Bayesian Quantitative Trait Loci Mapping for Multiple Traits

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ABSTRACT

Most quantitative trait loci (QTL) mapping experiments typically collect phenotypic data on multiple correlated complex traits. However, there is a lack of a comprehensive genomewide mapping strategy for correlated traits in the literature. We develop Bayesian multiple-QTL mapping methods for correlated continuous traits using two multivariate models: one that assumes the same genetic model for all traits, the traditional multivariate model, and the other known as the seemingly unrelated regression (SUR) model that allows different genetic models for different traits. We develop computationally efficient Markov chain Monte Carlo (MCMC) algorithms for performing joint analysis.We conduct extensive simulation studies to assess the performance of the proposed methods and to compare with the conventional single-trait model. Our methods have been implemented in the freely available package R/qtlbim (http://www.qtlbim.org), which greatly facilitates the general usage of the Bayesian methodology for unraveling the genetic architecture of complex traits.

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COMPLEX traits involve effects of a multitude of genes in an interacting network. Mapping quantitative trait loci (QTL) means inferring the genetic architecture (number of genes, their positions, and their effects) underlying these complex traits. The QTL mapping problem has several salient features: first, the predictor variables in the regression (the genotypes of QTL) are not observed; second, it is really a model selection problem as there are typically thousands of loci to choose from; and third, the genomic loci on the same chromosome are correlated. Much has been done in this regard, especially in the univariate case (e.g., Lander and Botstein 1989; Jiang and Zeng 1997; Broman and Speed 2002). Bayesian methods have been very successful in the QTL mapping framework (Satagopan and Yandell 1996; Yi and Xu 2002; Yi et al. 2003, 2005, 2007; Yi 2004); see a recent review by Yi and Shriner (2008).

Most of these methods are applicable to mapping QTL for a single trait. However, in QTL experiments typically data on more than one trait are collected and, more often than not, they are correlated. It seems natural to jointly analyze these correlated traits. There are two distinct advantages for jointly analyzing correlated traits: including information from all traits can increase the power to detect QTL and the precision of the estimated QTL effects. Biologically, it is imperative to jointly analyze correlated traits to answer questions like pleiotropy (one gene influencing more than one trait) and/or close linkage (different QTL physically close to each other influencing the traits). Testing these hypotheses is key to understanding the underlying biochemical pathways causing complex traits, which is the ultimate goal of QTL mapping.

Several methods have been developed to jointly analyze multiple correlated traits. Some of them use a maximum-likelihood-based approach ( Jiang and Zeng 1995; Jackson et al. 1999; Williams et al. 1999a,b; Vieira et al. 2000; Huang and Jiang 2003; Lund et al. 2003; Xu et al. 2005) or a least-squares approach (Knott and Haley 2000; Hackett et al. 2001). Most of these methods involve a single-QTLmodel or at most very few QTL. A problem with the likelihood-based approach is that with increasing complexity, due to the increase in the number of parameters to be estimated, the increase in degrees of freedom of the test statistic can restrain its practical use when the number of traits is large (Mangin et al. 1998). As a result, the advantage of joint analysis is lost over single-trait analysis. Another approach for joint analysis is to use a dimension reduction technique, namely, principal component analysis (PCA) or discriminant analysis (DA) or using canonical variables associated with the traits (Mangin et al. 1998; Mähler et al. 2002; Gilbert and Le Roy 2003, 2004), and then use the linear combination of traits to map QTL. …