title: Decomposing multilocus linkage disequilibrium.
abstract: We present a mathematically precise formulation of total linkage disequilibrium between multiple loci as the deviation from probabilistic independence and provide explicit formulas for all higher-order terms of linkage disequilibrium, thereby combining J. Dausset et al.'s 1978 definition of linkage disequilibrium with H. Geiringer's 1944 approach. We recursively decompose higher-order linkage disequilibrium terms into lower-order ones. Our greatest simplification comes from defining linkage disequilibrium at a single locus as allele frequency at that locus. At each level, decomposition of linkage disequilibrium is mathematically equivalent to number theoretic compositions of positive integers; i.e., we have converted a genetic decomposition into a mathematical decomposition.
authors.affiliation: Department of Biology, Arizona State University, Tempe, Arizona 85287-1501, USA. cycad@asu.edu
authors.forename: Root
authors.initials: R
authors.lastname: Gorelick
authors.forename: Manfred D
authors.initials: MD
authors.lastname: Laubichler
mesh_terms: D000483:Alleles; D005075:Biological Evolution; D004843:Epistasis, Genetic; D005787:Gene Frequency; D014644:Genetic Variation; D015810:Linkage Disequilibrium; D008433:Mathematics; D008957:Models, Genetic; D011336:Probability; D013045:Species Specificity