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Levin (1978) used allozyme electrophoresis to estimate genotype frequencies for the phosphoglucomutase-2 gene (Pgm-2) in Phlox cuspidata, a plant capable of self-fertilization. Genetic data were collected from 43 populations across the species range in southeast Texas. Using starch gel electrophoresis, the frequencies of two alleles (fast and slow running) and the frequencies of the heterozygous genotype were recorded for each population. A portion of the data is given in the table below (population numbers match Table 2 in Levin (1978)).

Subpopulation

19 43 68

Frequency of

Pgm-2 fast 0.0 0.93 0.17 0.51 Frequency of

Pgm-2 slow 1.0 0.07 0.83 0.49 Heterozygote frequency 0.0 0.14 0.34 0.40

Using the heterozygote and allele frequencies, compute the hierarchical heterozygosities H,, HS, and HTand use these to calculate FIS, FST, and FIT. Is there evidence that P. cuspidata individuals engage in selfing? Are the populations panmictic or subdivided?

The individual, subpopulation, and total population heterozygosities are identical in populations after compensating for the degree to which observed and expected heterozygosities are not met at different levels of population organization. The average observed heterozygosity is greater or less than the average expected heterozygosity for subpopulations:

to the extent that there is non-random mating (FIS ^ 0). Similarly, the average expected heterozygosity for subpopulations is less than the expected heterozygosity of the total population under panmixia:

to the extent that subpopulations have diverged allele frequencies (FST > 0). The total deviation from expected heterozygosity within and among subpopulations is then

Although equations 4.14-4.16 can be considered as rearrangements of equations 4.11-4.13, they also represent a different way to articulate and think of the biological impacts of allele frequency divergence among subpopulations and non-random mating within subpopulations. Each fixation index expresses the degree to which random mating expectations for the frequency of heterozygous genotypes are not met. Using these equations it is also possible to show how the total reduction in heterozygosity relates to the combined fixation due to non-random mating and subpopulation divergence:

Since using the fixation index to measure allele frequency divergence among subpopulations is the novel concept in this section, let's consider an additional example that focuses exclusively on FST. Figure 4.7 shows allele frequencies for a diallelic locus in two populations that are both composed of six subpopulations. The pattern of allele frequencies among the subpopulations is very different. On the right all subpopulations have the same allele frequencies, while on the left each subpopulation is at either complete fixation or complete loss for one allele. In both sets of populations HT = 2(0.5)(0.5) = 0.5. The only difference between the two sets of populations is how allele frequencies are organized, or HS. In the right-hand population, all six subpopulations have allele frequencies of V2, giving HS = (6(2)(0.5)(0.5))/6 = 0.5. In the left population, three subpopulations have an allele frequency of zero and three subpopulations have an allele frequency of one. This pattern gives HS = (3(2)(1.0)(0) + 3(2)(0)(1.0))/6 = 0.0. Using these expected heterozygosities for the subpopulations and total population gives FST = 0.0 on the right and Fst = 1.0 on the left.

The average allele frequency in the total population is the same in both cases. However, there is a major difference in the way that allele frequencies are organized. On the right all the subpopulations have identical allele frequencies, as would be expected if the subpopulations were really not subdivided at all. On the left the subpopulations are highly diverged in

Figure 4.7 Allele frequencies at a diallelic locus for populations that consist of six subpopulations. Allele frequencies within subpopulations are indicated by shading. On the left, individual subpopulations are either fixed or lost for one allele. On the right, all subpopulations have identical allele frequencies of p = q = 0.5. In both cases, the total population has an average allele frequency of p = 0.5 and an expected heterozygosity of HT = 2pq = 0.5. In contrast, the average expected heterozygosity for subpopulations is HS = 2pq = 0.5 on the right and HS = 2pq= 0.0 on the left. FST = 1.0 on the left since the subpopulations have maximally diverged allele frequencies. FST = 0.0 on the right since the subpopulations all have identical allele frequencies. Divergence of allele frequencies among subpopulations produces a deficit of heterozygosity relative to the Hardy-Weinberg expectation based on average allele frequencies for the total population.

Figure 4.7 Allele frequencies at a diallelic locus for populations that consist of six subpopulations. Allele frequencies within subpopulations are indicated by shading. On the left, individual subpopulations are either fixed or lost for one allele. On the right, all subpopulations have identical allele frequencies of p = q = 0.5. In both cases, the total population has an average allele frequency of p = 0.5 and an expected heterozygosity of HT = 2pq = 0.5. In contrast, the average expected heterozygosity for subpopulations is HS = 2pq = 0.5 on the right and HS = 2pq= 0.0 on the left. FST = 1.0 on the left since the subpopulations have maximally diverged allele frequencies. FST = 0.0 on the right since the subpopulations all have identical allele frequencies. Divergence of allele frequencies among subpopulations produces a deficit of heterozygosity relative to the Hardy-Weinberg expectation based on average allele frequencies for the total population.

allele frequencies as expected with strong population subdivision. Therefore, the different values of FST reflect the different degrees of allele frequency divergence among the sets of subpopulations. When all of the subpopulations are well mixed and have similar allele frequencies, HS and HT are identical. Biologically, an FST value of zero says that all subpopulations have alleles at the same frequencies as the total population and any single subpopulation has as many heterozygotes as any other subpopulation. As the populations diverge in allele frequency due to whatever process, HS will decrease and FST will approach one. Biologically, an FST value of one says that the genetic variation is partitioned completely as allele-frequency differences among the subpopulations with an absence of segregating alleles within subpopulations.

An alternative way to think about the pattern of population differentiation in allele frequency is using the variance in allele frequency relative to the amount of genetic variation in the total population to estimate FST. The estimate of allele-frequency differentiation among subpopulations is then

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