Bayesian estimation of dispersion parameters with a reduced animal model including polygenic and QTL effects

In animal breeding, Markov chain Monte Carlo algorithms are increasingly used to draw statistical inferences about marginal posterior distributions of parameters in genetic models. The Gibbs sampling algorithm is most commonly used and requires full conditional densities to be of a standard form. In this study, we describe a Bayesian method for the statistical mapping of quantitative trait loci (QTL), where the application of a reduced animal model leads to non-standard densities for dispersion parameters. The Metropolis Hastings algorithm is used to obtain samples from these non-standard densities. The flexibility of the Metropolis Hastings algorithm also allows us change the parameterization of the genetic model. Alternatively to the usual variance components, we use one variance component (= residual) and two ratios of variance components, i.e. heritability and proportion of genetic variance due to the QTL, to parameterize the genetic model. Prior knowledge on ratios can more easily be implemented, partly by absence of scale effects. Three sets of simulated data are used to study performance of the reduced animal model, parameterization of the genetic model, and testing the presence of the QTL at a fixed position. (C) Inra/Elsevier, Paris.