Question

A randomly mating population of 100 dairy cattle contains a recessive allele that causes dwarfism. If there are 16 dwarf calves in the population, what is the frequency of heterozygous carriers of the allele in the entire herd? (Assume that the population is in HW equilibrium).

Answer 1

Answer:

Frequency of heterozygous carriers of the allele in the entire herd is $0.48$ i.e $48$ out of $100$

Explanation:

It is given that a recessive allele pair produces a dwarf cow.

Let this recessive allele be represented by "t" and the dominant allele for tall height trait in cows be "T".

Given

Total population of randomly mating cows $= 100$

Total number of dwarf calves in the population $= 16$

Frequency of genotype "tt" producing dwarf calves is represented as $q^2$ in HW equilibrium equation.

Here

$q^ 2 = \frac{16}{100} \\q^2 = 0.16$

Frequency of recessive allele is equal to "q"

$q = \sqrt{0.16} \\q = 0.4$

As per first equilibrium equation of HW,

$p + q = 1\\p + 0.4 = 1\\p = 1-0.4\\p = 0.6$

Frequency of genotype "TT" producing dwarf calves is represented as $p^2$ in HW equilibrium equation.

$p^2 = 0.6^2 \\p^2 = 0.36$

As per HW's second equilibrium equation

$p^2 + q^2 + 2pq = 1$

Substituting the given values in above equation, we get -

$0.36 + 0.16 + 2pq = 1\\2pq = 1-0.16-0.36\\2pq = 0.48$

Frequency of heterozygous carriers of the allele in the entire herd is $0.48$ i.e $48$ out of $100$