Exploring efficient linear mixed models to detect quantitative trait locus-by-environment interactions

Genotype-by-environment (G × E) interactions are important for understanding genotype–phenotype relationships. To date, various statistical models have been proposed to account for G × E effects, especially in genomic selection (GS) studies. Generally, GS does not focus on the detection of each quantitative trait locus (QTL), while the genome-wide association study (GWAS) was designed for QTL detection. G × E modeling methods in GS can be included as covariates in GWAS using unified linear mixed models (LMMs). However, the efficacy of G × E modeling methods in GS studies has not been evaluated for GWAS. In this study, we performed a comprehensive comparison of LMMs that integrate the G × E modeling methods to detect both QTL and QTL-by-environment (Q × E) interaction effects. Model efficacy was evaluated using simulation experiments. For the fixed effect terms representing Q × E effects, simultaneous scoring of specific and nonspecific environmental effects was recommended because of the higher recall and improved genomic inflation factor value. For random effects, it was necessary to account for both G × E and genotype-by-trial (G × T) effects to control genomic inflation factor value. Thus, the recommended LMM includes fixed QTL effect terms that simultaneously score specific and nonspecific environmental effects and random effects accounting for both G × E and G × T. The LMM was applied to real tomato phenotype data obtained from two different cropping seasons. We detected not only QTLs with persistent effects across the cropping seasons but also QTLs with Q × E effects. The optimal LMM identified in this study successfully detected more QTLs with Q × E effects.