Bayesian model selection for genome-wide epistatic quantitative trait loci analysis

Abstract

The problem of identifying complex epistatic quantitative trait loci (QTL) across the entire genome continues to be a formidable challenge for geneticists. The complexity of genome-wide epistatic analysis results mainly from the number of QTL being unknown and the number of possible epistatic effects being huge. In this article, we use a composite model space approach to develop a Bayesian model selection framework for identifying epistatic QTL for complex traits in experimental crosses from two inbred lines. By placing a liberal constraint on the upper bound of the number of detectable QTL we restrict attention to models of fixed dimension, greatly simplifying calculations. Indicators specify which main and epistatic effects of putative QTL are included. We detail how to use prior knowledge to bound the number of detectable QTL and to specify prior distributions for indicators of genetic effects. We develop a computationally efficient Markov chain Monte Carlo (MCMC) algorithm using the Gibbs sampler and Metropolis-Hastings algorithm to explore the posterior distribution. We illustrate the proposed method by detecting new epistatic QTL for obesity in a backcross of CAST/Ei mice onto M16i.

Figure 1.—

Profiles of LOD scores from maximum-likelihood interval mapping. On the x-axis, large tick marks represent chromosomes and small tick marks represent markers.

Figure 2.—

Bayesian nonepistatic analysis: profiles of posterior inclusion probability and cumulative probability function. Black line, l_m = 1; red line, l_m = 3; blue line, l_m = 6. On the x-axis, large tick marks represent chromosomes and small tick marks represent markers.

Figure 3.—

Bayesian nonepistatic analysis: profiles of Bayes factor. Black line, l_m = 1; red line, l_m = 3; blue line, l_m = 6. On the x-axis, large tick marks represent chromosomes and small tick marks represent markers.

Figure 4.—

Bayesian epistatic analysis: profiles of posterior inclusion probability and cumulative probability function. Black line, l₀ = 4; red line, l₀ = 6; blue line, l₀ = 8. On the x-axis, large tick marks represent chromosomes and small tick marks represent markers.

Figure 5.—

Bayesian epistatic analysis: profiles of Bayes factor. Black line, l₀ = 4; red line, l₀ = 6; blue line, l₀ = 8. On the x-axis, large tick marks represent chromosomes and small tick marks represent markers.

Figure 6.—

Bayesian epistatic analysis: profiles of main effect and heritability explained by main effect. Black line, l₀ = 4; red line, l₀ = 6; blue line, l₀ = 8. On the x-axis, large tick marks represent chromosomes and small tick marks represent markers.