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 113 black horses and 42 chestnut horses. Assume that this population is at Hardy-Weinberg equilibrium for this locus.

Please round all answers correctly to 4 decimal digits.

1. What is the frequency of the B allele?

2. What is the frequency of the b allele?

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

Solution

Hardy and Weinberg described all the possible genotypes for a gene with two alleles. The binomial expansion representing this is, p2 + 2pq + q2 = 1.0

Where,       

p2 = proportion of homozygous dominant individuals

q2 = proportion of homozygous recessive individuals

2pq = proportion of heterozygotes.

Given that the frequency of chestnut horses (homozygous recessive, q2) is = 42/ 155 = 0.2709, q = 0.2709

Since, P+q = 1, or p = 1-0.2709 = 0.7291

The frequency of dominant allele, B (or P) = 0.7291.

The frequency of recessive allele, b (or q) = 0.2709

The number of horses in the population that are expected to be heterozygous for this locus is 2pq = 2* 0.7291*0.2709 = 0.3950

= 0.48*128 = 61.44 or approximately 61.