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The Hardy–Weinberg Principle states that in a large, randomly mating population, allele frequencies stay the same over time if the population is not evolving.

When a gene has two alleles at one locus, such as red and brown coat alleles in squirrels, their frequencies—represented by p and q—add up to one.

We can calculate the frequency of each genotype. The frequency of homozygous red and homozygous brown individuals is the square of the allele frequency—p² and q²—which gives the probability of inheriting the same allele from both parents.

Heterozygous individuals with red-brown coats can form in two ways: the egg can carry the red allele and the sperm the brown allele, or the egg can carry the brown allele and the sperm the red allele. So, the frequency of heterozygous individuals equals two times the product of the allele frequencies, or 2pq.

Together, these genotype frequencies sum to one. This principle is true only under specific, non-evolving conditions.

There must be no natural selection, and mating must be random with no preference for particular genotypes. There must be no gene flow from outside the population and no mutations within the population.

Finally, the population must be very large because random events can strongly change allele frequencies in small populations.

Although no real-world population can satisfy all of these conditions, the principle still offers a useful model for population analysis.