A recessive disease allele has a frequency of 0.1 in a population. Using Hardy-Weinberg, what fraction are carriers?
Let q = 0.1 for the recessive allele, so p = 1 - q = 0.9.
Let q = 0.1 for the recessive allele, so p = 1 - q = 0.9. Carriers are the heterozygotes, with frequency 2pq = 2 x 0.9 x 0.1 = 0.18. So about 18% of people are carriers, while only q^2 = 0.01 (1%) are actually affected. Carriers vastly outnumber the affected, which is why a rare recessive disease persists in a population.
Key point
Carrier frequency = 2pq = 0.18 (18%), far above the 1% (q^2) who are actually affected.
Common mistake
forgetting p = 1 - q, or confusing carriers with affected individuals.
Memory tip
carriers = 2pq, affected = q^2 -- for rare alleles carriers always dominate.
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