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Three-locus systems impose additional constraints on pairwise disequilibria.

W P Robinson·M A Asmussen·G Thomson
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Abstract

Combinations of allele frequencies and pairwise linkage disequilibrium terms, each of which is permissible at the two-locus level, may not always be permissible at the three-locus level. These additional constraints on the possible maximum and minimum values for the pairwise disequilibrium terms are formally determined and numerically analyzed. In some cases, the three-locus constraints on a pairwise disequilibrium (D) may be equivalent to the usual two-locus constraints, while in others, the positive or negative range may be restricted. This can result in situations where the allowable values of D are limited to only positive or only negative values up to the extreme case where there is only a single admissible value. No additional restrictions are placed on pairwise disequilibrium values when four loci are considered, other than those imposed by the three-way combinations containing the two loci of interest. A new measure of normalized pairwise linkage disequilibrium, allowing for the three-locus constraints, is defined and illustrated by an application to data from the human histocompatibility antigen (HLA) system. An analogous normalized three-way disequilibrium measure is also formulated.

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AllelesGene FrequencyGenetic LinkageGenetics, PopulationHaplotypesMathematicsModels, TheoreticalJournal ArticleResearch Support, U.S. Gov't, Non-P.H.S.Research Support, U.S. Gov't, P.H.S.

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W P Robinson, M A Asmussen, G Thomson. 1991. Three-locus systems impose additional constraints on pairwise disequilibria.. https://doi.org/10.1093/genetics%2F129.3.925

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