摘要The quantitative trait loci(QTL)-by-environment(Q × E)interaction effect is hard to detect because there are no effective ways to control the genomic background.In this study,we propose a linear mixed model that simultaneously analyzes data from multiple environments to detect Q × E interactions.This model in-corporates two different kinship matrices derived from the genome-wide markers to control both main and interaction polygenic background effects.Simulation studies demonstrate that our approach is more powerful than the meta-analysis and inclusive composite interval mapping methods.We further analyze four agronomic traits of rice across four environments.A main effect QTL is identified for 1000-grain weight(KGW),while no QTL are found for tiller number.Additionally,a large QTL with a significant Q × E interaction is detected on chromosome 7 affecting grain number,yield,and KGW.This region harbors two important genes,PROG1 and Ghd7.Furthermore,we apply our mixed model to analyze lodging in barley across six environments.The six regions exhibiting Q × E interaction effects identified by our approach overlap with the SNPs previously identified using EM and MCMC-based Bayesian methods,further validating the robustness of our approach.Both simulation studies and empirical data analyses show that our method outperforms all other methods compared.