Hardy-Weinberg Equation: Find Allele Frequencies
Use p + q = 1 and p² + 2pq + q² = 1 to find allele frequencies and the percent of carriers, with two worked AP Biology examples.
The two equations
- p + q = 1 (alleles)
- p² + 2pq + q² = 1 (genotypes)
p = dominant allele, q = recessive allele.
What each term is
- p² = homozygous dominant
- 2pq = heterozygous (carriers)
- q² = homozygous recessive
Start from q²: it is the only genotype you can see directly.
Example 1
9% of a population has a recessive trait. Find q, p, and the percent of carriers.
- q² = 0.09, so q = √0.09 = 0.3
- p = 1 − 0.3 = 0.7
- 2pq = 2(0.7)(0.3)
Carriers = 0.42 (42%)
Example 2
4% of people have a recessive condition. What fraction are carriers?
- q² = 0.04, so q = 0.2
- p = 0.8
- 2pq = 2(0.8)(0.2)
Carriers = 0.32 (32%)
Common mistake
q² = 0.09, so q = 0.09
Take the square root: q = √q².
2pq counts both ways to be a carrier (Aa and aA).
The recessive allele is q, not the dominant one.
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