title: On measures of association among genetic variables.
abstract: Systems involving many variables are important in population and quantitative genetics, for example, in multi-trait prediction of breeding values and in exploration of multi-locus associations. We studied departures of the joint distribution of sets of genetic variables from independence. New measures of association based on notions of statistical distance between distributions are presented. These are more general than correlations, which are pairwise measures, and lack a clear interpretation beyond the bivariate normal distribution. Our measures are based on logarithmic (Kullback-Leibler) and on relative 'distances' between distributions. Indexes of association are developed and illustrated for quantitative genetics settings in which the joint distribution of the variables is either multivariate normal or multivariate-t, and we show how the indexes can be used to study linkage disequilibrium in a two-locus system with multiple alleles and present applications to systems of correlated beta distributions. Two multivariate beta and multivariate beta-binomial processes are examined, and new distributions are introduced: the GMS-Sarmanov multivariate beta and its beta-binomial counterpart.
authors: Department of Animal Sciences, University of Wisconsin-Madison, Madison, WI, 53706, USA. gianola@ansci.wisc.edu
authors: Daniel
authors: D
authors: Gianola
authors: Eduardo
authors: E
authors: Manfredi
authors: Henner
authors: H
authors: Simianer
mesh_terms: D000483:Alleles; D003198:Computer Simulation; D008040:Genetic Linkage; D014644:Genetic Variation; D015810:Linkage Disequilibrium; D008954:Models, Biological; D015233:Models, Statistical; D015999:Multivariate Analysis; D010641:Phenotype; D040641:Quantitative Trait Loci