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

		FEMALES	FEMALES
		A (p)	a (q)
MALES	A (p)	AA (p${}^2$)	Aa (pq)
MALES	a (q)	Aa (qp)	aa (q${}^2$)

Table 1: Punnett square for Hardy Weinberg principle

The Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. These influences include mate choice, mutation, selection, genetic drift, gene flow and meiotic drive.

Consider a population of monoecious diploids, where each organism produces male and female gametes at equal frequency and has two alleles at each gene locus. Organisms reproduce by random union of gametes (the “gene pool” population model). A locus in this population has two alleles, A and a, that occur with initial frequencies f0(A) = p and f0(a) = q, respectively. The allele frequencies at each generation are obtained by pooling together the alleles from each genotype of the same generation according to the expected contribution from the homozygote and heterozygote genotypes, which are 1 and 1/2, respectively.

The Punnett square is used to calculate the different ways to form genotypes for the next generation. (See table 1) The sum of square of p${}^2$ + 2pq + q${}^2$ = 1. The binomial expansion of the Punnett square also gives the same relationships.

Hence, using the above equation Hardy-Weinberg explained that in a given population the frequency of occurrence of alleles of a gene is supposed to remain the same through generations.