Hardy-Weinberg principle
Allele frequencies stay constant from generation to generation unless something disturbs them: p² + 2pq + q² = 1. Any change from this means evolution.
The principle
In a population, each allele of a gene has a frequency (its share of all alleles of that gene). The Hardy-Weinberg principle says that these allele frequencies are stable and constant from generation to generation, so the gene pool stays the same. This state is called genetic equilibrium (Hardy-Weinberg equilibrium). The sum of all allele frequencies is 1. If measured frequencies differ from the expected ones, the direction of the difference shows the extent of evolutionary change.
Where p² + 2pq + q² = 1 comes from
- 1Take one gene with two alleles, A and a. Let p = frequency of A and q = frequency of a, so p + q = 1.
- 2With random mating, a gamete carries A with chance p and a with chance q.
- 3Chance of AA = p × p = p²; chance of aa = q × q = q².
- 4Aa can form two ways (A from father and a from mother, or the reverse), so its chance = 2pq.
- 5★All genotypes together: (p + q)² = p² + 2pq + q² = 1.
★ key step
Worked example: from allele frequency to genotypes
In a population, the frequency of the recessive allele a is 0.3. Find the frequency of the dominant allele and of the genotypes AA, Aa and aa, assuming equilibrium.
- Given: q = 0.3.
- Rule: p + q = 1, so p = 1 − 0.3 = 0.7.
- AA = p² = 0.7 × 0.7 = 0.49.
- Aa = 2pq = 2 × 0.7 × 0.3 = 0.42.
- aa = q² = 0.3 × 0.3 = 0.09.
- Check: 0.49 + 0.42 + 0.09 = 1.00.
p = 0.7; AA = 0.49, Aa = 0.42, aa = 0.09
Worked example: finding carriers
In a population of 1000 people, 160 show a recessive trait (aa). Assuming Hardy-Weinberg equilibrium, how many people are heterozygous carriers (Aa)?
- Frequency of aa: q² = 160 ÷ 1000 = 0.16.
- q = √0.16 = 0.4.
- p = 1 − 0.4 = 0.6.
- Frequency of Aa = 2pq = 2 × 0.6 × 0.4 = 0.48.
- Number of carriers = 0.48 × 1000 = 480.
- Check: AA = 0.36 × 1000 = 360; 360 + 480 + 160 = 1000.
480 heterozygous carriers
The five factors that disturb the equilibrium
| Factor | How it changes allele frequencies |
|---|---|
| Gene migration or gene flow | Alleles are added to one population and lost from another when individuals move, again and again |
| Genetic drift | Frequencies change by chance; the founder effect is an extreme case |
| Mutation | New alleles appear |
| Genetic recombination | New combinations form during gametogenesis |
| Natural selection | Variants that survive and reproduce better pass on more of their alleles |
Health workers use this equation to estimate how many people silently carry an allele for a disorder such as thalassemia, which is common in some Indian communities. That helps plan carrier screening before marriage or pregnancy.
2 marks: “State the Hardy-Weinberg principle. What does p² + 2pq + q² = 1 represent?” Allele frequencies in a population stay constant from generation to generation (genetic equilibrium). p² = AA, 2pq = Aa, q² = aa frequencies; it is the expansion of (p + q)².
3 marks: “List the five factors that affect Hardy-Weinberg equilibrium. Explain any two.” Gene flow, genetic drift, mutation, recombination, natural selection. E.g. gene flow adds and removes alleles through repeated migration; genetic drift changes frequencies by chance, as in the founder effect.
2 marks: “In a population, 4% of individuals show a recessive trait. Find the frequency of the dominant allele.” q² = 0.04, so q = 0.2; p = 1 − 0.2 = 0.8.
p + q = 1; square it for genotypes. Five things break the balance: My Good Dog Rarely Sleeps (Mutation, Gene flow, Drift, Recombination, Selection).