Question

The ability to taste the bitter compound phenylthiocarbamide (PTC) is an autosomal dominant trait. The inability to taste PTC is a recessive condition. In a sample of 500 people, 400 have the ability to taste PTC and 100 do not. Calculate the frequency of: a) recessive allele, b) dominant allele, c) each genotype

Answer 1

Answer:

a) 0.4472 or 44.72%

b) 0.5528 or 55.28%

c) Homozygous recessive genotype 'tt': 0.2 or 20%

Homozygous dominant genotype 'TT': 0.3056 or 30.56%

Heterozygous genotype 'tT' or 'Tt': 0.4944 or 49.44%

Explanation:

The Hardy-Weinberg equilibrium states that

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

Where p is the frequency of the dominant allele and q is the frequency of the recessive allele.

Let 'T' be the dominant allele and 't' the recessive allele

a) if 100 people do not taste PTC, they possess the homozygous recessive genotype tt. Thus, the frequency of the recessive allele is given by:

$q^2= \frac{100}{500} \\q= 0.4472$

b) Consequently, the frequency of the dominant allele is:

$p = 1- q\\p = 1 - 0.4472\\p=0.5528$

c) The frequency of each genotype is:

Homozygous recessive genotype 'tt':

$q^2= \frac{100}{500} \\q^2= 0.2$

Homozygous dominant genotype 'TT':

$p^2 = 0.5528^2\\p^2 = 0.3056$

Heterozygous genotype 'tT' or 'Tt':

$2pq=2*0.5528*.4472\\2pq = 0.4944$