Division of linkage disequilibrium between absolute linkage disequilibrium and linkage equilibrium

Abstract

Linkage disequilibrium is the association between alleles in the allele distributions across linked loci and is intermediate in character between the dependence and the independence of allele distribution. This ambivalence makes linkage disequilibrium difficult to understand and to treat mathematically. To overcome this difficulty, an attempt was made to divide linkage disequilibrium between absolute linkage disequilibrium, which is a complete dependence of allele distribution, and linkage equilibrium, which is a complete independence. A matrix description of linkage disequilibrium showed that (1) linkage disequilibrium is divided between absolute linkage disequilibrium and linkage equilibrium, (2) a linkage disequilibrium state is characterized by the allele frequency in the first locus p, the relative content of absolute linkage disequilibrium d and the linkage equilibrium variable c, and (3) r is the geometric mean of both orientation's d. Division of linkage disequilibrium may make linkage disequilibrium straightforward to understand and to treat mathematically. © The Japan Society of Human Genetics and Springer-Verlag 2005.