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The first section of the chapter reviewed the processes that contribute to the formation of allele frequency

Table 4.5 The mathematical and biological definitions of heterozygosity for three levels of population organization. In the summations, i refers to each subpopulation 1, 2, 3 . . . n and and q are the frequencies of the two alleles at a diallelic locus in subpopulation i.

The average observed heterozygosity within each subpopulation.

The average expected heterozygosity of subpopulations assuming random mating within each subpopulation.

The expected heterozygosity of the total population assuming random mating within subpopulations and no divergence of allele frequencies among subpopulations.

Ht = 2pq differences among populations. Given that these processes might be acting, it is necessary to develop methods to measure and quantify population structure. The parentage analyses such as those described in the last section can be carried out when genotype data are available both for a sample of candidate parents and a sample of progeny. An alternative situation is where genotype data are determined for individuals sampled within and among a series of geographic locations. This type of sampling is very commonly carried out in empirical studies and requires methods to quantify the pattern of population structure present among the subpopulations as well as the genotype frequencies found within subpopulations. It would be advantageous if such measures could be readily compared to reference situations, as is expected with no population structure. This was our approach when comparing observed and expected heterozygosity using the fixation index (F) in Chapter 2. We can now extend the fixation index to apply to cases where there are multiple subpopulations. In this more complex case there can be deviations from Hardy-Weinberg expected frequencies of heterozygotes at two levels: within each subpopulation due to non-random mating and among subpopulations due to population structure. This section of the chapter will develop and explain fixation-index-based measures of departure from expected heterozygosity commonly used to quantify population structure.

Let's look in detail at the case where we can measure the genotypes at a diallelic locus for a sample of individuals located in several different subpopulations. Recall that the heterozygosity in a population is just one minus the homozygosity (H = 1 - F) so the heterozygosity can be related to the fixation index.

With such genotype data it is possible to compute the observed and expected frequencies of the heterozygote genotype in several ways (Table 4.5). The first way is to simply take the average:

where H is the observed frequency of heterozygotes in each of the n subpopulations. We could call this H since it is the average of the observed heterozygote frequencies in all subpopulations. This is just the probability that a given individual is heterozygous or the average observed heterozygosity. As shown in Chapter 2, the heterozygosity within populations can be increased or decreased relative to Hardy-Weinberg expectations by non-random mating.

Next, we can determine the expected heterozygosity assuming each subpopulation is in Hardy-Weinberg equilibrium. This assumption means that the frequency of the heterozygous genotype is expected to be 2pq for a locus with two alleles. The average expected heterozygosity of subpopulations is then

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