Question

In a population of mice under Hardy-Weinberg conditions, black coat color is completely dominant to brown coat color. Only 4% of the population have brown coats. What proportion of the population is heterozygous?

Answer 1

Hardy-Weinberg Equation states that the allele and genotype frequency in a population remain constant that is 1 when there is no evolutionary influence present

we have Hardy-Weinberg Equation,that is P2 + 2pq  + q2 =1

P2 =% homozygous dominant individual

P= frequency of dominant allele

q2 = % homozygous recessive individual

q= frequency of recessive allele

2pq= % heterozygous individual

In the given question we can see brown is a recessive trait so % homozygous recessive individual is

q2 = 4% i.e 0.04

therefore the frequency of a recessive allele is q= 0.04^1/2(square root of 0.04)=0.2

so we know p + q= 1 i.e

  p+0.2=1

p= 1-0.2

p= 0.8

2pq= % heterozygous individual

2pq= 2[0.8X0.2]

=2[0.16]

=[0.32]

=32%

the heterozygous populayion is 32%