Wahlund effect

The Wahlund effect is the reduction in the overall heterozygosity of a population as a result of subpopulation structures. Essentially, if two or more subpopulations have independent allele frequencies then the overall heterozygosity is reduced, irrespective of whether those subpopulations are in Hardy-Weinberg equilibrium. The most common cause is a geographical barrier to gene flow between the subpopulations, followed by independent genetic drift in each subpopulation.

The simplest example is where you have a population, P, with the allele frequencies of A and a given by p and q, respectively (where p + q = 1). Suppose this population is split into two subpopulations, P1 and P2, and that all the dominant A alleles are in subpopulation P1 and all the recessive a alleles are in subpopulation P2 (this is a feasible consequence of genetic drift). This means there are no heterozygotes, even though the subpopulations are in Hardy-Weinberg equilibrium.

To make a slight generalisation of the above example, let p1 and p2 represent the allele frequencies of A in P1 and P2 (and likewise let q1 and q2 represent the frequencies of a). Suppose the allele frequencies in the two subpopulations P1 and P2 are unequal (i.e. p1 does not equal p2 and q1 does not equal q2) and suppose that each subpopulation is in Hardy-Weinberg equilibrium, so that the genotype frequencies in each subpopulation are p2, 2pq and q2 (where the sum of these is 1). Then the heterozygosity of the overall population is given by the mean of the two:

= (2p1q1) + (2p2q2) / 2

Which cancels out to give p1q1 + p2q2, or p1(1 - p1) + p2(1 - p2), which is always smaller than 2p(1 − p) ( = 2pq) unless p1 = p2