The Hardy–Weinberg equation and its conditionsSpec D4.1.13, D4.1.14
In short
The Hardy–Weinberg equation, p² + 2pq + q² = 1, predicts genotype frequencies from the two allele frequencies p and q, where p + q = 1. It holds only when a population is in genetic equilibrium: large, randomly mating, with no mutation, migration or selection. Frequencies that do not fit show a condition is not met.
For a gene with two alleles, p and q denote the two allele frequencies. Where one allele is dominant, p is usually the dominant allele and q the recessive allele. Every allele copy is one or the other, so p + q = 1, and with random combination of gametes the genotype frequencies are p², 2pq and q².
| Term | Genotype frequency |
|---|---|
| p² | Homozygous dominant (AA) |
| 2pq | Heterozygous (Aa) |
| q² | Homozygous recessive (aa) |
Allele and carrier frequencies
In a population, 1 in 2500 people has a recessive genetic condition. Calculate the frequency of carriers (practice figures).
- q² = 1 ÷ 2500 = 0.0004
- q = √0.0004 = 0.02
- p = 1 − q = 0.98
- 2pq = 2 × 0.98 × 0.02 = 0.0392
Answer: Carrier frequency = 0.0392, about 3.9% or 1 in 26 people.
Start from q², the homozygous recessive frequency, because it is the only genotype you can identify from the phenotype. Never take the square root of the dominant phenotype frequency.
Conditions for genetic equilibrium
- A very large population, so chance changes (genetic drift) are negligible.
- Random mating.
- No mutation.
- No migration into or out of the population (no gene flow).
- No natural selection: all genotypes survive and reproduce equally.
If observed genotype frequencies do not fit the Hardy–Weinberg equation, one or more conditions is not being met, for example mating is non-random or survival rates vary between genotypes.
Quick check
What generates new alleles?
Show answer
Mutation: a random change in the base sequence of a gene.
Why are acquired characteristics not inherited?
Show answer
They are not encoded in the base sequence of genes.
What is fitness?
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The survival value and reproductive potential of a genotype.
HL only What does 2pq represent in the Hardy–Weinberg equation?
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The frequency of heterozygotes.
HL only Is antibiotic resistance an example of artificial selection?
Show answer
No, it is natural selection; nobody chose which bacteria would reproduce.
Written and checked against the IB Biology HL specification · Updated October 2026