Question

In a certain population which is in Hardy Weinberg equilibrium, 36 % of individuals are homozygous for curly hair (CC). The gene for curly hair is dominant over the gene for straight hair, c. What percentage of the population has curly hair?

• A. 16%
• B. 32%
• C. 64%
• D. 84%

Answer 1

The correct option is D 84%

The Hardy-Weinberg equation is an algebraic equation which is an expression of the Hardy-Weinberg law. The frequencies of alleles and the genotypic ratios in a population can be calculated with the help of this equation.
According to Hardy Weinberg equation, if there are two alleles for a particular gene where A represents the dominant allele and a represents the recessive allele, then the frequency of A is p and a is q.
Combined frequencies of all alleles for a gene in a population is equal 1.
Therefore, p+q=1.
The frequency of homozygous dominant individuals (AA) in the population would be equal to pxp or $p^2$
The frequency of homozygous recessive individuals (aa) in the population would be equal to qxq or $q^2$
Since there are two ways of forming the heterozygote Aa, (allele A from the father and a from mother and vice versa) the frequency of heterozygous dominant individuals (Aa) in the population would be 2pq.
The sum of all three genotypic frequencies is $p^2+2pq+q^2=1$ which is a binomial expansion of ${(p+q)}^2$

p = frequency of the dominant allele (A)
q = frequency of the recessive allele (a)
$p^2$ = frequency of homozygous dominant individuals (AA)
$q^2$ = frequency of homozygous recessive individuals (aa)
2pq = frequency of heterozygous dominant individuals (Aa)


As per the question given, let us denote p as the frequency of the dominant allele (C) and q as the frequency of the recessive allele (c).
The frequency of CC individuals is given as 36%, which means that $p^2$ = 0.36 and p = 0.6.
Since p + q = 1, q = 1–0.6 = 0.4.
The question asks for the percentage of the population with curly hair; this includes both homozygous (CC) and heterozygous individuals (Cc).
The genotype frequencies can be found using the equation $p^2+2pq+q^2$
CC =$p^2$ = ${(0.6)}^2$ = 0.36 = 36% homozygous curly hair (CC)
Cc = 2pq = 2(0.6)(0.4) = 0.48 = 48% heterozygous curly hair (Cc)
cc = $q^2$ = $0.4^2$ = 0.16 = 16% straight hair (cc)
Therefore, the percentage of the population with curly hair is 36% +
48% = 84%.