Three-Locus Systems Impose Additional Constraints on Pairwise Disequilibria
W.P. Robinson, M.A. Asmussen, G. Thomson
Genetics ,
129(3), 925-930 (1991)
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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