Question

In a random mating population of $28800$ individuals, the percentage of dominant homozygous individuals is $p$. Find out the percentage of heterozygous individuals.
A. $21\%$
B. $42\%$
C. $32\%$
D. $9\%$

Answer 1

-Genotypes are usually represented using capital or lowercase letters where the capital letter represents the dominant allele and the lowercase letter represents the recessive allele.
-In homozygous genotype, both alleles are the same and a dominant homozygous genotype is the one in which both the alleles are same and dominant.

Complete step by step answer:
-The Hardy Weinberg equation can be used to calculate the genetic variations in a population.
-This law states that the sum of all genotype frequencies can be represented as a binomial expansion. -It is the square of the sum of $p$ and $q$. Here “$p$” and “$q$” are the frequencies of the dominant alleles and the recessive alleles respectively.
-Hardy Weinberg equation is as following-
${p^2} + {q^2} + 2pq = {(p + q)^2} = 1$
where “$0.3$" represents the frequency of heterozygotes in the population.
-Based on the data given, $2pq$ is $49\%$ or $0.49$, thus the frequency of the dominant allele ($p$) is $0.7$.
-Since $p{\text{ }} + {\text{ }}q{\text{ }} = {\text{ }}1$, the frequency of the recessive allele “$q$” is $0.3$.
-The frequency of heterozygotes in the population will be calculated by multiplying the frequencies of dominant and recessive alleles with $2$ i.e., “$2pq$”.
-After multiplication, the value obtained here is $0.42$.
Therefore, the percentage of heterozygotes present in the population will be $42\%$
The correct answer is option (B). The percentage of heterozygous individuals is $42\%$

Note: In population genetics, the Hardy Weinberg law, also known as Hardy Weinberg equilibrium, suggests that the allele and genotype frequencies in a population will always remain constant from generation to generation in the absence of factors responsible for the evolution.
Hardy Weinberg equilibrium is an ideal state which never occurs in nature because there is always a chance that any rule will be violated.