Bayesian Quantitative Trait Loci Mapping for Multiple Traits

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. C OMPLEX 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. 2003Yi et al. , 2005Yi et al. , 2007Yi 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...

Bayesian Detection of Expression Quantitative Trait Loci Hot Spots

“…However, one important difference is the assignment in (2) of a regression specific error variance s 2 k , allowing for transcript-related residual heterogeneity and making our formulation more flexible. A more general model, seemingly unrelated regressions (SUR) introduces additional dependence between the responses Y through the noise e k , modeling the correlation between the residuals of different responses (Banerjee et al 2008). However, it becomes computational unfeasible when the size of q is large, which is typical in eQTL experiments.…”

“…There is a vast literature on multi-mapping QTL (see the review by Yi and Shriner 2008); some of the models have been extended to the analysis of a small number of traits simultaneously (Banerjee et al 2008;Xu et al 2008). Several styles of approaches have been adopted ranging from adaptive shrinkage (Yi and Xu 2008;Sun et al 2010) to variable selection within a composite model space framework that sets an upper bound on the number of effects (Yi et al 2007).…”

Multiple-trait genome-wide association study based on principal component analysis for residual covariance matrix

“…Because of a large number of matrix calculations and the increased degrees of freedom of the test statistic (Weller et al, 1996), however, the multivariate analysis of all traits is extremely impractical when the number of quantitative traits is large. More recently, Verzilli et al (2005) and Banerjee et al (2008) employed seemingly unrelated regression model (Zellner, 1962) to map QTLs of correlated traits. With two multivariate models and the associated Bayesian algorithms, their modeling scheme outperforms the conventional multivariate model in terms of QTL identification.…”

Identification of QTLs of resistance to white mold in common bean from multiple markers by using Bayesian analysis

“…Thus, if α is accepted, a new position is established and a new genotype is suggested for the x matrix of genotypes of the QTLs, closing an MCMC cycle (Satagopan et al, 1996;Wang et al, 2005;Banerjee et al, 2008). The other a posteriori conditional distributions for the b and v parameters are similar to those described by Xu (2003).…”