p^{2} + 2pq + q^{2} = 1. Explain this algebraic equation on the basis of Hardy Weinberg's principle.

#### Solution

The Hardy-Weinberg equation is a mathematical equation that can be used to calculate the genetic variation of a population at equilibrium.

The Hardy-Weinberg equation is expressed as:

p^{2} + 2pq + q^{2} = 1

where p is the frequency of the "A" allele and q is the frequency of the "a" allele in the population. In the equation, p^{2} represents the frequency of the homozygous genotype AA, q^{2} represents the frequency of the homozygous genotype aa, and 2pq represents the frequency of the heterozygous genotype Aa. In addition, the sum of the allele frequencies for all the alleles at the locus must be 1, so (p + q)^{2} = 1. If the p and q allele frequencies are known, then the frequencies of the three genotypes may be calculated using the Hardy-Weinberg equation. In population genetics studies, the Hardy-Weinberg equation can be used to measure whether the observed genotype frequencies in a population differ from the frequencies predicted by the equation. If there is any difference in the frequencies, it indicates the extent of evolutionary change.