Read the given passage and answer the questions that follow :-
In a given population one can find out the frequency of occurrence of alleles of a gene or a locus. This frequency is supposed to remain fixed and even remain the same through generations. Hardy-Weinberg principle stated it using algebraic equations. This principle says that allele frequencies in a population are stable and is constant from generation to generation. The gene pool remains a constant. This is called genetic equilibrium.
What is the expression for the Hardy-Weinberg equation?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → p2 + q2 + 2pq = 1
The equation is not written in the passage, which only says the principle was stated using algebraic equations. In a diploid, p and q are the frequencies of allele A and allele a. The frequency of AA individuals is p2, of aa is q2 and of Aa is 2pq. Together these make up the whole population, so they add up to 1; this is the binomial expansion of (p + q)2.
Option (1) p2 + q2 − 2pq = 1 — Incorrect. The heterozygote term 2pq is added, not subtracted, because heterozygotes are a part of the population.
Option (2) p2 + q2 + 2pq = 1 — Correct. p2 + 2pq + q2 = 1, the sum of the three genotype frequencies.
Option (3) p2 + q2 − 2pq = 0 — Incorrect. The sign of 2pq is wrong, and the total of all frequencies is 1, not 0.
Option (4) p2 + q2 + 2pq = 0 — Incorrect. The terms are right, but genotype frequencies of a population add up to 1, not 0.
NCERT Extract:
Hardy-Weinberg Principle – “… In a diploid, p and q represent the frequency of allele A and allele a. The frequency of AA individuals in a population is simply p2. … Similarly of aa is q2, of Aa 2pq. Hence, p2+2pq+q2=1. This is a binomial expansion of (p+q)2.”