Problem III Individuals that express the disease sickle cell

Problem III. Individuals that express the disease sickle cell anemia are homozygous for a recessive allele for a hemoglobin gene. The frequency of individuals expressing the disease in a particular population is 0.0025. If we assume that the population is at HWE, what is the frequency of the recessive sickle cell allele? If the population is at HWE, what is the expected frequency of carriers of the disease (heterozygotes)? If mating is random, what is the probability that two carriers will mate?

Solution

Since the population in at HWE, it will follow the hardy-winberg equilibrium,

So, according to the HWE,

p² + q² +2pq = 1

where, p² is frequency of homozygous dominent

q² is frequency of homozygous recessive and

2pq is frequency of heterozygous (carriers)

So, according to the question,

q² = 0.0025

q = 0.05

so, p = 1.00 - 0.05

p = 0.95

2pq = 2*0.05*0.95

= 0.095

So, the frequency of recessive sickle cell allele is 0.05

frequency of carriers is 0.095.