Figure 4.9 The distribution of FST values for 1000 replicate neutral loci in a finite island model of 200 subpopulations where each subpopulation contains 10 individuals and the rate of gene flow is 10% of each subpopulation (m = 0.10). In the distribution, 95% of the replicate loci show FST values between 0.1459 and 0.2002 whereas the average of all 1000 replicate loci is 0.1586 (based on the average of HT and HS then used to calculate FST). Replicate loci exhibit a range of Fst values since allele frequencies among subpopulations are partly a product of the stochastic process of genetic drift. In an infinite island model with Nem = 1.0 the expected value of Fst is 0.2.
based on the product of subpopulation average allele frequencies. HT and HS both cannot exceed 0.5, the maximum heterozygosity for a diallelic locus. In addition, HS is an average of H1 and H2, so when subdivided populations have different allele frequencies HS will always be less than the expected heterozygosity of the total population. These conditions assure that HT > HS when there is random mating within the subpopulations. This relationship between HT and HS is shown graphically in Fig. 4.10. This phenomenon is called the Wahlund effect after the Swedish geneticist Sten Gosta William Wahlund who first described it in 1928. One result is that FST will be greater or equal to zero since the numerator in the expression for FST is HT - HS.
Ht Hi
P Pi
Allele frequency (p)
Figure 4.10 A graphical demonstration of the Wahlund effect for a diallelic locus in two demes. If there is random mating within subpopulations (H1 and H2) and in the total population (HT), the heterozygosity of each falls on the parabola of Hardy-Weinberg expected frequency. The average heterozygosity of subpopulations (HS) is at the mid-point between the deme heterozygosities. Therefore, HS can never be greater than HT based on the average allele frequency (the mid-point between the deme allele frequencies p1 and p2). Greater variance in allele frequencies of the demes is the same as a wider spread of deme allele frequencies in the two-deme case.
Ht Hi
P Pi
Allele frequency (p)
Figure 4.10 A graphical demonstration of the Wahlund effect for a diallelic locus in two demes. If there is random mating within subpopulations (H1 and H2) and in the total population (HT), the heterozygosity of each falls on the parabola of Hardy-Weinberg expected frequency. The average heterozygosity of subpopulations (HS) is at the mid-point between the deme heterozygosities. Therefore, HS can never be greater than HT based on the average allele frequency (the mid-point between the deme allele frequencies p1 and p2). Greater variance in allele frequencies of the demes is the same as a wider spread of deme allele frequencies in the two-deme case.
The Wahlund effect can also be shown in another fashion that more clearly connects it to variation in allele frequencies among subpopulations. The goal will now be to show that the difference between the expected heterozygosity in the total population (HT) and the average expected heterozygosity of the subpopulations (HS) depends on the variance in allele frequencies among the subpopulations.
The variance in allele frequencies among a set of subpopulations is
where pi is the allele frequency in subpopulation i. It also turns out that for a diallelic locus, var(p) equals var(q) since p = 1 - q. This result will be used later.
The average expected heterozygosity of the subpopulations,
Wahlund effect The decreased expected frequency of heterozygotes in subpopulations with diverged allele frequencies compared with the expected frequency of heterozygotes in a panmictic population of the same total size with the same average allele frequencies.
hs = 11 2pi1i j=i can also be expressed as
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