Hardy–Weinberg principle
Allele and genotype frequencies remain constant without evolutionary influences.
In population genetics, the Hardy–Weinberg principle—also called the Hardy–Weinberg equilibrium, model, theorem, or law—describes how allele and genotype frequencies stay unchanged across generations when no evolutionary forces act on the population. These forces include genetic drift, mate choice, assortative mating, natural selection, sexual selection, mutation, gene flow, meiotic drive, genetic hitchhiking, population bottleneck, founder effect, and inbreeding.
For a single gene with two alleles, A and a, where their frequencies are p and q respectively, random mating produces expected genotype frequencies of p² for AA homozygotes, q² for aa homozygotes, and 2pq for heterozygotes. Without selection, mutation, genetic drift, or similar influences, p and q remain constant between generations, so the population reaches equilibrium. G. H. Hardy and Wilhelm Weinberg first proved this mathematically. Hardy’s paper aimed to refute the idea that a dominant allele would naturally increase in frequency—a notion possibly stemming from a misinterpreted lecture question. Today, testing for Hardy–Weinberg genotype frequencies mainly checks for deviations from equilibrium due to forces like selection, inbreeding, or genotyping errors, rather than primarily for population stratification.
Imagine a population of monoecious diploids, where each organism produces male and female gametes equally, and each gene locus has two alleles. The population is treated as infinitely large, and reproduction occurs through random union of gametes (the gene pool model). Initial frequencies of alleles A and a are p and q. Each generation’s allele frequencies come from pooling the alleles of the current generation’s genotypes: homozygotes contribute 1 copy, heterozygotes contribute ½. A Punnett square shows how next-generation genotypes form, with each genotype’s proportion equal to the product of the row and column allele frequencies from the current generation. The sum of all entries is p² + 2pq + q² = 1, since genotype frequencies must total one. Because p + q = 1, the binomial expansion (p + q)² = p² + 2pq + q² = 1 gives the same relationships. Adding up the Punnett square or binomial expansion yields the expected offspring genotype proportions after one generation.
These frequencies define Hardy–Weinberg equilibrium. Note that genotype frequencies after the first generation may diff
- field
- Population genetics
- known_for
- Hardy–Weinberg principle (Hardy–Weinberg equilibrium, model, theorem, or law)
- named_after
- G. H. Hardy and Wilhelm Weinberg
Lore & Background
The principle was derived independently by G. H. Hardy and Wilhelm Weinberg. Hardy's paper was focused on debunking the view that a dominant allele would automatically tend to increase in frequency, a view possibly based on a misinterpreted question at a lecture. In the simplest case of a single locus with two alleles, A and a, with frequencies p and q, the expected genotype frequencies under random mating are p² for AA, q² for aa, and 2pq for Aa. In the absence of selection, mutation, genetic drift, or other forces, allele frequencies p and q remain constant between generations, so equilibrium is reached.
Reader's Guide
The Hardy–Weinberg principle provides a null model for population genetics, describing the expected genotype frequencies in a population that is not evolving. It assumes a large population, random mating, and no evolutionary influences such as genetic drift, mate choice, natural selection, mutation, or gene flow. The principle shows that after one generation of random mating, genotype frequencies reach equilibrium and remain constant thereafter, even if they differ from the initial generation. Today, tests for Hardy–Weinberg genotype frequencies are used primarily to test for population stratification and other forms of non-random mating. The principle is essential for understanding how evolutionary forces alter allele and genotype frequencies over time.
Did You Know?
- The principle is named after G. H. Hardy and Wilhelm Weinberg, who first demonstrated it mathematically.
- Hardy's paper was focused on debunking the view that a dominant allele would automatically tend to increase in frequency.
- In the simplest case, expected genotype frequencies under random mating are p², 2pq, and q².
- Tests for Hardy–Weinberg frequencies are used primarily to test for population stratification and non-random mating.
Frequently Asked Questions
Who is the Hardy–Weinberg principle named after?
It takes its name from two independent researchers—G. H. Hardy, a British mathematician, and Wilhelm Weinberg, a German physician—who each derived the same equilibrium relationship in 1908. Their shared result showed that allele and genotype frequencies in a population remain stable from one generation to the next when no evolutionary pressures are at play.
What does the Hardy–Weinberg principle actually do?
It provides a mathematical baseline: given two alleles with frequencies p and q, it predicts the expected genotype frequencies (p², 2pq, q²) under random mating. Any real population that deviates from those predictions signals that some evolutionary force—selection, drift, migration, mutation, or non-random mating—is actively reshaping the gene pool.
What conditions must hold for Hardy–Weinberg equilibrium to apply?
The population must be effectively infinite in size, mating must be completely random, and there must be no mutation, migration, or selection acting on the locus in question. In practice, no natural population perfectly meets every condition, which is exactly why the principle is so useful as a null model.
Why is the Hardy–Weinberg principle considered foundational in population genetics?
It gives geneticists a simple null hypothesis to test against real data, turning the question 'is evolution happening?' into a straightforward statistical comparison. Without that baseline, it would be far harder to detect and quantify the effects of natural selection, genetic drift, or gene flow.
What is the Hardy–Weinberg equation and what do p and q mean?
For a single locus with two alleles, p represents the frequency of allele A and q represents the frequency of allele a, with p + q always equaling 1. The expected genotype frequencies then follow as p² for homozygous dominant, 2pq for heterozygous, and q² for homozygous recessive.
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