3. The persistence of the sickle-cell anemia alle CHbs) at the Hemoglobin locus

Question

3. The persistence of the sickle-cell anemia alle CHbs) at the Hemoglobin locus is explained by the fact that heterozygotes (Hb/Hbk) are protected against malaria. However, this leads to sickle-cell anemia in Hb Hb homozygotes. In Equatorial Guinea, the frequency of the Hb allele has historically been 0.3. Recent efforts in Equatorial Guinea have drastically reduced the population of the malaria-carrying mosquitos. Based relative fitness values: on this success, a resear cher proposes that the different genotypes have the following Relative fitness values AFTER mosquito control: WHbS/HbS0 WHbSHbA = 1.0 WHbAHbA = 0.85 (a) What is the expected equilibrium frequency for the HbS allele after mosquito control reduced the mosquito population size? (6 points; show you work clearly for full credit) 3 of 8 (A) (b) Given the historical frequency of the HbS allele in the Equatorial Guinea population of 0.3, and the anticipated relative fitness values after mosquito control, do you expect the Hbs allele to increase irn frequency, decrease in frequency or remain the same? Briefly explain you answer. (4 points; 1-2 sentences) e) If malaria was completely removed from the population, what would be the frequency of Hbs that maximizes mean population fitness? Briefly explain your reasoning. (4 points. Note: you should be able to answer this question in 1-2 sentences without any calculations)

Explanation / Answer

Given,

Frequency of HbS = p = 0.3
Frequency of HbA = q = 1 - p = 0.7
Fitness of HbA/HbA = W(AA) = 0.85
Fitness of HbA/HbS = W(AS) = 1.0
Fitness of HbS/HbS = W(SS) = 0.0

a)
at equilibrium let the expected frequency of the HbS allele be p'
p' = p2*W(SS) + 0.5*2*p*q*W(AS)
p' = 0.3*0.3*0 + 0.5*2*0.3*0.7*1
p' = 0 + 0.21 = 0.21

b)
p' = 0.21
i.e. at equilibrium the allele frequency of HbS is reduced from 0.3 originally to 0.21
Since relative fitness of HbS/HbS W(SS) = 0 and p' = 0.21 (less than p) we can say that frequency of HbS allele will decrease in subsequent generations after equilibrium.

c)
If the malaria is removed from the population then there is no need for the individuals to carry a HbS allele for protection against malaria. Hence there will be no fitness advantage of having HbS (rather it will be a disadvantage since it can cause sickle cell anemia to your progeny if you and your partner are both HbS/HbA genotype). Therefore, frequency of HbS should be zero for maximum mean population fitness.

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