We first consider a diallelic marker with alleles A1 and A2 and population frequencies of p1 and 1 – p1. For genotypes A1A1, A1A2, A2A2 the population frequencies are denoted p11, p12, p22. Let n11, n12, n22 denote the observed genotype frequencies which, under independent sampling, follow the multinomial distribution: (1)Pr(n∣p)=n!n11!n12!n22!p11n11p12n12p22n22, where n = (n11, n12, n22), p = (p11, p12, p22), and n=∑i,j=1≥iknij. In a large random-mating population, in the absence of migration, mutation, natural selection, and assortative mating, HWE corresponds to the frequencies of A1 homozygotes, heterozygotes, and A2 homozygotes being p12, 2p1(1 – p1), and (1 – p1)2. Hence the HWE model and the saturated model have one and two parameters, respectively. There are various ways in which the saturated model space can be parameterized (Weir, 1996). We will consider the fixation index parameter (also called the inbreeding coefficient), f, whose use gives p11=p12+p1(1−p1)f,p12=2p1(1−p1)(1−f),p22=(1−p1)2+p1(1−p1)f, so that f = 0 recovers the HWE model. Examining point and interval estimates for f yields insight into departures from HWE: positive values are manifested in an excess of homozygotes (and may
