- Sampling of 200 persons for their ABO blood group was done from an urban area. The types of blood group observed in the given population are as follows:
A = 60, B = 32, AB = 10 and O = 98
Which of the following gives the correct frequency of blood group determining alleles lA, lB and lO in the given population?
(1) lA = 0.19, lB = 0.11, lO = 0.7
(2) lA = 0.27, lB = 0.63, lO = 0.09
(3) lA = 0.16, lB = 0.14, lO = 0.7
(4) lA = 0.38, lB = 0.22, lO = 0.7How to Calculate ABO Blood Group Allele Frequencies from Population Data
The ABO blood group system in humans is determined by three alleles: IA, IB, and IO. These alleles combine to form four phenotypes (A, B, AB, and O), and their frequencies in a population can be estimated using Hardy-Weinberg equilibrium principles. Here’s how to calculate the allele frequencies from observed blood group counts.
Step 1: Record the Observed Data
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Total sampled individuals: 200
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Blood group A: 60
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Blood group B: 32
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Blood group AB: 10
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Blood group O: 98
Step 2: Understand the Genotype-Phenotype Relationship
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A: IAIA or IAIO
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B: IBIB or IBIO
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AB: IAIB
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O: IOIO
Step 3: Calculate Phenotype Frequencies
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Frequency of A = 60 / 200 = 0.30
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Frequency of B = 32 / 200 = 0.16
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Frequency of AB = 10 / 200 = 0.05
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Frequency of O = 98 / 200 = 0.49
Step 4: Calculate the Frequency of IO (r)
The frequency of the IO allele (r) can be estimated as the square root of the frequency of blood group O:
r=0.49=0.7
Step 5: Calculate the Frequencies of IA (p) and IB (q)
Using the formulas for ABO allele frequencies under Hardy-Weinberg equilibrium:
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p=1−B+O
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q=1−A+O
But a more direct method, given the relationships and the fact that the sum of all allele frequencies must be 1:
p+q+r=1
Since r = 0.7,
p+q=1−0.7=0.3
Now, the frequency of AB (IAIB) is 2pq. Since AB = 0.05,
2pq=0.05 ⟹ pq=0.025
Also, from the frequency of A (which is p^2 + 2pr) and B (which is q^2 + 2qr), but with r much larger than p or q, p and q will be relatively small. Let’s check the options for the closest match.
Step 6: Match with the Provided Options
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(1) IA = 0.19, IB = 0.11, IO = 0.7
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(2) IA = 0.27, IB = 0.63, IO = 0.09
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(3) IA = 0.16, IB = 0.14, IO = 0.7
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(4) IA = 0.38, IB = 0.22, IO = 0.7
Given r = 0.7 and p + q = 0.3, only options (1) and (3) fit. To match pq = 0.025 (from AB), try p = 0.16 and q = 0.14:
p×q=0.16×0.14=0.0224
This is very close to 0.025, and with rounding, matches the observed AB frequency.
Step 7: Final Answer
The correct frequencies of the blood group determining alleles are:
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IA = 0.16
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IB = 0.14
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IO = 0.7
Correct answer: (3) IA = 0.16, IB = 0.14, IO = 0.7
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