The Hardy–Weinberg equilibrium describes situations in which allele and genotype frequencies do not change.

Allele and genotype frequencies change over time only if specific forces act on the population. This principle was demonstrated independently in 1908 by the English mathematician G. H. Hardy and the German physician Wilhelm Weinberg, and has become known as the Hardy-Weinberg equilibrium. In essence, the Hardy–Weinberg equilibrium describes the situation in which evolution does not occur. In the absence of evolutionary forces (such as natural selection), allele and genotype frequencies do not change.

To determine whether or not evolutionary forces are at work, we need to determine whether or not a population is in Hardy–Weinberg equilibrium. The Hardy–Weinberg equilibrium specifies the relationship between allele frequencies and genotype frequencies when a number of key conditions are met. In these cases, we can conclude that evolutionary forces are not acting on the gene in the population we are studying. In many ways, then, the Hardy–Weinberg equilibrium is most interesting when we find instances in which allele or genotype frequencies depart from expectations. This finding implies that one or more of the conditions are not met and that evolutionary mechanisms are at work.

A population that is in Hardy–Weinberg equilibrium meets these conditions:

  1. There can be no differences in the survival and reproductive success of individuals. Let’s examine what happens when this condition is not met. Given two alleles, A and a, consider what occurs when a, a recessive mutation, is lethal. All aa individuals die. Therefore, in every generation, there is a selective elimination of a alleles, meaning that the frequency of a will gradually decline (and the frequency of A correspondingly increase) over the generations. As we discuss below, we call this differential success of alleles selection.

  2. Populations must not be added to or subtracted from by migration. Again, let’s see what happens when this condition is not met. Consider a second population adjacent to the one we used in the preceding example in which all the alleles are A and all individuals have the genotype AA. Then there is a sudden influx of individuals from the first population into the second. The frequency of A in the second population changes in proportion to the number of immigrants.

  3. There can be no mutation. If A alleles mutate into a alleles (or other alleles, if the gene has multiple alleles), and vice versa, then again we see changes in the allele frequencies over the generations. In general, because mutation is so rare, it has a very small effect on changing allele frequencies on the timescales studied by population geneticists.

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  4. The population must be sufficiently large to prevent sampling errors. Small samples are likely to be more misleading than large ones. Campus-wide, a college’s sex ratio may be close to 50:50, but in a small class of 8 individuals it is not improbable that we would have 6 women and 2 men (a 75 : 25 ratio). Sample size, in the form of population size, also affects the Hardy–Weinberg equilibrium such that it technically holds only for infinitely large populations. A change in the frequency of an allele due to the random effects of limited population size is called genetic drift.

  5. Individuals must mate at random. For the Hardy–Weinberg equilibrium to hold, mate choice must be made without regard to genotype. For example, an AA homozygote when offered a choice of mate from among AA, Aa, or aa individuals should choose at random. In contrast, non-random mating occurs when individuals do not mate randomly. For example, AA homozygotes might preferentially mate with other AA homozygotes. Non-random mating affects genotype frequencies from generation to generation, but does not affect allele frequencies.