Linkage disequilibrium

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Linkage disequilibrium (LD) is the non-random association of alleles at two or more loci on a chromosome. It describes a situation in which some combinations of alleles or genetic markers occur more or less frequently in a population than would be expected from their distance. In population genetics, linkage disequilibrium is said to characterize the haplotype distribution at two or more loci.

Formally, if we define pair-wise LD, we consider indicator variables on alleles at two loci, say <math>I_1, I_2<math>. We define the LD parameter <math>\delta<math> as:

<math>\delta := Cov(I_1, I_2) = p_1 p_2 - h_{12}
 <math>

Here <math>p_1, p_2 <math> denote the marginal allele frequencies at the two loci and <math>h_{12}<math> denotes the haplotype frequency in the joint distribution of both alleles. Various derivatives of this parameter have been developed. In the genetic literature the wording "two alleles are in LD" usually means to imply <math>\delta \ne 0<math>. Contrariwise, linkage equilibrium, denotes the case <math>\delta = 0<math>.

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