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*p*^{2} + 2*pq* + *q**2* = 1

The Hardy–Weinberg principle states that both allele and genotype frequencies in a population remain constant--that is, they are in equilibrium--from generation to generation unless specific disturbing influences are introduced. Those disturbing influences include non-random mating, mutations, selection, limited population size, random genetic drift and gene flow. It is important to understand that outside the lab, one or more of these "disturbing influences" are always in effect. That is a Hardy Weinberg equilibrium is unlikely in nature. Nonetheless, the idea of genetic equilibrium is a basic principle of population genetics that provides a baseline for measuring genetic change.

In the simplest case of a single locus with two alleles: the dominant allele is denoted A and the recessive a and their frequencies are denoted by *p* and *q*;

freq(A)=*p*; freq(a)=*q*; *p* + *q* = 1.

If the population is in equilibrium, then we will have freq(AA)=*p*^{2} for the AA homozygotes in the population

freq(aa)=*q*^{2} for the aa homozygotes

and freq(Aa)=2*pq* for the heterozygotes.

The overall equation for the Hardy-Weinberg equilibrium is expressed in this way:

Based on these equations, we can determine useful but difficult-to-measure facts about a population. For example, a patient's child is a carrier of a recessive mutation that causes cystic fibrosis in homozygous recessive children. The parent wants to know the probability of her grandchildren inheriting the disease. In order to answer this question, the genetic counselor must know the chance that the child will reproduce with a carrier of the recessive mutation. This fact may not be known, but disease frequency is known. We know that the disease is caused by the homozygous recessive genotype; we can use the Hardy-Weinberg principle to work backward from disease occurrence to the frequency of heterozygous recessive individuals.

This concept is also known by a variety of names: HWP, Hardy–Weinberg equilibrium, HWE, or Hardy–Weinberg law. It was named after G. H. Hardy and Wilhelm Weinberg.