Question

The following are ABO phenotypes from a population sample of one hundred persons. The number of individuals representing the four phenotypic classes are: type A, twenty; type B, forty-eight; type AB, sixteen; type O, sixteen. What are the three frequencies of the three different alleles (I^A, I^B and i)? What do you have to assume about this population to determine the allele frequencies from this data?

Answer 1

To determine the allele frequencies from this data, it will be needed to assume that the population follows Hardy - Weinberg principle.

Genotype of blood group A can be iAiA or iAi

Genotype of blood group B can be iBiB or iBi

Genotype of blood group AB is iAiB

Genotype of blood group O is ii.

According to Hardy-Weinberg principle, the genotypic frequencies with 3 alleles will be -

p2+ 2pq + q2 + 2pr + r2 + 2pr = 1

p- allele frequency of A, q - allele frequency of B, 2pq- allele frequency of AB, r2- allele frequency of O

N ( p² + 2pr ) = the number of type A people in the population,

N ( q² + 2qr ) = the number of type B people in the population,

N ( 2pq ) = the number of type AB people in the population, and

N ( r² ) = the number of type O people in the population.

N ( r² ) = 16 = 100 X r²

r² = 16/100 = 0.16

r = 0.4

p² + 2pr = 20/ 200 = 0.1

p² + 2p (0.4) = 0.1

p² + 0.8 p - 0.1 = 0

According to the quadratic equation solving -

p = 0.16

p + q + r = 1

0.16 + 0.4 + q = 1

q = 1- 0.56

q = 0.44