Question

4. In purebred Holstein cattle, about one calf in 100 is spotted red rather than black. The trait is autosomal, and red is recessive to black.

a. What is the frequency of the red alleles in the population?

b. What is the frequency of black homozygous cattle in the population?

c. What is the frequency of black heterozygous cattle in the population?

Answer 1

Frequency of Red spotted Calf = 1/100 = 0.01

Since this is a recessive trait, only Homozygous recessive individuals display this trait. Therefore;
Frequency of Homozygous recessive phenotype = q² = 0.01

a)

Frequency of recessive (red) allele = q = 0.1

b)

Frequency of the dominant (back) allele = p = 1 - q = 1 - 0.1 = 0.9
Frequency of the Black Homozygous cattle = p² = 0.9 * 0.9 = 0.81

c)

Frequency of the Black Heterozygous cattle = 2pq = 2 * 0.9 * 0.1 = 0.18