Bayesian mapping of quantitative trait loci under complicated mating designs

Quantitative trait loci (QTL) are easily studied in a biallelic system. Suc h a system required the cross of two inbred lines presumably fixed for alte rnative alleles of the QTL. However, development of inbred lines call be ti me consuming and cost ineffective for species with long generation interval s and severe inbreeding depression. In addition, restriction of the investi gation to a biallelic system can sometimes be misleading because many poten tially important allelic interactions do not have a chance to express and t hus fail to be detected. A complicated mating design involving multiple all eles mimics the actual breeding system. However, it is difficult to develop the statistical model and algorithm using the classical maximum-likelihood method. In this study, we investigate the application of a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm to QTL mappi ng under arbitrarily complicated mating designs. We develop the method unde r a mixed-model framework where the genetic values of founder alleles are t reated as random and the nongenetic effects are treated as fixed. With the MCMC algorithm, we first draw the gene flows from the founders to the desce ndants fur each QTL and then draw samples of the genetic parameters. Finall y, we are able to simultaneously infer the posterior distribution of the nu mber, the additive and dominance variances, and the chromosomal locations o f all identified QTL.