Question

1 - A population that is at equilibrium has two alleles, A and a. The frequency of the recessive allele a is 0.3. What is the frequency of individuals that are homozygous recessive?

2 - A population that is at equilibrium has two alleles, A and a. The frequency of the dominant allele A is 0.3. What is the frequency of individuals that are homozygous recessive?

Answer 1

A population is in equilibrium when no evolutionary forces are acting on it follows Hardy Weinberg Equilibrium principle.

Let us consider two alleles for a specific gene and denote them as A (dominant allele) and a (recessive allele).

Frequency of the dominant allele, A = p

Frequency of the recessive allele, a = q

Then, by principle:

p+q = 1

and,

p2 + 2pq + q2 = 1

where, p2 is the frequency for homozygous AA

2pq is the frequency for heterozygous Aa

q2 is the frequency for homozygous aa

(1)  A population that is at equilibrium has two alleles, A and a. The frequency of the recessive allele a is 0.3.

q = 0.3

q2 = (0.3)2 = 0.09

Therefore, the frequency of individuals that are homozygous recessive (aa) = 0.09

(2) A population that is at equilibrium has two alleles, A and a. The frequency of the dominant allele A is 0.3.

p = 0.3

p + q = 1

q = 1 - p = 1 - 0.3 = 0.7

q2 = (0.7)2 = 0.49

Therefore, the frequency of individuals that are homozygous recessive (aa) = 0.49