## Method box Estimating fixation indices

Throughout this section a single locus with two alleles has been used to demonstrate hierarchical heterozygosities and fixation indices. These conditions are highly idealized, meaning that this section is really presenting the conceptual derivation of a parameter. In practice, there are numerous details involved in obtaining fixation-index parameter estimates FIS, FST, and FIT. Loci commonly have more than two alleles, so each allele provides a different estimate of the fixation index that is averaged within a locus. Multiple loci are also used, requiring computation of a multilocus average. It is also common that sample sizes are variable among subpopulations and that some genotype data may be missing at some loci for some individuals. Additionally, different types of genetic markers may require adjustments for dominance (inability to distinguish dominant homozygotes and heterozygotes) or patterns and rates of mutation that can be incorporated into fixation-index estimators. Finally, empirical studies may have more than three levels of hierarchy, may wish to test for variation in allele frequency associated with subpopulations as well as other variables, and require statistical estimates of uncertainty in parameter estimates such as confidence intervals.

Gst is an estimator based on multilocus versions of the observed and expected heterozygosities or gene diversities (Nei 1973). 9 or 9ST(pronounced "theta"; Weir 1996) and ^^ (Excoffier et al. 1992) are estimators based on analysis of variance of allele frequencies within and among subpopulations. The estimator pST (pronounced "roe") or RST is frequently used with microsatellite or simple sequence repeat (SSR) loci to account for high rates of stepwise mutation that can obscure population structure (Slatkin 1995; see Chapter 5). An estimator of FST is also available for DNA sequence data based on mean number of pairwise differences between sequences taken either from the same subpopulation or from different subpopulations (Hudson et al. 1992). Many commonly employed estimators are implemented in computer programs or software applications that can be obtained over the internet.

subpopulations diverge in allele frequency, the expected heterozygosity of the subpopulations is less than the expected heterozygosity of the total population, resulting in high values of the fixation indices (Fig. 4.8b). An additional point is that FST can vary considerably among independent replicate loci sampled in an identical fashion from the same subpopulations. Figure 4.9 shows the range of FST values obtained for 1000 independent loci in a simulation of the finite island model (see section 4.5) where genetic drift and gene flow among subpopulations were the processes acting to change allele frequencies. The range of Fst values for individual loci under the influence of identical population genetic processes is due to the random nature of genetic drift. Each locus has experienced random fluctuations in allele frequencies that has resulted in a range of allele frequency variance among subpopulations. This random variation in FST due to genetic drift seen in the simulation underscores the need for estimates of FST to be obtained from the average of multiple loci.

### 4.4 Population subdivision and the Wahlund effect

• Genetic variation can be present as heterozygosity within a panmictic population or as differences in allele frequency among diverged subpopulations.

The last section of the chapter showed how departures from Hardy-Weinberg expected frequencies of heterozygotes can be used to quantify departures from random mating within demes and allele-frequency divergence among demes. This section will further explore heterozygosity within and among several demes, with two main goals. The first is to explore the consequences of population subdivision on expected genotype frequencies. The second is to show why FST functions to estimate allele frequency divergence among demes.

Consider the case of a diallelic locus for two randomly mating demes. The expected heterozygosity for each deme is:

2G 4G 6G 8G IGG Generation i -

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