You cannot see which people carry a recessive allele, but if you know how many show the recessive phenotype you can calculate it. Two short equations let you work out allele and genotype frequencies, as long as the population meets a few conditions.
For a gene with a dominant allele A (frequency p) and a recessive allele a (frequency q): p + q = 1 (allele frequencies) and p2 + 2pq + q2 = 1 (genotype frequencies), where p2 = AA, 2pq = Aa and q2 = aa. Only the recessive phenotype reveals its genotype, so the usual method is: q2 = frequency of the recessive phenotype, q = √q2, p = 1 − q, then calculate 2pq (carriers) and p2. The principle predicts that allele frequencies stay constant from generation to generation only if the population is large, mating is random, there is no selection, no mutation and no migration (gene flow) in or out, and the organism is diploid and reproduces sexually. If observed frequencies differ from the prediction, one of these conditions is not being met.
Start with Recessive phenotype (q²) at 0.16. The panel shows q = 0.40, p = 0.60, AA 0.36 (144 of 400) and Aa 0.48 (192). Then set q² to 0.25 and to 0.01 and predict the numbers before you read them.
Do not take the square root of the dominant phenotype frequency to find p. People with the dominant phenotype are AA and Aa, so their frequency is p2 + 2pq, not p2. Always start from the recessive phenotype.
Four quick checks. Each correct answer earns XP and records this skill on your profile.
The simulator starts at q² = 0.16 in a population of 400. How many individuals show the recessive phenotype?
You set q² to 0.25. What value of p does the panel show?
At q² = 0.16, the panel shows Aa (2pq) = 0.48. Which calculation gives this?
You set q² to 0.01, so only 1% of the population shows the recessive phenotype. Which statement about the yellow carriers is correct?
The principle describes a population that is not evolving. Each condition removes one way that allele frequencies could change.
| Condition | What happens if it is broken |
|---|---|
| very large population | genetic drift changes allele frequencies by chance |
| random mating | if individuals choose mates by phenotype, or inbreed, genotype frequencies change |
| no selection | alleles that give an advantage increase in frequency |
| no mutation | new alleles appear or one allele changes into another |
| no migration (gene flow) | individuals arriving or leaving bring in or remove alleles |
| diploid, sexual reproduction, non-overlapping generations | the equations are based on random fusion of gametes |
The Hardy-Weinberg principle does not say that the dominant allele becomes more common. Without selection, a dominant allele stays at the same frequency, however rare it is.
Unlocks once the four checks above are done. Worth more XP, written to A Level Paper 4 standard.
In a population, 9% of individuals show a recessive phenotype. What percentage are heterozygous?
A population of 200 contains 98 AA, 84 Aa and 18 aa individuals. What is the frequency of allele A?
Which situation would make the Hardy-Weinberg principle unreliable for predicting genotype frequencies?
Why must q be calculated from the recessive phenotype rather than from the dominant phenotype?
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