Allele Frequency Formula
Calculate allele frequency from genotype counts using Hardy-Weinberg equilibrium.
Returns p and q allele frequencies for population genetics analysis.
The Formula
p = (2 × AA + Aa) / (2 × total individuals)
Allele frequency measures how common a particular allele is within a population. It is calculated by counting alleles across all individuals in the sample.
Variables
| Symbol | Meaning |
|---|---|
| p | Frequency of allele A (dominant) |
| q | Frequency of allele a (recessive), where q = 1 - p |
| AA | Number of homozygous dominant individuals |
| Aa | Number of heterozygous individuals |
| aa | Number of homozygous recessive individuals |
Example 1
In a sample of 200 people: 98 AA, 84 Aa, 18 aa. Find allele frequencies.
Total alleles = 2 × 200 = 400
A alleles = 2(98) + 84 = 196 + 84 = 280
p = 280 / 400 = 0.70
q = 1 - 0.70 = 0.30
Allele A frequency = 0.70, Allele a frequency = 0.30
Example 2
In 50 plants: 10 RR, 25 Rr, 15 rr. Find allele frequencies.
Total alleles = 2 × 50 = 100
R alleles = 2(10) + 25 = 45
p = 45 / 100 = 0.45
R frequency = 0.45, r frequency = 0.55
When to Use It
Use the allele frequency formula when:
- Analyzing genetic diversity within a population
- Setting up Hardy-Weinberg calculations
- Tracking allele frequency changes over generations
- Studying evolutionary pressures on specific traits
Key Notes
- Allele frequency sums to 1: For a gene with two alleles A and a, p + q = 1 where p = frequency of A and q = frequency of a. For multiple alleles, the sum of all frequencies equals 1.
- Hardy-Weinberg genotype frequencies: At equilibrium, genotype frequencies are p² (AA), 2pq (Aa), and q² (aa), and p² + 2pq + q² = 1. This predicts genotype ratios from allele frequencies alone.
- Hardy-Weinberg assumptions: The model requires random mating, no mutation, no migration, no genetic drift, and no natural selection. Deviations from predicted frequencies reveal which assumption is violated.
- Genetic drift affects small populations: In small populations, random sampling can cause large swings in allele frequency across generations. In large populations, allele frequencies remain more stable by chance alone.
- Application in medicine: If the frequency of a recessive disease is q² (e.g., cystic fibrosis ≈ 1/2,500), then q = 1/50 and the carrier frequency is 2pq ≈ 2/50 ≈ 4%. This is used in genetic counseling.