Chapter 26, Problem 1NST

The ability to taste the compound phenylthiocarbamide (PTC) is controlled by a dominant allele T. Individuals homozygous for the recessive allele t are unable to taste PTC. In a genetics class of 125 students, 88 can taste PTC and 37 cannot. Calculate the frequency of the T and t alleles in this population and the frequency of the genotypes.

Summary Introduction

To determine: The frequency of the T and t alleles and frequency of the genotypes in the given problem.

Introduction: The Hardy-Weinberg law is a mathematical model developed by the British mathematician, Godfrey H. Hardy and the German physician, Wilhelm Weinberg. This law explains the allele and genotype frequencies in a population; that is, indefinably large, randomly mating, and not subjected to any evolutionary forces like mutation, migration, or selection.

Explanation of Solution

In the given question, the ability to taste the compound phenylthiocarbamide (PTC) is regulated by a dominant allele T. An individual having homozygous recessive allele t cannot taste PTC. In a genetics class, there are 125 students. Out of them, 88 can taste PTC, and 37 cannot.

According to the Hardy-Weinberg equation:

$\begin{array}{l}p+q=1\\ p^2+q^2+2pq=1\end{array}$

Where, p and q represent the frequencies of the alleles T and t, respectively.

The students who can taste the PTC will have genotypes either Tt or TT, and those who cannot taste PTC will have genotype tt.

It is given that,

$\begin{array}{c}{q}^2=\frac{37}{125}\\ =0.54\end{array}$

Therefore, the frequency of t allele, q $=0.54$

$\begin{array}{c}p=1-q\\ =1-0.54\\ =0.456\end{array}$

Therefore, the frequency of T allele, p $=0.456$

The frequencies of the genotypes are calculated by using the formula $p^2+q^2+2pq=1$ as follows:

Frequency of TT

$\begin{array}{l}=p^2\\ ={\left(0.456\right)}^2\\ =0.208\end{array}$

Frequency of tt

$\begin{array}{l}=q^2\\ ={\left(0.54\right)}^2\\ =0.296\end{array}$

Frequency of Tt

$\begin{array}{l}=2pq\\ =2\left(0.456\right)\left(0.544\right)\\ =0.496\end{array}$

Conclusion

Thus, the frequency of the T and t alleles are 0.456 and 0.54, respectively. The frequency of genotypes TT, tt, and Tt are 0.208, 0.0.296, and 0.496, respectively.