Hardy-Weinberg Practice Problems Explained

Hardy-Weinberg questions ask you to connect allele frequencies with genotype frequencies under a population model. First identify which quantity the question gives you. An affected-person frequency and a carrier frequency require different starting steps.

Know what each term represents

For a simplified two-allele autosomal locus, p and q are allele frequencies and p + q = 1. The expected genotype frequencies are p², 2pq, and q². Under a fully penetrant recessive disease model, q² represents the affected genotype frequency and 2pq represents heterozygous carriers.

Example 1: from disease frequency to carriers

Assume an autosomal recessive condition has an affected frequency of 1 in 10,000 in a population satisfying the model.

• q² = 1/10,000 = 0.0001
• q = 0.01, so p = 0.99
• Carrier frequency = 2pq = 2 × 0.99 × 0.01 = 0.0198, or 1.98%

The exact result is about 1 in 50.5. The common rare-allele approximation 2q gives 2%, or about 1 in 50. Showing both teaches the difference: the approximation is close here, but it is not the exact calculation. Taking the disease frequency itself as the carrier frequency skips the key relationship.

Example 2: from carriers to an approximate disease frequency

Suppose the carrier frequency is approximately 1 in 25 and the disease allele is rare. Using 2pq ≈ 2q gives q ≈ 1/50, then q² ≈ 1/2,500. This is an approximation. If a problem requires an exact value, solve 2q(1 − q) for q rather than replacing p with 1.

Recognize when the model is a poor fit

The simple model assumes random mating and no evolutionary forces changing allele frequencies, along with the relevant disease-model assumptions. Population structure, selection, nonrandom mating, incomplete penetrance, and more complex genetic mechanisms can make a classroom estimate unsuitable for a clinical risk calculation.

Do not apply the autosomal recessive q² shortcut to every inheritance pattern. Start with the biological and population assumptions, then select the equation.

Use the free Math Workbook for written practice and EveryGene Academy for case-based questions. Review Bayesian risk when a test result changes an individual's probability.

Source context: Original worked calculations using the classical population model. NHGRI genetics glossary provides related terminology. Label the model as a simplified two-allele autosomal recessive example; population structure and disease-model assumptions limit clinical application.

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