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Consider a gene with a dominant and recessive allele in a population conforming to the H-W...

Consider a gene with a dominant and recessive allele in a population conforming to the H-W conditions. Assuming the frequency of the recessive allele in the entire population is q, show that the frequency of the recessive allele in individuals with the dominant phenotype i q/(1 +q).

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Answer #1

Genetic variation in a population can be estimated via Hardy-Weinberg equation.

p2 refers to square of p, q2 represents here square of q.

The equation is p2 + 2pq + q2 = 1 , where p2 is frequency of dominant allele, 2pq is frequency of heterozygous genotype, and q2 is the frequency of the recessive allele.

In the problem , q is the frequency of the recessive allele in the entire population, thus q2 in the equation can be replaced by q, and "2pq" can be listed as 2pq0.5 (square root of q).

p2 + 2pq0.5 + q= 1

also p+q =1 (sum of all alleles at the locus)

So p + q0.5 =1

we can thus equate p2 + 2pq0.5 + q = p + q0.5

Solving for 2pq0.5, we can get that the recessive allele frequency in dominant phenotypes is q/(1+q)
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