A Two-Stage Method for Improving the Prediction Accuracy of Complex Traits by Incorporating Genotype by Environment Interactions in Brassica napus

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.