Linkage Disequilibrium Mapping

The genetic variants that one might be interested in mapping arise through, for example, novel mutations or immigration of carriers of mutant alleles into a population. When a mutation initially arises, it has a particular chromosomal location and specific neighbouring marker alleles. At this incipient point in time, the mutation is completely associated with the adjacent alleles; it is only observed when the marker alleles are also present.51 Marker alleles that were in the neighbourhood of the disease gene when its mutation was introduced into the population will generally remain nearby over numerous generations (that is, in disequilibrium). One can estimate whether a particular marker locus appears to be in disequilibrium with a disease locus. In particular, if specific marker allele frequencies are higher among diseased versus normal chromosomes (for example, in unrelated unaffected subjects), this suggests linkage between that locus and a disease locus. The extent of this disequilibrium depends on the number of subsequent generations since the mutation was introduced into the population, the recombination between the disease and marker alleles, mutation rates and selective values. This allelic disequilibrium is commonly referred to as 'linkage disequilibrium', although linkage need not be present for disequilibrium to exist; allelic association is a better term to describe the general phenomenon.16

While model-based and model-free linkage analysis approaches have proved successful for mapping many disease and trait genes, in some gene mapping investigations the limited number of meioses occurring within available pedigrees limits one's ability to detect recombination events between closely spaced (<1 cM) loci.52 One can instead use information on all recombinations occurring since the incipient mutation, and attempt to map disease genes more finely by disequilibrium.

Mapping by disequilibrium entails determining the relative location of a disease locus by comparing marker allele locations with estimators of the relation between the corresponding alleles and disease alleles.53,54,55 These include measures of association and recombination between disease and marker alleles. As with linkage analysis, relevant properties of the disease locus are inferred based on phenotype.

The most basic linkage disequilibrium efforts contrast single markers with disease. Let B denote a single marker allele that is being evaluated in relation to a disease allele A. Standard linkage disequilibrium models assume that a randomly mating population is in a steady state; a constant size and in equilibrium between the effects of genetic drift and recombination. These steady-state assumptions imply that the number of generations that have passed since the mutation was introduced is of the same order as the constant effective population size, Ne. Under these conditions, the squared correlation between linked disease and marker alleles is p2 = D2/iPA(i-PA)PB(i-pBn, using the notation given in the above subsection on disequilibrium concepts. For a particular data set, one can estimate the squared correlation by substitution of observed frequencies. This observed squared correlation is equivalent to y2/n, where y2 is the standard test statistic from a 2 x 2 table of observed haplotype counts (Table II), and n is the total number of haplotypes.60

Table II. Observed haplotype counts for two diallelic loci

Disease allele

Marker allele B b

Total

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