Multiparent populations (MPP) have become popular resources for complex trait mapping because of their wider allelic diversity and larger population size compared with traditional two-way recombinant inbred (RI) strains. In mice, the collaborative cross (CC) is one of the most popular MPP and is derived from eight genetically diverse inbred founder strains. The strategy of generating RI intercrosses (RIX) from MPP in general and from the CC in particular can produce a large number of completely reproducible heterozygote genomes that better represent the (outbred) human population. Since both maternal and paternal haplotypes of each RIX are readily available, RIX is a powerful resource for studying both standing genetic and epigenetic variations of complex traits, in particular, the parent-of-origin (PoO) effects, which are important contributors to many complex traits. Furthermore, most complex traits are affected by >1 genes, where multiple quantitative trait locus mapping could be more advantageous. In this paper, for MPP-RIX data but taking CC-RIX as a working example, we propose a general Bayesian variable selection procedure to simultaneously search for multiple genes with founder allelic effects and PoO effects. The proposed model respects the complex relationship among RIX samples, and the performance of the proposed method is examined by extensive simulations.

Improving the prediction accuracy of a complex trait of interest is key to performing genomic selection (GS) for crop breeding. For the complex trait measured in multiple environments, this paper proposes a two-stage method to solve a linear model that jointly models the genetic effects and the genotype × environment interaction (G × E) effects. In the first stage, the least absolute shrinkage and selection operator (LASSO) penalized method was utilized to identify quantitative trait loci (QTL). Then, the ordinary least squares (OLS) approach was used in the second stage to reestimate the QTL effects. As a case study, this approach was used to improve the prediction accuracies of flowering time (FT), oil content (OC), and seed yield per plant (SY) in Brassica napus (B. napus). The results showed that the G × E effects reduced the mean squared error (MSE) significantly. Numerous QTL were environment-specific and presented minor effects. On average, the two-stage method, named OLS post-LASSO, offers the highest prediction accuracies (correlations are 0.8789, 0.9045, and 0.5507 for FT, OC, and SY, respectively). It was followed by the marker × environment interaction (M × E) genomic best linear unbiased prediction (GBLUP) model (correlations are 0.8347, 0.8205, and 0.4005 for FT, OC, and SY, respectively), the LASSO method (correlations are 0.7583, 0.7755, and 0.2718 for FT, OC, and SY, respectively), and the stratified GBLUP model (correlations are 0.6789, 0.6361, and 0.2860 for FT, OC, and SY, respectively). The two-stage method showed an obvious improvement in the prediction accuracy, and this study will provide methods and reference to improve GS of breeding.