Derivation of a Bayes factor to distinguish between linked or pleiotropic quantitative trait loci

Abstract

A simple procedure to calculate the Bayes factor between linked and pleiotropic QTL models is presented. The Bayes factor is calculated from the marginal prior and posterior densities of the locations of the QTL under a linkage and a pleiotropy model. The procedure is computed with a Gibbs sampler, and it can be easily applied to any model including the location of the QTL as a variable. The procedure was compared with a multivariate least-squares method. The proposed procedure showed better results in terms of power of detection of linkage when low information is available. As information increases, the performance of both procedures becomes similar. An example using data provided by an Iberian by Landrace pig intercross is presented. The results showed that three different QTL segregate in SSC6: a pleiotropic QTL affects myristic, palmitic, and eicosadienoic fatty acids; another pleiotropic QTL affects palmitoleic, stearic, and vaccenic fatty acids; and a third QTL affects the percentage of linoleic acid. In the example, the Bayes factor approach was more powerful than the multivariate least-squares approach.