Hg p p var p

The next step is again to use the fact that p = 1 - q to replace p - p2 with its equivalent expression pq and multiply the terms inside the parentheses by 2 to finally obtain

Recall from equation 4.21 that HT = 2pq. Making this substitution gives

Using an equivalent set of substitutions and algebraic rearrangements, it is also possible to show that the expected frequencies of homozygote genotypes in the total population are and

The changes to homozygosity and heterozygosity caused by allele-frequency divergence among populations are exactly analogous to the consequences of consanguineous mating in a single population. In section 2.5 it was shown that freq(AA) = p2 + fpq where f is the probability of identity by descent. The Wahlund effect describes a similar phenomenon where allele-frequency divergence of populations leads to an increase of homozygosity in subpopulations compared to the heterozygosity expected based on total population allele frequencies.

These equations show that in a subdivided population, the expected genotype frequencies in the total population are a function of the average allele frequencies as well as the variance in allele frequencies among subpopulations. A set of subpopulations in panmixia is equivalent to a situation where there is no variance in allele frequency (var(p) = 0). In that case, Ht = HS and FSTis zero since HT - HS is also zero. This result is consistent with the intuitive expectation that extensive gene flow homogenizes allele frequencies among subpopulations. However, when subpopulations have diverged in allele frequencies

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