Question

Question:

The phenylketonuria occurs in 1 of 10,000 individuals in a population. It is
caused by an autosomal recessive allele. Calculate the frequency of heterozygotes
in the population

Answer 1

Phenylketonuria is caused by mutations in the gene coding for the enzyme Phenylalanine Hydroxylase, rendering it inefficient, generally phenylaline hydroxylase reduces phenylaline, but since the former is unable to function, levels of phenylaline increase in human body, leading to skin depigmentation, stunted growth and rapid hair loss.

Since, phenylketonuria is an autosomal recessive disorder, and here it occurs in 1 of 10,000 individuals.

$\sf {q}^{2} = \dfrac{1}{10000} \\ \\ \longrightarrow \sf \: q = \sqrt{0.0001} \\ \\ \longrightarrow \sf \: q =0.01$

According to Hardy Weinberg Equilibrium,

$\sf \: ( {p + q)}^{2} = 1 - - - - - - (1)$

where p is the frequency of occurrence of the dominant gene while q is the frequency gene.

Now,

$\sf \: p + q = 1 \\ \\ \longrightarrow \sf \: p = 1 - q = 0.99$

Here, 2pq represents the frequency of heterozygous dominant individuals.

$\longrightarrow \sf \: 2pq = 2 \times 0.01 \times 0.99 \\ \\ \longrightarrow \sf \: 2pq = 0.0198$

In other words, there are 198 heterozygous individuals in a population of 10,000.