Calculating haplotype frequencies

In the absence of selection and in an infinite population with random mating, the equilibrial frequency of haplotypes can be calculated as follows:

Take two loci with two alleles each.

The haplotype frequencies can be written in terms of the gene frequencies at each locus, plus or minus a correction factor, D .

Let the gene frequencies be:

A1 = p₁, A2 = p₂, B1 = q₁, B2 = q₂. Then

Haplotype Frequency in population
A1B1 = p₁q₁ + D
A1B2 = p₁q₂ - D
A2B1 = p₂q₁ - D
A2B2 = p₂q₂ + D

Note the total frequencies add up to one
: p₁q₁ + p₁q₂> + p₂>q₁ + p₂q₂ = 1

The sum of the two +D and two -D factors is zero.

D is a measure of linkage disequilibrium and is conventionally defined by adding it to the frequencies of A1B1 and A2B2 and subtracting it from those of A1B2 and A2B1 ; it could equally well be defined the other way round.

Linkage equilibrium occurs when D = 0 and means that the alleles at the two loci are combined independently.

The two B alleles would then be found with any one A allele (such as A1) in the same frequencies as they are found in the whole population.