Black coat color in horses is conferred by the presence of a

Black coat color in horses is conferred by the presence of a dominant B allele. Chestnut horses are genotype bb. A population of wild horses consists of 224 black horses and 22 chestnut horses. Assume that this population is at Hardy-Weinberg equilibrium for this locus.

(a) Please round all answers correctly to 4 decimal digits.

What is the frequency of the B allele?

__________________

(b) Please round all answers correctly to 4 decimal digits.

What is the frequency of the b allele?

_______________________

(c) Please round all answers correctly to 4 decimal digits.

How many horses in the population are expected to be heterozygous for this locus?

_______________________

Solution

According to Hardy-Weinberg equation, p² + 2pq + q² = 1 and p+q = 1

Here, P is the frequency of the B allele and q is the frequency of the b allele. p² is the frequency of the homozygous genotype BB, q² is the frequency of the homozygous genotype bb, and 2pq is the frequency of the heterozygous genotype Bb.

In the question, it is given that a population of wild horses consists of 224 black horses and 22 chestnut horses and Chestnut horses are genotype bb.

Total number of horses = 224 +22 = 246

Therefore frequency bb genotype ( q²) = 22/246 = 0.0894

q = square root of 0.0894 = 0.2989.

Therefore, q (frequency of the b allele) = 0.2989

since p+q = 1,

p = 1 - 0.2989 = 0.7011

p (frequency of the B allele) = 0.7011

Frequency of the heterozygous genotype (Bb) = 2pq

= 2 * 0.2989 * 0.7011

= 0.4191

Therefore, number of heterozygous horses in the population = 0.4191 * 246

= 103

Answers

a) What is the frequency of the B allele?

0.7011

b) What is the frequency of the b allele?

0.2989

c) How many horses in the population are expected to be heterozygous for this locus?

103