Hardy-Weinberg Equation
Predict allele and genotype frequencies in a stable population.
The foundation of population genetics and evolution studies.
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The Formula
p² + 2pq + q² = 1 and p + q = 1
The Hardy-Weinberg equation predicts genotype frequencies in a population that is not evolving. It uses two alleles of a gene: the dominant allele (p) and the recessive allele (q).
Variables
| Symbol | Meaning |
|---|---|
| p | Frequency of the dominant allele |
| q | Frequency of the recessive allele |
| p² | Frequency of the homozygous dominant genotype (AA) |
| 2pq | Frequency of the heterozygous genotype (Aa) |
| q² | Frequency of the homozygous recessive genotype (aa) |
Example 1
In a population, 16% show the recessive phenotype. Find all genotype frequencies.
q² = 0.16, so q = √0.16 = 0.4
p = 1 - q = 1 - 0.4 = 0.6
p² = 0.36 (homozygous dominant)
2pq = 2 × 0.6 × 0.4 = 0.48 (heterozygous carriers)
AA = 36%, Aa = 48%, aa = 16%
Example 2
The dominant allele frequency is 0.7. Find the genotype distribution.
p = 0.7, q = 1 - 0.7 = 0.3
p² = 0.49, 2pq = 0.42, q² = 0.09
AA = 49%, Aa = 42%, aa = 9%
When to Use It
Use the Hardy-Weinberg equation when:
- Predicting genotype frequencies from allele frequencies
- Testing whether a population is in genetic equilibrium
- Estimating the number of carriers of a recessive trait
- Studying evolution — deviations from Hardy-Weinberg indicate evolutionary forces
Key Notes
- Equations: p + q = 1 and p² + 2pq + q² = 1: p is the frequency of the dominant allele, q of the recessive. The genotype frequencies p², 2pq, and q² represent homozygous dominant, heterozygous, and homozygous recessive, respectively.
- Five equilibrium conditions: Hardy-Weinberg equilibrium holds only when there is no mutation, no migration, no natural selection, random mating, and a very large population. Violating any condition causes allele frequencies to shift — meaning evolution is occurring.
- Used as a null hypothesis: Comparing observed genotype frequencies to H-W predictions tests whether a population is evolving. Significant deviation signals selection, drift, non-random mating, or migration.
- Calculating carrier frequency: If a recessive disease affects 1 in 10,000 people (q² = 0.0001), then q = 0.01 and p ≈ 0.99. The carrier frequency (2pq) ≈ 2 × 0.99 × 0.01 ≈ 1 in 50 — much higher than the disease prevalence.
- Applications: Hardy-Weinberg equations are used in genetic counseling to estimate carrier frequency, in forensic DNA analysis to calculate match probabilities, and in evolutionary biology to quantify selection pressure.