Overview
This lecture explains how to solve Hardy-Weinberg equilibrium problems, including identifying allele and genotype frequencies and applying the formula to typical genetics questions.
Gene Pools and Allele Frequency
- A gene pool is the collection of all alleles in a population.
- The frequency of the dominant allele is represented by p; the recessive by q.
- p + q = 1 always, where p is dominant allele frequency and q is recessive allele frequency.
- To calculate p or q, divide the number of that allele by the total number of alleles.
Hardy-Weinberg Principle and Formula
- Hardy-Weinberg equilibrium predicts genotype frequencies in a population that is not evolving.
- The formula is: p² + 2pq + q² = 1.
- p² = frequency of homozygous dominant individuals.
- 2pq = frequency of heterozygous individuals.
- q² = frequency of homozygous recessive individuals.
- Squaring p or q gives the proportion of individuals with two of the same allele.
Solving Hardy-Weinberg Problems
- If given the percentage of homozygous recessive individuals, that is q².
- To find q, take the square root of q²; p = 1 − q.
- If given an allele frequency, use it directly as p or q.
- Calculate genotype frequencies using p², 2pq, and q².
- For heterozygotes, calculate 2pq.
- For homozygous dominant, use p²; for homozygous recessive, use q².
Example Problems Walkthrough
- 16% non-tasters = q² = 0.16, so q = 0.4, p = 0.6.
- Tasters = 84% (since 16% are non-tasters).
- Dominant allele frequency (p) = 0.6; recessive allele (q) = 0.4.
- Heterozygous individuals = 2 × 0.6 × 0.4 = 0.48 or 48%.
- Mutation with q = 0.2: Homozygous recessive = 0.2² = 0.04 or 4%; heterozygous = 2 × 0.8 × 0.2 = 0.32 or 32%.
Key Terms & Definitions
- Gene Pool — all alleles present in a population.
- Allele Frequency (p, q) — proportion of each allele type in the gene pool.
- p² — frequency of homozygous dominant genotype.
- q² — frequency of homozygous recessive genotype.
- 2pq — frequency of heterozygous genotype.
- Heterozygous — genotype with one dominant and one recessive allele (e.g., Aa).
- Homozygous — genotype with two identical alleles (AA or aa).
Action Items / Next Steps
- Practice identifying what is given in Hardy-Weinberg problems (q² or allele frequency).
- Solve additional practice problems using p² + 2pq + q² = 1.
- Review definitions of key terms.