Question

A large population of laboratory rats was allowed to breed randomly for a number of generations. In this population, a dominant allele at the A locus codes for agouti fur (A), and a recessive allele codes for black fur (a). At the beginning of the breeding cycles, 49% of the rats had black fur. At the end of the breeding cycles, this percentage was the same. The rest of the animals had agouti fur with heterozygotes indistinguishable from homozygous dominants.What percentage of this population is probably heterozygous for the fur color trait assuming the rats are following Hardy-Weinberg population genetics?

A. 7%
B. 30%
C. 42%
D. 49%
E. 70%

Answer 1

Frequency of heterozygous animals with agouti fur is
`42` %

Step-by-step explanation:

As per the Hardy Weinberg's equation -

`q^2` represents the frequency of population with phenotype expressed by homozygous recessive genotype

`p^ 2` represents the frequency of population with phenotype expressed by homozygous dominant genotype

and
`2pq` represents the frequency of population with phenotype expressed by homozygous recessive genotype

Given -

`q^2 = 0.49\\q = 0.7`

As per first principle of Hardy Weinberg's equilibrium

`p + q = 1`

Substituting the value of q in above equation, we get -

`p = 1- 0.7 \\p = 0.3`

As per second principle of Hardy Weinberg's equilibrium

`p^2 + q^2 + 2pq = 1\\`

Substituting the given values in above equation, we get -

`0.09 + 0.49 + 2pq = 1\\2pq = 1 - 0.58 \\2pq = 0.42`

Frequency of heterozygous animals with agouti fur is
`42` %