How does Hardy Weinberg principal explain equilibrium of allelic frequency ?

Explanation

Hardy- Weinberg equilibrium was explained independently by Hardy of U.K. and Weinberg of Germany . It is a principal stating that the allelic frequencies in a population will remain constant from generation to generation under certain conditions . They are :
1) Size of the population should be large .
2) Mating should be random (panmictic ) .
3) There should no evolutionary forces like Natural Selection or mutations or large scale migrations .
4) There should be no differential reproductive success, among the organisms of a population .
5) All the members of a population should be homogenous in age .
Significance of Hardy - Weinberg equilibrium : Any deviation from one or more of these conditions will distrub the equilibrium by changing allelic frequency or genotypic or both . These changes in frequencies are significant in producing variations , which are the raw materials for evolution .
Hardy-Weinberg Equation : It is a mathematical model which explains the genetic equilibrium in a population . In a stable population for a gene with two alleles .A. (dominant) and .a. (recessive) , three genotypes namely .A A. (homozygous dominant), .Aa. (heterozygous) and .aa. (recessive) are possible . If the frequency of .A. is .p. and that of .a. is .q. , then the genotypic frequencies of AA, Aa and aa can be expressed by the equation `p^(2)+2pq+q^(2)=1"or"(p+q)^(2)=1` . In mathematical terms if `(p+q)^(2)=1` , then `(p+q)=1` . Where
p= frequency of dominant allele, q=frequency of the recessive allele,
`p^(2)` = frequency of the homozygous dominant genotype,
`2pq` = frequency of the heterozygous dominant genotype and
`q^(2)` = frequency of the recessive genotype .