Population Subdivision, Hardy–Weinberg Equilibrium and the Wahlund Effect

Abstract

After having introduced the Hardy–Weinberg principle and its underlying assumptions, the authors describe the main causes of departures from equilibrium. They then stress the importance of species subdivision into different local subpopulations/demes. This geographical structure affects allele frequencies over space and consequently the proportions of different genotypes in the local populations. It leads to the Wahlund effect, which can be defined as the excess of homozygotes or the deficit in heterozygotes observed in a sample of individuals obtained from a structured population, even when the local populations are randomly mating. Finally, the authors briefly outline the extension of the Wahlund effect at two loci and its consequences in association studies.

Key Concepts:

  • The Hardy–Weinberg principle states that genotype frequencies can be predicted from gene/allele frequencies and remain constant over generations in random‐mating populations under the simple assumptions of no mutation, selection or migration.

  • Many deviations from random mating can be observed in natural populations, such as assortative mating or other mating systems that lead to inbreeding or outbreeding.

  • Species subdivision (into subpopulations, social groups and families) is also a common pattern encountered in natural populations that can cause substantial spatial genetic structure and departure from random mating depending on the sampling unit.

  • The Wahlund effect is both the apparent excess of homozygotes and the deficit of heterozygotes observed at single locus data in a large ‘sample’ of individuals due to the existence of population subdivision.

  • The Wahlund effect can be extended at multiple loci where it leads to an apparent excess of double homozygotes and either an excess or a deficit of heterozygote combinations, depending on allele frequency variation at different loci across populations.

  • An important consequence of the Wahlund effect due to unknown population stratification is the creation of allelic association or linkage disequilibrium between different loci in the total sample of individuals.

  • Unknown population structure can, therefore, have a major impact on association studies by creating false‐positive tests, and a large range of methods have been developed that allow to correct or control genetic structure.

  • Population structure and sampling units (or sampling strategy) are increasingly recognised as important factors when making inference in population genetics under models that assume HW and ignore structure.

Keywords: Hardy–Weinberg equilibrium; Wahlund effect; population subdivision; linkage disequilibrium; association studies

Figure 1.

HW equilibrium and Wahlund effect. The solid curve represents the proportion of heterozygotes in a population at HW equilibrium for a biallelic locus, where p1 is the allelic frequency of one of the two alleles. The population P is subdivided in two subpopulations or strata, P1 and P2, which are both at HW equilibrium for different allelic frequencies (p1=0.2 and 0.6, respectively). P1 and P2 are both on the solid curve, whereas P is necessarily below, indicating that the Wahlund effect leads to a heterozygote deficit.

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Garnier‐Géré, Pauline, and Chikhi, Lounès(Nov 2013) Population Subdivision, Hardy–Weinberg Equilibrium and the Wahlund Effect. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0005446.pub3]