Hardy-Weinberg and Allele Frequencies

The Hardy-Weinberg principle states that, absent evolutionary forces, allele and genotype frequencies stay constant across generations, giving population genetics its fundamental null model.

Definition

The Hardy-Weinberg principle predicts that, in a large randomly mating population with no selection, mutation, migration, or drift, allele frequencies remain constant and genotype frequencies follow the expansion p-squared, 2pq, and q-squared for two alleles. Departures from these expectations indicate that one or more evolutionary forces are at work.

Scope

This topic covers the Hardy-Weinberg equilibrium and its assumptions, the relationship between allele and genotype frequencies, the use of expected equilibrium proportions to detect non-random mating and selection, and the recursion equations that track allele-frequency change under each evolutionary force.

Core questions

• What assumptions must hold for a population to be at Hardy-Weinberg equilibrium?
• How are genotype frequencies predicted from allele frequencies at equilibrium?
• What do deviations from Hardy-Weinberg proportions reveal about a population?
• How do recursion equations describe allele-frequency change under selection, drift, mutation, and migration?

Key theories

Hardy-Weinberg equilibrium

Without disturbing forces, sexual reproduction alone does not change allele frequencies, and genotype frequencies reach predictable equilibrium proportions in a single generation of random mating.

Mechanisms

Under random mating, gamete frequencies equal allele frequencies, so genotype frequencies are obtained by expanding the binomial of allele frequencies, reaching equilibrium in one generation for an autosomal locus. The equilibrium is disturbed by any evolutionary force: selection changes allele frequencies according to fitness differences, drift introduces random change scaled by effective population size, mutation and migration add new alleles, and non-random mating alters genotype proportions without necessarily changing allele frequencies. Comparing observed to expected genotype frequencies provides a test for these departures.

Clinical relevance

Hardy-Weinberg expectations are used in medical and forensic genetics to estimate carrier frequencies for recessive disorders, to check genotyping data quality in association studies, and to compute the rarity of DNA profiles.

History

The principle was derived independently by the mathematician G. H. Hardy and the physician Wilhelm Weinberg in 1908, resolving an early objection that dominant alleles would inevitably spread. It became the cornerstone null model of population genetics in the modern synthesis.

Key figures

• G. H. Hardy
• Wilhelm Weinberg

Seminal works

• hartlClark2007
• saetreRavinet2019
• futuyma2017

Frequently asked questions

Does Hardy-Weinberg equilibrium mean a population is not evolving?

It means that, at the locus examined, no evolutionary force is detectably changing allele frequencies; a population can be at equilibrium for some loci while evolving at others.

How quickly is Hardy-Weinberg equilibrium reached?

For a single autosomal locus under random mating, genotype frequencies reach the equilibrium proportions in a single generation.