Bayesian Analysis of Quantitative Trait Locus Data Using Reversible Jump Markov Chain Monte Carlo

Abstract

The advent of molecular markers has created a great potential for the understanding of quantitative inheritance, in plants as well as in animals. Taking the newly available data into account, biometrical models have been constructed for the mapping of quantitative trait loci (QTLs). In current approaches, the lack of knowledge on the number and location of most important QTLs contributing to a trait is a major problem. In this paper, we utilize reversible jump Markov chain Monte Carlo (MCMC) methodology (Green 1995) in order to compute the posterior quantities required for fully Bayesian inference. It yields posterior densities not only for the parameters, given the number of QTL, but also for the number of QTL itself. As an example, the algorithm is applied to simulated data, according to a standard design in plant breeding. KEYWORDS: Quantitative trait locus; breeding scheme; Bayesian inference; reversible jump Markov chain Monte Carlo.

Biased estimators of quantitative trait locus heritability and location in interval mapping

“…By comparison to standard, classical estimates, Bayesian estimators are shrunken in the direction specified by the prior distribution, which in itself is a different form of bias that can be severe if the prior is selected inappropriately. Although Bayesian methods are becoming more mainstream in the QTL mapping community (Satagopan et al, 1996;Uimari and Hoeschele, 1997;Stephens and Fisch, 1998;Yi and Xu, 2000;Sen and Churchill, 2001;Vogl and Xu, 2002;Yi and Xu, 2002;Yi et al, 2003a;Xu, 2003;Kilpikari and Silanpää, 2003;Yi et al, 2003b;Bogdan et al, 2004;Jannink and Fernando, 2004;van de Ven, 2004;Zhang et al, 2005;Hayashi and Awata, 2005), we feel that there is a need for a more systematic investigation of the influence that the choice of priors has on the resulting estimates. Our hope is that work toward solving the bias problem will continue, but our larger hope is that readers will be aware that bias exists in the estimators rendered from QTL mapping methodologies and will view their results with a cautious eye.…”

Advances in Bayesian multiple quantitative trait loci mapping in experimental crosses

“…The likelihood function p(y|X E , y, g, H) depends on how many loci are included in the model, and whether or not we simultaneously model main effects of QTL, covariates, gene-gene interactions (epistatic effects) and gene-environment interactions (G Â E effects). Most of earlier Bayesian multiple QTL mapping methods only considered main effects of multiple QTL Sillanpää and Arjas, 1998;Stephens and Fisch, 1998;Gaffney, 2001;Xu, 2003). Recently, Bayesian methods have been extended to simultaneously include main and epistatic effects of QTL (Yi and Xu, 2002;Yi et al, 2003aYi et al, , b, 2005, and arbitrary covariates and G Â E effects (Yi et al, 2007b).…”

“…The RJ-MCMC technique has become a widely used tool in Bayesian multiple QTL mapping (Hoeschele, 2001). Over the past decade, a variety of RJ-MCMC algorithms have been proposed to map multiple non-epistatic QTL Sillanpää and Arjas, 1998;Stephens and Fisch, 1998;Yi and Xu, 2000;Gaffney, 2001), and epistatic QTL in experimental crosses (Yi and Xu, 2002;Yi et al, 2003a, b).…”

“…Over the past decade, a variety of Bayesian methods have been developed to map multiple QTL for complex traits in experimental crosses Sillanpää and Arjas, 1998;Stephens and Fisch, 1998;Hoeschele, 2001;Sen and Churchill, 2001;Gaffney, 2001;Yi and Xu, 2002;Xu, 2003;Yi et al, 2003aYi et al, , b, 2005Narita and Sasaki, 2004;Wang et al, 2005;Zhang et al, 2005). In this review, we describe these recently developed and still developing Bayesian multiple QTL mapping methods.…”

QTL mapping in outbred half-sib families using Bayesian model selection

“…With the development of the Bayesian model selection approach, the issues in multiple-QTL mapping have been solved both for inbred line crosses lines (Satagopan and Yandell, 1996;Heath, 1997;Uimari and Hoeschele, 1997;Sillanpää and Arjas, 1998;Stephens and Fisch, 1998;Gaffney, 2001;Xu, 2003;Yi et al, 2003Yi et al, , 2005 and for outbred populations (Meuwissen and Goddard, 2004;Liu et al, 2007;Yi and Xu, 2000). The stochastic search variable selection algorithm was first developed by George and McCulloch (1993) and used by Meuwissen and Goddard (2004) to fine map multiple QTL in outbred half-sib families.…”