In a different population, suppose that 38.40% of people are blood type A, and 4
ID: 68383 • Letter: I
Question
In a different population, suppose that 38.40% of people are blood type A, and 46.24% are blood type O.
Assuming this population is in Hardy-Weinberg equilibrium, what percentage of the population is blood type B? What percentage is blood type AB? Enter your answers to two decimal places.
(Hint:If a gene has three alleles, then six genotypes are predicted by applying the Hardy-Weinberg equilibrium equation. In the case of ABO blood groups, four phenotypes are possible: A, B, AB, and O.To determine the frequency of each phenotype, let p designate the frequency of allele IA, let q designate the frequency of allele IB, and let r designate the frequency of allele i.
The A phenotype is composed of genotypes IAIAand IAi. Thus, the frequency of individuals with phenotype A will be p 2 + 2pr.
The B phenotype is composed of genotypes IBIBand IBi. Thus, the frequency of individuals with phenotype B will be q 2 + 2qr.
The AB phenotype is determined by one genotype: IAIB. Thus, the frequency of individuals with phenotype AB will be 2pq.
The O phenotype is determined by one genotype: ii. Thus, the frequency of individuals with phenotype O will be r 2.)
Explanation / Answer
From the question:
Let us consider
p be the frequency of A
q be the frequency of B and,
r be the frequency of O.
So we basically have a three allele system which could be denoted as :
p + q + r = 1
Therefore Hardy-Weinberg equation in this case would be:
(p + q + r)2 = 1
p2 +q2 + r2 + 2pq +2qr + 2pr = 1
Frequency of A = p2 + 2pr
Frequency of B = q2 + 2qr
Frequency of O = r2
Frequency of AB = 2pq
From question, we know that people with O blood type are 46.24
That is r2 = .4624 therefore r = 0.68
People having blood type A = 38.40
Therefore p2 + 2pr = .3840
p2 + 2p* (0.68) = .3840 (solving this quadratic equation we get,)
p = .24
So, p + q + r = 1
.24 + q + .68 = 1
q = 0.08
So people with blood group B = q2 + 2qr = (0.08)2 + 2*(0.08)*(0.68) = .1152
So % of population with blood group B = 11.52%
Similarly,
So people with blood group AB = 2pq = 2*(.24)*(0.08) = .0324
So % of population with blood group AB = 3.24%