Suppose 64% of a remote mountain village can taste phenylthiocarbamide (PTC) and must, therefore, have at least one copy of the dominant PTC taster allele. If this population conforms to Hardy-Weinberg expectations for this gene, what percentage of the population must be heterozygous for this trait?

The correct answer is 48 percent.

Explanation:

Let the dominant allele be signified by letter T and the recessive allele be signified by letter t.

On the basis of Hardy-Weinberg equation, the frequency of T is denoted by p and the frequency of t by q. Therefore, p+q = 1.

p^2 signifies the frequency of TT, 2pq the frequency of Tt and q^2 the frequency of tt, which is denoted by the equation:

p^2 + 2pq + q^2 = 1

Based on the given information, 64 percent of the population are tasters, thus, 36 percent would be the non-tasters, and would exhibit the homozygous recessive genotype, that is, tt.

Thus, the frequency of tt will be 0.36, that is, q^2 will be 0.36 or q = 0.6.

p+q = 1, p = 1-q and so p = 1-0.6, p = 0.4

The frequency of Tt is 2pq = 2*0.6*0.4 = 0.48.

Hence, 48 percent of the population would be the heterozygous for this trait.

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