## 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 = p_{1}, A2 = p_{2}, B1 = q_{1}, B2 = q_{2}. Then

Haplotype Frequency in population

A1B1 = p_{1}q_{1} + D

A1B2 = p_{1}q_{2} - D

A2B1 = p_{2}q_{1} - D

A2B2 = p_{2}q_{2} + D

Note the total frequencies add up to one

: p_{1}q_{1} + p_{1}q_{2}> + p_{2}>q_{1} + p_{2}q_{2} = 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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