How is the Hardy-Weinberg equation used?

The Hardy-Weinberg principle states that both allele and genotype frequencies will remain the same in successive generations of a growing population if (i) mating is random; (ii) no mutations occur; (iii) population is large enough (in other words, there is no genetic drift); (iv) there is no migration (neither immigration nor emigration); (v) there is no natural selection.

If we have only two alleses (such as Rhesus positive and negative (recollect blood type and rhesus factor)), shown as A and a, then the usual symbols for encountering their frequencies are p and q, respectively. Since there is no other possibility (in terms of probability) p+q = 1 or p=1-q.

Genotypic frequencies are generally designated as capitalized letters. Therefore, P is the frequency of AA, H (hybrid) is the frequency of Aa, and Q is the frequency of aa.

Now we have P + Q + H = 1.

Suppose a population having the genotypic frequencies of P=0.64, H=0.32 and Q=0.04. Now anyone can compute the allele frequencies as follows:

p=P+(H/2) = 0.64+(0.32/2) = 0.80 q = 1-p = 0.20

Let me tabulate some offspring genotype frequencies

(1) Parental genotype frequencies (2) Parental allele frequencies P H Q p q 0.64 0.32 0.04 0.80 0.20 (3) Mating genotype Frequency (4) Offspring frequencies AA Aa aa AAxAA P^2 0.64^2 1 0.4096 0 0 AAxAa ......................................................................................... AAxaa AaxAa Aaxaa aaxaa Q^2...........

The Hardy-Weinberg equation is used to predict the frequencies of genotypes in a population under certain conditions of allele frequency and assuming that specific evolutionary factors are absent. It is commonly applied in population genetics to determine whether a population is evolving, by comparing the observed genotype frequencies to those expected under Hardy-Weinberg equilibrium.