Abstract

Reversible jump Markov chain Monte Carlo (RJ-MCMC) has been proposed as a suitable methodology to estimate the number of putative quantitative trait loci (QTL) which may affect a phenotype of interest in experimental crosses. It permits estimation of the distribution for the effects and locations of QTL within a genome. This thesis provides a flexible Bayesian model framework that accommodates any combination of additive and dominance effects for each QTL. In addition, it can be extended to include epistasis. Sampling is performed using RJ-MCMC. Improvements in the Markov chain sampling that result in dramatic decreases in the number of iterations required are outlined. Many QTL, even with two in the same marker interval, can be reliably detected.

Bayes factors are examined as a means of model selection. In the absence of good prior information about the number and location of QTL this seems prudent, since the posterior for the number of QTL is greatly shaped by the prior. The choice of prior is shown to affect the bias and variance of our estimate for the Bayes factor.

We consider, a model space that is characterized by a vector containing the number of QTL on each chromosome. The frequentist properties of using the Bayes factor in model selection are examined via simulation, and the method is shown to be conservative, with good type I error rates.

Simulation results for zero, one, two, and eight loci are compared with results from those produced using composite interval mapping. Sensitivity to prior specification is also examined. In particular, the variance of the prior for QTL effects is shown to have a modest effect on our estimate for the Bayes factor. This sensitivity was reduced by sampling the prior variance. Flowering time data from B. napus experiments are analyzed.

A means of generating initial values for the chain (that can be applied to any RJMCMC analysis) is proposed. This is especially useful in models of high dimension. In addition, a new method for long-range update of the QTL position is provided.