## Multi-locus population genetics - What is a haplotype?

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.

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