On measures of association among genetic variables
2012
Manfredi, Eduardo | Simianer, Henner
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 variablesfrom independence. New measures of association based on notions of statistical distancebetween distributions are presented. These are more general than correlations, which arepairwise 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 quantitativegenetics 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 linkagedisequilibrium in a two-locus system with multiple alleles and present applications to systems of correlated beta distributions. Two multivariate beta and multivariate betabinomial processes are examined, and new distributions are introduced: the GMSSarmanov multivariate beta and its beta-binomial counterpart.
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