Hardy-Weinberg equilibrium

The Hardy-Weinberg Equilibrium is a theory developed by G.H. Hardy, Wilhelm Weinberg, and William Castle. Although by rights it should be called the Hardy-Weinberg-Castle Equilibrium, it is usually referred to as Hardy-Weinberg. The theorem holds that, given a set of basic assumptions, a given set of allele frequencies will not change.

Assumptions

Hardy-Weinberg operates under a set of basic assumptions:

1. Population Size is Infinite
2. Mating is completely random
3. There is no mutation
4. There is no migration. Note that this term is used differently from the vernacular, and refers to individuals leaving or entering the population
5. There is no selection, whether natural or otherwise

Obviously, there are no populations in reality to which all of these assumptions apply, but populations can exist which are relatively close.

Equilibrium

Assume a given gene has 2 alleles. Let p=frequency of allele A, while q=frequency of allele a.

p+q=1

In a population of 100 individuals, assume that 50 are homozygous AA, and 50 are homozygous aa.

Therefore, p=0.5 and q=0.5

If a cross is performed, the expected values are as follows:

1. AA=p*p=0.5*0.5=0.25
2. Aa=p*q=0.5*0.5=0.25
3. aA=q*p=0.5*0.5=0.25
4. aa=q*q=0.5*0.5=0.25

Thus, the population would now contain 25 homozygous AA, 25 homozygous aa, and since aA and Aa are the same, 50 heterozygous Aa.

Note that the allele frequencies are still 0.5 and 0.5.