Question

With the help of an algebraic equation, how did Hardy-Weinberg explain that in a given population the frequency of occurrence of alleles of a gene is supposed to remain the same through generations?

Answer 1

Hardy-Weinberg principle states that the frequency of occurrence of alleles of a gene in a population remains constant through generations unless disturbances such as mutations, non-random mating etc. are introduced.

This principle can be understood with the help of the mathematical expression known as Hardy-Weinberg equation. Let us assume that a gene has two alleles in a population, A and a. If p is the frequency of occurrence of dominant allele A, and q is the frequency of occurrence of dominant allele a, the genotype frequency in the offsprings are represented as:

`(p + q)^2 =p^2 + 2pq + q^2 = 1`

where, the frequency of genotypes, AA is p², that of aa is q² and that of Aa is 2pq

Hence, the sum total of all ​allelic frequencies remains constant, i.e. 1

Answer 2

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 (total genes and their alleles in a population) remains a constant. this is called genetic equilibrium. Sum total of all the allelic frequencies is 1. Individual frequencies, for example, can be named p, q, etc. 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. This is simply stated in another way, i.e., the probability that an allele A with a frequency of p appears on both the chromosomes of a diploid individual is simply the product of the probabilities.

i.e `p^2`. Similarly of aa is q², of Aa 2pq. Hence, `p^2 + 2pq + q^2 = 1`. This is a binomial expansion of (p + q)². When frequency measured, differs from expected values, the difference (direction) indicates the extent of evolutionary change. Disturbance in genetic equilibrium, or Hardy-Weinberg equilibrium, i.e., change of frequency of alleles in a population would then be interpreted as resulting in evolution.