INTRODUCTION TO BAYESIAN QUANTITATIVE TRAIT LOCUS ANALYSIS FOR POLYPLOIDS

Quantitative Trait Locus (QTL) mapping in polyploids is complicated by the un-observable parental QTL con guration, especially the number of copies (dosage) of the QTL. Existing techniques estimate the parental QTL con guration using a profile likelihood approach and do not address the uncertainty in the estimates. In this paper, a Bayesian method is proposed to jointly model the parameters including the parental QTL configuration, QTL location, and QTL effects. Inference for parameters is obtained by integrating the posterior distribution of the parameters via a Markov chain Monte Carlo (MCMC) sampler, which is a hybrid of the Metropolis-Hastings, Gibbs, and reversible jump samplers. Here, because the size of the parameter space varies for different parental QTL dosages, the reversible jump is utilized in order to allow the sampler to move between parameter spaces with di erent dimensionalities. Additional advantage of this Bayesian technique resides in its flexibility to incorporate prior information and treat missing data augmented. As an example, our method is applied to alfalfa experimental data to identify QTL related to winter hardiness