Hardy-Weinberg Equilibrium

Hardy-Weinberg Equilibrium is a foundational principle in population genetics stating that, under a specific set of idealized conditions, both allele frequencies and genotype frequencies in a population will remain unchanged from one generation to the next. Named after G.H. Hardy and Wilhelm Weinberg, who independently derived it in 1908, it serves as the null hypothesis of population genetics — the mathematical baseline describing what a population looks like when no evolution is occurring.

The principle connects directly to Allele Frequency: given the frequency of the dominant allele (p) and recessive allele (q), Hardy-Weinberg predicts the expected proportion of each genotype in the population — homozygous dominant (p²), heterozygous (2pq), and homozygous recessive (q²) — assuming random mating and no evolutionary pressures. This is exactly what the Hardy-Weinberg Calculator computes, taking allele or genotype frequencies as input and returning the expected equilibrium distribution.

Five specific conditions must hold for a population to remain in true Hardy-Weinberg equilibrium: no mutation, no migration, no natural selection, an infinitely large population (no genetic drift), and completely random mating. Real populations rarely satisfy all five perfectly, which makes the principle most useful as a comparison tool — geneticists calculate observed allele frequencies using the Allele Frequency Calculator, then check whether the observed genotype counts match Hardy-Weinberg's predictions. A significant mismatch is strong evidence that one of the five evolutionary forces is actively acting on that population.

p² + 2pq + q² = 1

Where p is the frequency of the dominant allele, q is the frequency of the recessive allele (with p + q = 1), p² is the expected frequency of homozygous dominant individuals (AA), 2pq is the expected frequency of heterozygous individuals (Aa), and q² is the expected frequency of homozygous recessive individuals (aa).

In a population, the recessive allele frequency is measured at q = 0.3 (so p = 1 - 0.3 = 0.7). Under Hardy-Weinberg Equilibrium, the expected genotype frequencies are:

Homozygous dominant (AA): p² = 0.7² = 0.49 (49%) Heterozygous (Aa): 2pq = 2 × 0.7 × 0.3 = 0.42 (42%) Homozygous recessive (aa): q² = 0.3² = 0.09 (9%)

Check: 0.49 + 0.42 + 0.09 = 1.0. If a real survey of that population found genotype frequencies noticeably different from these predicted values — say, far fewer heterozygotes than 42% — it would suggest selection, non-random mating, or another evolutionary force is at work.

• The formula converts allele frequencies into genotype frequencies: p² + 2pq + q² = 1 takes the same p and q used to describe allele frequency and predicts the full genotype distribution across a population.
• Five strict assumptions rarely all hold in nature: no mutation, no migration, no selection, infinite population size, and random mating are the theoretical requirements, and real populations almost always violate at least one.
• Deviation from equilibrium reveals evolution in action: comparing observed genotype counts to Hardy-Weinberg predictions is one of the most common ways biologists detect that selection, drift, or another force is shaping a population.
• Carrier frequency (2pq) is critical in medical genetics: for recessive genetic disorders, Hardy-Weinberg lets researchers estimate how many unaffected people carry one copy of a disease allele, even when only the homozygous recessive (affected) frequency is directly observable.
• The square root trick recovers q from disease prevalence: if the frequency of an affected homozygous recessive individual (q²) is known from clinical data, taking its square root gives q, from which p, carrier frequency, and full genotype distribution can all be derived.