Short on time? This page is the recap. For explanations, figures and worked examples, use the full study guide.
Recap
- The Hardy–Weinberg model predicts allele and genotype frequencies in a population that is not evolving.
- p and q are the frequencies of two alleles of one gene. They are proportions (0 to 1) of all the alleles in the population.
- If gametes combine at random, genotype frequencies are p², 2pq and q².
- Five conditions keep frequencies constant: large population, no migration, no new mutations, random mating, no natural selection.
- No real population meets all five. Use the prediction as a null hypothesis: a clear mismatch means at least one condition is broken.
Key relationships
| Equation | Meaning |
|---|---|
| p + q = 1 | all alleles of the gene; true for any population with two alleles |
| p² + 2pq + q² = 1 | genotype frequencies AA, Aa, aa under equilibrium |
| p = (2 × AA + Aa) ÷ 2N | counting alleles; N = number of individuals |
| q = √(q²) | from the recessive phenotype; assumes equilibrium |
| χ² = Σ (o − e)² ÷ e | tests observed genotype numbers against expected |
| Condition broken | Force acting | Main effect |
|---|---|---|
| large population | genetic drift | random allele-frequency change |
| no migration | gene flow | alleles added or removed |
| no new mutations | mutation | new alleles appear |
| random mating | inbreeding or mate choice | genotype frequencies shift (fewer heterozygotes with inbreeding) |
| no natural selection | selection | fitter alleles rise in frequency |
Assumptions behind the numbers
- One gene, two alleles, diploid organisms, sexual reproduction.
- √(q²) is only valid if the population is in equilibrium. If every genotype can be seen, count alleles instead.
- When expected numbers use an allele frequency known in advance, chi-square df = 3 − 1 = 2 (critical value 5.99 at p = 0.05).
Mistakes to avoid
- Writing pq instead of 2pq for heterozygotes.
- Treating q² (recessive phenotype) as q.
- Saying dominant alleles become more common on their own.
- Thinking equilibrium means p = q = 0.5.
- Saying inbreeding alone changes allele frequencies.
- Saying “fail to reject” proves the population is not evolving.
Quick self-check
- 16% of a population shows a recessive phenotype. Find q, p and the carrier frequency. (q = √0.16 = 0.4; p = 0.6; 2pq = 0.48)
- A sample has AA 45, Aa 40, aa 15. Find p by counting. ((2 × 45 + 40) ÷ 200 = 130 ÷ 200 = 0.65)
- Which condition does a tiny island population most clearly break? (Large population size: drift will act.)
Next: practice questions.