Wahlund effect

In population genetics, the Wahlund effect is a reduction of heterozygosity (that is when an organism has two different alleles at a locus) in a population caused by subpopulation structure. Namely, if two or more subpopulations have different allele frequencies, 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 formula_1, with allele frequencies of A and a given by formula_2 and formula_3 respectively (formula_4). Suppose this population is split into two equally-sized subpopulations, formula_5 and formula_6, and that all the "A" alleles are in subpopulation formula_5 and all the "a" alleles are in subpopulation formula_6 (this could occur due to drift). 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 formula_9 and formula_10 represent the allele frequencies of A in formula_5 and formula_6 respectively (and formula_13 and formula_14 likewise represent a).
Let the allele frequency in each population be different, i.e. formula_15.
Suppose each population is in an internal Hardy–Weinberg equilibrium, so that the genotype frequencies AA, Aa and aa are "p"2, 2"pq", and "q"2 respectively for each population.
Then the heterozygosity (formula_16) in the overall population is given by the mean of the two:
which is always smaller than formula_18 (formula_19) unless formula_20
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.
"F"-statistics.
The reduction in heterozygosity can be measured using "F"-statistics.