Hardy Weinberg Equilibrium Calculator

The Hardy-Weinberg relation is a null model, and its power comes from how quickly it is reached. Under random mating with no selection, mutation, migration or drift, genotype frequencies settle at p squared, 2pq and q squared after a single generation regardless of the starting genotype proportions, and neither the allele frequencies nor the genotype frequencies change thereafter. Because equilibrium is the default outcome of doing nothing, any statistically meaningful departure from it points to a specific biological or technical cause. A structural consequence worth remembering is that the heterozygote term 2pq is maximized when p and q both equal 0.5, where it reaches exactly 0.5; at a two-allele locus heterozygotes can never make up more than half a population. The most common practical use is estimating carrier burden for recessive disease. If a disorder affects 1 in 2,500 people, then q squared is 0.0004, q is 0.02, and the carrier frequency 2pq is about 3.9 percent, roughly 1 in 25. For rare alleles 2pq is approximately 2q, so unaffected carriers outnumber affected individuals by about 2 divided by q, a ratio of 200 to 1 when q is 0.01. The chi-square test of fit uses one degree of freedom: three genotype classes, minus one because the counts must sum to the sample total, minus one more because the allele frequency was estimated from the same data. Its critical value is 3.841 at alpha 0.05, and it should be replaced by an exact test when expected counts fall below about 5. Note that X-linked loci require separate treatment, since hemizygous males have no heterozygous class at all.

The principle was published twice in 1908 by two people who did not know of each other. Reginald Punnett had been challenged by the statistician Udny Yule, who argued that a dominant allele should inevitably spread until dominant and recessive phenotypes stood at 3 to 1. Unable to answer formally, Punnett put the question to his Cambridge colleague G. H. Hardy, a pure mathematician, who replied with a short letter in Science in 1908 demonstrating that allele and genotype frequencies remain stable across generations under random mating. Hardy regarded the result as too elementary to be of much interest. In the same year Wilhelm Weinberg, a physician in Stuttgart, published a more thorough independent derivation in German in the proceedings of a Wuerttemberg natural history society. Weinberg's paper went largely unnoticed in the English-language literature for decades until Curt Stern drew attention to it in 1943, after which the joint name became standard usage. The relation went on to serve as the baseline of population genetics, the fixed point against which Fisher, Haldane and Wright measured the effects of selection, drift and migration. Its applications broadened well beyond evolutionary theory. Medical genetics uses it for carrier frequency estimation in counselling, forensic genetics uses it to compute DNA profile match probabilities from allele frequency tables, and modern genome-wide association studies run Hardy-Weinberg tests as a routine quality control filter, where a failure in healthy controls usually signals a genotyping artifact rather than real biology.