An Efficient Bayesian Model Selection Approach for Interacting Quantitative Trait Loci Models with Many Effects

Article excerpt

ABSTRACT

We extend our Bayesian model selection framework for mapping epistatic QTL in experimental crosses to include environmental effects and gene-environment interactions. We propose a new, fast Markov chain Monte Carlo algorithm to explore the posterior distribution of unknowns. In addition, we take advantage of any prior knowledge about genetic architecture to increase posterior probability on more probable models. These enhancements have significant computational advantages in models with many effects. We illustrate the proposed method by detecting new epistatic and gene-sex interactions for obesity-related traits in two real data sets of mice. Our method has been implemented in the freely available package R/qtlbim (http://www.qtlbim.org) to facilitate the general usage of the Bayesian methodology for genomewide interacting QTL analysis.

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MAPPING quantitative trait loci (QTL) involves inferring the genetic architecture of complex traits in terms of genomic regions, gene effect, gene action, and possible interactions, given observed phenotype and marker genotype data (LYNCH and WALSH 1998). The variation of most complex traits results from interacting networks of multiple QTL and environmental factors (REIFSNYDER et al. 2000; CARLBORG and HALEY 2004; MOORE 2005; STYLIANOU et al. 2006; VALDARet al. 2006;WANG et al. 2006). Inclusion of gene- gene interactions (epistasis) and gene-environment interactions in mapping QTL is expected to aid the discovery of more QTL, improve the accuracy and precision of estimates of their genomic positions and genetic effects, and enhance our ability to understand the genetic basis of complex traits ( JANSEN 2003; CARLBORG and HALEY 2004).

Identification of genomewide interacting QTLhas been a formidable challenge for geneticists and statisticians, mainly due to numerous possible variables associated with hundreds or thousands of genomic loci (markers and/or loci within marker intervals) that lead to a huge number of possiblemodels (e.g., YI et al. 2005). The problem is further complicated by the facts that the genomic loci on the same chromosome are highly correlated and the genotypes at many loci are unobservable. Traditional QTL mapping methods utilize prespecified simple statistical models, which fit the effects of only one or two QTL whose putative positions are scanned across the genome (e.g., LANDER and BOTSTEIN 1989; HALEY and KNOTT 1992; JANSEN and STAM 1994; ZENG 1994). Although successful in many applications, such approaches require prohibitive corrections formultiple testing and ignore the nature of complex traits in statistical modeling.

Multiple-QTL mapping has been viewed as a model selection issue (BROMAN and SPEED 2002; SILLANPÄÄ and Corander 2002; YI 2004). Rather than fitting prespeci- fied models to the observed data, model selection approaches proceed by identifying theQTL models from a set of potential QTL models that are best supported by the data. Various model selection methods have been recently proposed for genomewide multiple-QTL mapping from both frequentist and Bayesian perspectives. Frequentist approaches sequentially add or delete QTL using forward and backward or stepwise selection procedures and apply criteria such as P-values or a modified Bayesian information criterion (BIC) to identify the "best multiple-QTL model" (Kao et al. 1999; CARLBORG et al. 2000; REIFSNYDER et al. 2000; Bogdan et al. 2004; Baierl et al. 2006). Such methods usually pick a single "good" (and maybe useful) model, ignoring the uncertainty about the model itself in the final inference (Raftery et al. 1997; George 2000; Kadane and Lazar 2004).

Several Bayesian model selection approaches for mapping multiple QTL have been developed over the past decade (Satagopan and Yandell 1996; Satagopan et al. 1996;Heath 1997; SILLANPÄÄ and Arjas 1998; Stephens and Fisch 1998; Gaffney 2001; Hoeschele 2001; Sen and Churchill 2001; Xu 2003;WANG et al. …