Question

In a large herd of 5468 sheep, 76 animals have yellow fat, and the rest of the members of the herd have white fat. Yellow fat is inherited as a recessive trait. This herd is assumed to be in Hardy-Weinberg equilibrium.

A. What are the frequencies of the white and yellow fat alleles in this population?

B. Approximately how many sheep with white fat are heterozygous carriers of the yellow allele?

Answer 1

Let R and r be the white fat allele and yellow fat allele respectively.

Total Population is 5468.

Hardy Weinberg Equilibrium :

$\sf \: {p}^{2} + 2pq + {q}^{2} = 1$

Here,

• p² is the frequency of dominant allele
• 2pq is the frequency of heterozygous dominant allele
• q² is the frequency of recessive allele.

Allelic Frequency is given as :

$\sf \: Allele \: \% = \dfrac{No.of phenotypes \: in \: the \: population}{Total \: Population}$

Allelic Frequency of rr :

$\sf \: q {}^{2} = \dfrac{76}{5468} \\ \\ \implies \sf \: q = \sqrt{0.0014} \\ \\ \implies \sf \: q = 0.12 \: \%$

Allelic Frequency of RR :

$\sf \: p + q = 1 \\ \\ \implies \sf \: p = 1 - 0.12 \\ \\ \implies \sf \: p = 0.88 \: \%$

Frequency of Heterozygous Phenotype :

$\sf \: 2pq = 2 \times 0.12 \times 0.88 = 0.2112 \sim \: 0.21$

No.of carriers in the population :

$\sf \: Allelic \: Frequency * Total \: Population \\ \\ \longrightarrow \sf \: 0.21 \times 5468 \\ \\ \longrightarrow \sf 1148$

1148 sheep are heterozygous carriers of the yellow allele.