Hardy-Weinberg Equilibrium Calculator

What Is Hardy-Weinberg Equilibrium? The Hardy-Weinberg (HW) principle states that allele and genotype frequencies in a population remain constant from generation to generation in the absence of evolutionary forces. It was independently derived by Godfrey Hardy, a British mathematician, and Wilhelm Weinberg, a German physician, in 1908. The principle serves as the null hypothesis of population genetics — a baseline to detect evolution.

The Hardy-Weinberg Equations For a gene with two alleles (A and a), where p = frequency of A and q = frequency of a: p + q = 1 (allele frequencies sum to 1) p² + 2pq + q² = 1 (genotype frequencies sum to 1) p² = frequency of homozygous dominant (AA) 2pq = frequency of heterozygous (Aa) q² = frequency of homozygous recessive (aa)

The Five Assumptions Hardy-Weinberg equilibrium requires all five conditions to hold simultaneously:

1. Large population size (no genetic drift)
2. No mutation (allele frequencies don’t change due to mutation)
3. No migration (no gene flow from other populations)
4. Random mating (no sexual selection or assortative mating)
5. No natural selection (all genotypes have equal fitness) Real populations violate at least one of these conditions — so HW is always an approximation.

How to Calculate Allele Frequencies from Observed Genotypes If you observe: AA=360, Aa=480, aa=160 (total = 1000 individuals): Total alleles = 2000. Copies of A = 360×2 + 480 = 1200. p = 1200/2000 = 0.6. q = 1 − p = 0.4. Expected HW genotypes: AA = 0.36 × 1000 = 360, Aa = 0.48 × 1000 = 480, aa = 0.16 × 1000 = 160. This population is in HW equilibrium (observed = expected).

Deviations from HW Equilibrium Excess homozygotes (vs expected): suggests inbreeding, assortative mating, or population subdivision. Excess heterozygotes (vs expected): heterozygote advantage (balancing selection) — example: sickle cell anemia and malaria resistance. Chi-square test is used to statistically test whether observed genotypes differ significantly from HW expectations.

Applications Estimating carrier frequency: if q² (recessive disease frequency) = 1/10,000, then q = 0.01, p = 0.99, carrier frequency 2pq ≈ 1/50. Cystic fibrosis: ~1 in 2,500 Europeans are affected (q²), so q ≈ 0.02 and carrier frequency ≈ 1 in 25. Forensic genetics: DNA profiling uses HW to calculate the probability of a random match in a population. Conservation biology: monitoring HW in small populations detects inbreeding and loss of diversity.