Wahlund effect

In population genetics, the Wahlund effect causes reduced heterozygosity in populations due to subpopulation structure. If two or more subpopulations that are in Hardy-Weinberg equilibrium have different allele frequencies then overall the heterozygosity is reduced.

Contents

1 Overview

1.1 Simple example
1.2 Generalization

2 F-statistics

3 History

4 References

Overview

Simple 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 $P 2$ . 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. $p_1 \ne q_1$ .

Suppose each populations is in Hardy-Weinberg equilibrium, so that the the genotype frequencies AA, Aa and aa are p², 2pq, and q² respectively for each population.

Then the heterozygosity in the overall population is given by the average of the two:

$f (A a)$	$= {2p_1q_1 + 2p_2q_2 \over 2}$
	$= p 1 q 1 + p 2 q 2$

$H < 2 p q$

i.e. it is less than that is expected from Hardy — Weinberg expectation.

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 heterozyogisities of the subpopulations, weighted by he subpopulation size.

de Finetti diagram (see Li 1955)

F-statistics

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

History

The Wahlund effect was first documented by the Swedish geneticist Sten Wahlund in 1928.

References

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

Categories: Population genetics