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The figure below shows a family with a double cousin mating. For clarity, ind...

Mar 15, 2024

In a certain population, the frequency of blood group 0 is 64%. The frequency of blood group B is 8.25%. What is the frequency of allele A in the population? (Hint: The law of Hardy Weinberg can be applied to loci with multiple – i.e. more than two – alleles. Calculations are equivalent to the calculations applied to loci with two alleles: frequencies of all homozygous genotypes are calculated by squaring the frequency of the relevant allele; frequencies of all heterozygous genotypes are calculated as 2 x i x j, where i and j are the frequencies of the ith and jth allele, respectively.) Give your answer as a number to 2 decimal places eg 0.50 (4 Marks)

Answer

0.28

Solution

Calculate the frequency of allele O (i) using the given percentage for blood group O :

The frequency of blood group O is given as 64%, which is equivalent to 0.64. Since blood group O is homozygous for the O allele (ii), the frequency of allele O is the square root of the frequency of the blood group O genotype: $$ i = \sqrt{0.64} = 0.8 $$

Calculate the frequency of allele B (j) using the given percentage for blood group B :

The frequency of blood group B is given as 8.25%, which is equivalent to 0.0825. Since blood group B can be homozygous for the B allele (BB), the frequency of allele B is the square root of the frequency of the blood group B genotype: $$ j = \sqrt{0.0825} = 0.287 $$ (rounded to three decimal places for intermediate calculation)

Use the Hardy-Weinberg principle to calculate the frequency of allele A (p) :

According to the Hardy-Weinberg principle, the sum of the frequencies of all alleles at a locus must equal 1. Therefore, the frequency of allele A (p) can be calculated as: $$ p = 1 - i - j $$ Substituting the values of i and j: $$ p = 1 - 0.8 - 0.287 = 0.28 $$ (rounded to two decimal places as per the question's instructions)

Key Concept

Hardy-Weinberg Equilibrium

Explanation

The Hardy-Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. In this case, it is used to calculate the frequency of an allele in a population with multiple alleles.