Wahlund effect


In population genetics, the Wahlund effect is a reduction of heterozygosity in a population caused by subpopulation structure. Namely, if two or more subpopulations have different allele frequencies then the overall heterozygosity is reduced, even if the subpopulations themselves are in a Hardy–Weinberg equilibrium. The underlying causes of this population subdivision could be geographic barriers to gene flow followed by genetic drift in the subpopulations.
The Wahlund effect was first documented by the Swedish geneticist Sten Wahlund in 1928.

Simplest example

Suppose there is a population, with allele frequencies of A and a given by and respectively. Suppose this population is split into two equally-sized subpopulations, and, and that all the A alleles are in subpopulation and all the a alleles are in subpopulation . Then, there are no heterozygotes, even though the subpopulations are in a Hardy–Weinberg equilibrium.

Case of two alleles and two subpopulations

To make a slight generalization of the above example, let and represent the allele frequencies of A in and respectively.
Let the allele frequency in each population be different, i.e..
Suppose each population is in an internal Hardy–Weinberg equilibrium, so that the genotype frequencies AA, Aa and aa are p2, 2pq, and q2 respectively for each population.
Then the heterozygosity in the overall population is given by the mean of the two:
which is always smaller than unless

Generalization

The Wahlund effect may be generalized to different subpopulations of different sizes. The heterozygosity of the total population is then given by the mean of the heterozygosities of the subpopulations, weighted by the subpopulation size.
The reduction in heterozygosity can be measured using F-statistics.