Wahlund effect

In population genetics, the Wahlund effect refers to 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 $$P$$, with allele frequencies of A and a given by $$p$$ and $$q$$ respectively ($$p + q = 1$$). Suppose this population is split into two equally-sized subpopulations, $$P_1$$ and $$P_2$$, and that all the A alleles are in subpopulation $$P_1$$ and all the a alleles are in subpopulation $$P_2$$ (this could easily 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 $$p_1$$ and $$p_2$$ represent the allele frequencies of A in $$P_1$$ and $$P_2$$ respectively (and $$q_1$$ and $$q_2$$ likewise represent a).

Let the allele frequency in each population be different, i.e. $$p_1 \ne p_2$$.

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 ($$H$$) in the overall population is given by the mean of the two:

which is always smaller than $$2p(1-p)$$ ( = $$2pq$$) unless $$p_1=p_2$$
 * $$H$$
 * $$= {2p_1q_1 + 2p_2q_2 \over 2}$$
 * $$= {p_1q_1 + p_2q_2}$$
 * $$= {p_1(1-p_1) + p_2(1-p_2)}$$
 * }
 * $$= {p_1(1-p_1) + p_2(1-p_2)}$$
 * }
 * $$= {p_1(1-p_1) + p_2(1-p_2)}$$
 * }

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.


 * De Finetti diagram (see Li 1955)

F-statistics
The reduction in heterozgosity can be measured using F-statistics.