Learning Objective: At the end of this lesson, the learner will be able to calculate allele and genotype frequencies in a population under Hardy-Weinberg equilibrium and apply this principle to predict carrier and disease prevalence.
Principle
In a population with random mating, allele and genotype frequencies remain constant across generations if certain conditions are met.
Let:
- p = frequency of allele A
- q = frequency of allele a
- p + q = 1
Genotype frequencies:
| Genotype | Frequency |
|---|---|
| AA | p² |
| Aa | 2pq |
| aa | q² |
Sum: p² + 2pq + q² = 1
X-linked recessive:
- Frequency in males: q
- Frequency in females: q²
Hardy-Weinberg Assumptions
- No mutation at the locus
- No natural selection
- Random mating
- No migration
- Large population size
Example: Cystic Fibrosis (Autosomal Recessive)
- Prevalence: 1/3200 → q² = 1/3200 → q ≈ 0.017
- p + q = 1 → p ≈ 0.983
- Carrier frequency: 2pq = 2 × 0.983 × 0.017 ≈ 0.035 → 3.5%
Key Point: For rare autosomal recessive diseases, p ≈ 1 simplifies calculations.
High-Yield Tips
- Use 2pq to calculate carrier frequency for autosomal recessive traits.
- q² gives the homozygous recessive disease frequency.
- X-linked recessive: male frequency = q; female frequency = q².
- Hardy-Weinberg equilibrium is a baseline model; deviations indicate evolutionary forces.
