A variational Bayesian method of QTL mapping for recombinant inbred lines in a four-way cross design

Recently, recombinant inbred lines derived from intercrossing multiple parents (multiple RILs) were generated in Arabidopsis thaliana and mice. In such multiple RILs, the resolution of QTL mapping is improved due to the accumulated recombination events as in the standard RILs derived from a cross between two founders and the chance of detecting novel QTLs is increased due to high allelic diversity of QTLs among multiple parents. In this report, we considered RILs derived from a four-way cross among four inbred lines, hereafter called four-way RILs, and developed an effective Bayesian method for QTL mapping in four-way RILs. We considered a linear model for the Bayesian QTL mapping, where phenotype was regressed on all available markers, and adopted a computationally cost-effective variational procedure to provide approximated posterior distributions for the regression coefficients that were regarded as effects of QTLs linked to the markers. Using simulated data sets of four-way RILs, we evaluated the efficiency of the proposed method in detecting and localizing QTLs. As results, the power of detecting simulated QTLs and the precision of estimates for the allelic effects of QTLs were actually high while the method required much less computational time comparing with MCMC-based Bayesian analysis. Moreover, we applied the method to the analysis of an actual data set of RILs derived from a cross two F1 cultivars of tomato, which are equivalent to four-way RILs in genetic structure.