# Wahlund effect

In population genetics, the Wahlund effect refers to 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 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 ${\displaystyle P}$, with allele frequencies of A and a given by ${\displaystyle p}$ and ${\displaystyle q}$ respectively (${\displaystyle p+q=1}$). Suppose this population is split into two equally-sized subpopulations, ${\displaystyle P_{1}}$ and ${\displaystyle P_{2}}$, and that all the A alleles are in subpopulation ${\displaystyle P_{1}}$ and all the a alleles are in subpopulation ${\displaystyle P_{2}}$ (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 ${\displaystyle p_{1}}$ and ${\displaystyle p_{2}}$ represent the allele frequencies of A in ${\displaystyle P_{1}}$ and ${\displaystyle P_{2}}$ respectively (and ${\displaystyle q_{1}}$ and ${\displaystyle q_{2}}$ likewise represent a).

Let the allele frequency in each population be different, i.e. ${\displaystyle p_{1}\neq p_{2}}$.

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 (${\displaystyle H}$) in the overall population is given by the mean of the two:

 ${\displaystyle H}$ ${\displaystyle ={2p_{1}q_{1}+2p_{2}q_{2} \over 2}}$ ${\displaystyle ={p_{1}q_{1}+p_{2}q_{2}}}$ ${\displaystyle ={p_{1}(1-p_{1})+p_{2}(1-p_{2})}}$

which is always smaller than ${\displaystyle 2p(1-p)}$ ( = ${\displaystyle 2pq}$) unless ${\displaystyle p_{1}=p_{2}}$

## 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.

## References

• Li, C.C. (1955) ...
• Wahlund, S. (1928). Zusammensetzung von Population und Korrelationserscheinung vom Standpunkt der Vererbungslehre aus betrachtet. Hereditas 11:65–106.