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 are in a Hardy–Weinberg equilibrium but have different allele frequencies, the overall heterozygosity is reduced compared to if the whole population was in 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 described by the Swedish geneticist Sten Wahlund in 1928.
Simplest example Suppose there is a population P {\displaystyle P} , with allele frequencies of A and a given by p {\displaystyle p} and q {\displaystyle q} respectively ( p + q = 1 {\displaystyle p+q=1} ). Suppose this population is split into two equally-sized subpopulations, P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} , and that all the A alleles are in subpopulation P 1 {\displaystyle P_{1}} and all the a alleles are in subpopulation P 2 {\displaystyle P_{2}} (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 p 1 {\displaystyle p_{1}} and p 2 {\displaystyle p_{2}} represent the allele frequencies of A in P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} , respectively (and q 1 {\displaystyle q_{1}} and q 2 {\displaystyle q_{2}} likewise represent a). Let the allele frequency in each population be different, i.e. p 1 ≠ p 2 {\displaystyle p_{1}\neq p_{2}} . 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 ( H {\displaystyle H} ) in the overall population is given by the mean of the two:
H = 2 p 1 q 1 + 2 p 2 q 2 2 = p 1 q 1 + p 2 q 2 = p 1 ( 1 − p 1 ) + p 2 ( 1 − p 2 ) {\displaystyle {\begin{aligned}H&={2p_{1}q_{1}+2p_{2}q_{2} \over 2}\\[5pt]&={p_{1}q_{1}+p_{2}q_{2}}\\[5pt]&={p_{1}(1-p_{1})+p_{2}(1-p_{2})}\end{aligned}}}
which is always smaller than 2 p ( 1 − p ) {\displaystyle 2p(1-p)} (
= 2 p q {\displaystyle {}=2pq} ) unless p 1 = p 2 {\displaystyle p_{1}=p_{2}}
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.
See also Hardy–Weinberg principle Cryptic relatedness F-statistics Coefficient of relationship Coefficient of inbreeding
References