ABO Blood Group System and Allele Frequencies

The ABO blood group system in humans is a classic example of multiple alleles and codominance. It is determined by three alleles: I^A, I^B, and I^O. The alleles I^A and I^B are codominant with respect to each other, and both are dominant over the allele I^O.

The genotypes and corresponding phenotypes (blood groups) are as follows:

• Genotype I^AI^A or I^AI^O → Blood Group A
• Genotype I^BI^B or I^BI^O → Blood Group B
• Genotype I^AI^B → Blood Group AB
• Genotype I^OI^O → Blood Group O

Population Data Analysis

We are given data from a sample of 200 persons in an urban area, showing the distribution of ABO blood groups:

Calculating Allele Frequencies

We want to find the frequencies of the alleles I^A, I^B, and I^O in this population. Let the frequency of allele I^A be p, the frequency of allele I^B be q, and the frequency of allele I^O be r. According to the Hardy-Weinberg principle, the sum of allele frequencies is 1, i.e., $p + q + r = 1$.

The frequencies of the genotypes are related to the allele frequencies as follows:

• Frequency(I^AI^A) = $p^2$
• Frequency(I^BI^B) = $q^2$
• Frequency(I^OI^O) = $r^2$
• Frequency(I^AI^B) = $2pq$
• Frequency(I^AI^O) = $2pr$
• Frequency(I^BI^O) = $2qr$

The frequencies of the phenotypes are the sum of the frequencies of the corresponding genotypes:

• Frequency(Blood Group A) = Frequency(I^AI^A) + Frequency(I^AI^O) = $p^2 + 2pr$
• Frequency(Blood Group B) = Frequency(I^BI^B) + Frequency(I^BI^O) = $q^2 + 2qr$
• Frequency(Blood Group AB) = Frequency(I^AI^B) = $2pq$
• Frequency(Blood Group O) = Frequency(I^OI^O) = $r^2$

We can estimate the allele frequencies from the observed phenotype frequencies. The easiest allele frequency to calculate is that of I^O (r), because only the genotype I^OI^O results in blood group O.

Frequency(Blood Group O) = $r^2 = 0.49$

So, the frequency of allele I^O is:

$r = \sqrt{0.49} = 0.7$

Next, we can use the cumulative frequencies of blood groups A and O, and B and O:

Frequency(Blood Group A) + Frequency(Blood Group O) = $(p^2 + 2pr) + r^2 = (p + r)^2$

Frequency(Blood Group B) + Frequency(Blood Group O) = $(q^2 + 2qr) + r^2 = (q + r)^2$

Using the observed frequencies:

$(p + r)^2 = 0.30 + 0.49 = 0.79$

$p + r = \sqrt{0.79} \approx 0.8888$

$(q + r)^2 = 0.16 + 0.49 = 0.65$

$q + r = \sqrt{0.65} \approx 0.8062$

Now we can find p and q using the value of r = 0.7:

$p = (p + r) - r \approx 0.8888 - 0.7 \approx 0.1888$

$q = (q + r) - r \approx 0.8062 - 0.7 \approx 0.1062$

Let's check if the sum of frequencies is close to 1:

$p + q + r \approx 0.1888 + 0.1062 + 0.7 = 0.995$

This sum is close to 1, with the slight difference due to rounding the square roots. The frequencies are approximately $p \approx 0.19$, $q \approx 0.11$, and $r = 0.7$.

These values correspond to the frequencies of alleles I^A, I^B, and I^O, respectively.

Frequency of I^A $\approx$ 0.19

Frequency of I^B $\approx$ 0.11

Frequency of I^O = 0.70

These calculated allele frequencies match one of the given options.