess is the same for all genes and expressions are given for its sampling variance. (2) If the homozygote excess is due to population admixture, f is not the same for all genes. The above estimator is probably close to the best for all f values.

[学科分类] 医学（综合）