Before we consider the implications of the Hardy–Weinberg law, we need to take a closer look at the three assumptions that it makes about a population. First, it assumes that the population is large. How big is “large”? Theoretically, the Hardy–Weinberg law requires that a population be infinitely large in size, but this requirement is obviously unrealistic. In practice, many large populations have genotypes in the predicted Hardy–Weinberg proportions, and significant deviations arise only when population size is rather small. Later in the chapter, we will examine the effects of small population size on allelic frequencies.

The second assumption of the Hardy–Weinberg law is that members of the population mate randomly, which means that each genotype mates relative to its frequency. For example, suppose that three genotypes are present in a population in the following proportions: f(AA) = 0.6, f(Aa) = 0.3, and f(aa) = 0.1. With random mating, the frequency of mating between two AA homozygotes (AA × AA) will be equal to the product of their frequencies: 0.6 × 0.6 = 0.36, whereas the frequency of mating between two aa homozygotes (aa × aa) will be only 0.1 × 0.1 = 0.01.

The third assumption of the Hardy–Weinberg law is that the allelic frequencies of the population are not affected by natural selection, migration, or mutation. Although mutation occurs in every population, its rate is so low that it has little short-term effect on the predictions of the Hardy–­Weinberg law (although it may shape allelic frequencies over long periods when no other forces are acting). Although natural selection and migration are significant factors in real populations, we must remember that the purpose of the Hardy–Weinberg law is to examine only the effect of reproduction on the gene pool. When this effect is known, the effects of other factors (such as migration and natural selection) can be examined.

A final point is that the assumptions of the Hardy–­Weinberg law apply to a single locus. No real population mates randomly for all traits, and no population is completely free of natural selection for all traits. The Hardy–­Weinberg law, however, does not require random mating and the absence of selection, migration, and mutation for all traits; it requires these conditions only for the locus under consideration. A population may be in Hardy–Weinberg equilibrium for one locus but not for others.