In 1908, English mathematician Godfrey H. Hardy and German physician Wilhelm Weinberg independently derived a mathematical model describing what happens to the frequency of alleles in a population over time. Their combined ideas became known as the Hardy-Weinberg theorem. It states that the mixing of alleles at meiosis and their subsequent recombination do not alter the frequencies of the alleles in future generations, if certain assumptions are met. Stated another way, if certain assumptions are met, evolution will not occur because the allelic frequencies will not change from generation to generation, even though the specific mixes of alleles in individuals may vary.
The assumptions of the Hardy-Weinberg theorem are as follows:
1. The population size must be large. Large size ensures that gene frequency will not change by chance alone.
2. Mating within the population must be random. Every individual must have an equal chance of mating with any other individual in the population. If this condition is not fulfilled, then some individuals are more likely to reproduce than others, and natural selection may occur.
3. Individuals cannot migrate into, or out of, the population. Migration may introduce new genes into the gene pool or add or delete copies of existing genes.
4. Mutations must not occur. If they do, mutational equilibrium must exist. Mutational equilibrium exists when mutation from the wild-type allele to a mutant form is balanced
by mutation from the mutant form back to the wild type. In either case, no new genes are introduced into the population from this source.
These assumptions must be met if allelic frequencies are not changing—that is, if evolution is not occurring. Clearly, these assumptions are restrictive, and few, if any, real populations meet them. This means that most populations are evolving. The Hardy-Weinberg theorem, however, does provide a useful theoretical framework for examining changes in gene frequencies in populations.
The next section explains how, when the assumptions are not met, evolutionary change occurs.