What is Hardy-Weinberg equilibrium?
In an idealized population, allele and genotype frequencies stay constant from one generation to the next. For a gene with two alleles — A at frequency p and a at frequency q (with p + q = 1) — the genotype frequencies are p² (AA), 2pq (Aa) and q² (aa). Independently derived by G. H. Hardy and Wilhelm Weinberg in 1908, it is the null model of population genetics: departures from it point to an evolutionary force at work.
The equation and its assumptions
The equilibrium is summarized by p² + 2pq + q² = 1. It holds only under five assumptions: random mating, no selection, no mutation, no migration and an infinite population (no genetic drift). When observed genotype counts differ significantly from the expected frequencies — tested with a chi-square goodness-of-fit test — one or more of these assumptions is being violated.
How to use the calculator
Give the tool an allele frequency or the observed genotype counts. It computes p and q, the expected p² : 2pq : q² proportions, the expected counts and the chi-square statistic so you can judge whether the population is in equilibrium.
Note: the model assumes a single autosomal locus with two alleles in a diploid, sexually reproducing population. Extensions exist for multiple alleles, X-linked loci and overlapping generations, but the two-allele case is the standard teaching and screening tool.
Frequently asked questions
What is Hardy-Weinberg equilibrium?
A state in which allele and genotype frequencies in a population stay constant across generations because no evolutionary force is acting. It is the null model that observed populations are compared against.
What is the Hardy-Weinberg equation?
p^2 + 2pq + q^2 = 1, where p and q are the frequencies of two alleles (p + q = 1), and p^2, 2pq and q^2 are the frequencies of the homozygous dominant, heterozygous and homozygous recessive genotypes.
What are the assumptions of Hardy-Weinberg equilibrium?
Random mating, no natural selection, no mutation, no gene flow (migration) and an infinitely large population (no genetic drift). If a population deviates from the expected frequencies, at least one assumption is violated.
How do you calculate allele frequencies?
From genotype counts, the frequency of an allele is the number of copies of that allele divided by the total number of alleles. For a recessive phenotype, q = sqrt(q^2) where q^2 is the frequency of the recessive homozygotes.
References
- G. H. Hardy (1908), "Mendelian Proportions in a Mixed Population", Science 28(706):49–50.
- W. Weinberg (1908), "Über den Nachweis der Vererbung beim Menschen", Jahreshefte des Vereins für vaterländische Naturkunde in Württemberg.
- D. L. Hartl & A. G. Clark, Principles of Population Genetics, 4th ed. (Sinauer Associates).
- A. J. F. Griffiths et al., Introduction to Genetic Analysis (W. H. Freeman).