Hardy-Weinberg Equilibrium

Hardy-Weinberg equilibrium describes the genetic state of an idealised population in which allele frequencies remain constant from generation to generation and genotype frequencies settle into a fixed relationship with those allele frequencies. It is the null model of population genetics: the distribution of genotypes expected when no evolutionary force is acting.

Definition

Hardy-Weinberg equilibrium is the condition, in a large randomly mating population free of selection, mutation, migration, and drift, in which allele frequencies stay constant and the genotype frequencies for two alleles with frequencies p and q equal p-squared, 2pq, and q-squared.

Scope

The entry covers the assumptions behind the equilibrium, the algebraic relationship between allele and genotype frequencies, the meaning of deviations from it, and how the principle is used as a baseline and as a data-quality check in genetic studies. It is presented as a conceptual and methodological topic, not as clinical guidance.

Core questions

• What assumptions must hold for genotype frequencies to match Hardy-Weinberg proportions?
• How are expected genotype frequencies calculated from allele frequencies?
• What does a statistically significant departure from equilibrium indicate?

Key concepts

• Random mating (panmixia)
• Allele frequencies p and q
• Expected genotype proportions p-squared, 2pq, q-squared
• Null model for evolutionary change
• Departure from equilibrium
• Exact and chi-square tests of HWE

Key theories

Hardy-Weinberg principle

For a biallelic locus with allele frequencies p and q (p plus q equal 1) in a large, randomly mating, force-free population, genotype frequencies become p-squared, 2pq, and q-squared after a single generation and stay constant thereafter.

Mechanisms

The principle follows from combining gametes at random: if a parental generation contributes alleles in frequencies p and q to a shared gamete pool, random union of gametes produces offspring genotypes in the binomial proportions p-squared, 2pq, and q-squared, and these proportions are reached in one generation and then maintained. The result holds only while the idealising assumptions are met; violating any of them — selection, mutation, migration, drift, or non-random mating — moves the population away from these expected proportions, which is why the model functions as a reference point for detecting evolutionary forces.

Clinical relevance

In genetic studies the principle is used to derive expected carrier and genotype frequencies from observed allele frequencies and, importantly, as a quality-control filter: marked deviation from Hardy-Weinberg proportions in a control sample can flag genotyping error or population structure. It describes how expected frequencies and data integrity are assessed and is not a basis for individual diagnostic or treatment decisions.

Evidence & guidelines

Statistical tests for departure from Hardy-Weinberg proportions are a routine quality-control step in genetic association studies; Wigginton and colleagues describe an exact test that is preferred over the chi-square approximation when genotype counts are small.

History

In 1908 the mathematician G. H. Hardy and, independently, the physician Wilhelm Weinberg showed that Mendelian inheritance does not by itself cause dominant traits to increase or rare alleles to disappear: in the absence of disturbing forces, allele frequencies are conserved and genotypes reach stable proportions. The result, initially prompted by a misconception that dominant alleles should spread, became a cornerstone of population genetics.

Key figures

• G. H. Hardy
• Wilhelm Weinberg

Seminal works

• hardy-1908
• weinberg-1908

Frequently asked questions

What are the assumptions of Hardy-Weinberg equilibrium?

A large population, random mating, and no selection, mutation, migration, or genetic drift. When these hold, allele frequencies stay constant and genotype frequencies follow the p-squared, 2pq, q-squared pattern.

Why does a deviation from Hardy-Weinberg equilibrium matter in genetic studies?

Because the proportions are expected only when no force acts, a significant deviation signals something real — selection, non-random mating, or population structure — or a technical problem such as genotyping error, which is why testing for it is a standard data-quality check.