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In this example there is a clear deficit of heterozygotes relative to Hardy-Weinberg expectations. The population contains 59% fewer heterozygotes than would be expected in a population with the same allele frequencies that was experiencing random mating and the other conditions set out in the assumptions of Hardy-Weinberg. Interpreted as a correlation between the allelic states of the two alleles in a genotype, this value of the fixation index tells us that the two alleles in a genotype are much more frequently of the same state than expected by chance.

In biological populations, a wide range of values has been observed for the fixation index (Table 2.9). Fixation indices have frequently been estimated with allozyme data (see Box 2.2). Estimates of F are generally correlated with mating system. Even in species where individuals possess reproductive organs of one sex only (termed dioecious individuals), mating among relatives can be common and ranges from infrequent to almost invariant. In other cases, mating is essentially random or complex mating and social systems have evolved to prevent consanguineous mating. Pure-breed dogs are an example where mating among relatives has been enforced by humans to develop lineages with specific phenotypes and behaviors, resulting in high fixation indices in some breeds. Many plant species possess both male and female sexual functions (hermaphrodites) and exhibit an extreme form of consanguineous mating, self-fertilization, that causes rapid loss of heterozygosity. In the case of Ponderosa pines in Table 2.9, the excess of heterozygotes may be due to natural selection against homozygotes at some loci (inbreeding depression). This makes the important point that departures from Hardy-Weinberg expected genotype frequencies estimated by the fixation index are potentially influenced by processes in addition to the mating system. Genetic loci free of the influence of other processes such as natural selection are often sought to estimate F. In addition, F can be estimated using the average of multiple loci, which will tend to reduce bias since loci will differ in the degree they are influenced by other processes and outliers will be apparent.

Extending the fixation index to loci with more than two alleles just requires a means to calculate the expected heterozygosity (He) for an arbitrary number of alleles at one locus. This can be accomplished by adding up all of the expected frequencies of each possible homozygous genotype and subtracting this total from one or summing the expected frequencies of all heterozygous genotypes:

where k is the number of alleles at the locus, the and 2pipj terms represent the expected genotype k frequencies based on allele frequencies, and the I

(pronounced "sigma") indicates summation of the frequencies of the k homozygous genotypes. This quantity is also called the gene diversity (Nei 1987). The expected heterozygosity can be adjusted

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