Department of Animal Sciences, University of Wisconsin-Madison, Madison, WI, 53706, USA.
Anim Genet. 2012 Jul;43 Suppl 1:19-35. doi: 10.1111/j.1365-2052.2012.02326.x.
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.
系统涉及许多变量是非常重要的在人口和数量遗传学,例如,多性状预测的育种值和探索多基因座关联。我们研究了联合分布的一组遗传变量的独立性。新的关联措施基于分布之间的统计距离的概念。这些是更一般的相关性,这是成对的措施,并且缺乏一个明确的解释超出二元正态分布。我们的措施是基于对数(Kullback-Leibler)和相对的“距离”之间的分布。协会的索引发展和说明的数量遗传学设置变量的联合分布是多元正态或多元 t,我们展示了如何索引可以用来研究连锁不平衡在一个两基因座系统与多个等位基因和目前的应用程序相关联的 beta 分布。两个多元 beta 和多元贝塔二项式过程进行了研究,并引入了新的分布:GMS-Sarmanov 多元 beta 和它的贝塔二项式对应的。
