IIIVmrMLM.QEI: An effective tool for indirect detection of QTN-by-environment interactions in genome-wide association studies.

Although 3VmrMLM-MEJA and several indirect indicators have been employed to identify QTN-by-environment interactions (QEIs) in genome-wide association studies (GWAS), there is no convenient, flexible, and accurate method to comprehensively identify QEIs. To address this issue, 3VmrMLM-random was first extended to 3VmrMLM-fixed. Next, the two single-environment QTN detection methods were integrated with trait differences and regression parameters to indirectly detect QEIs. Finally, these indirect indicators were extended to include environmental factors (EFs, such as temperature) and four environmental variation indicators. As a result, both 3VmrMLM-random and 3VmrMLM-fixed, alongside all the indirect indicators, were incorporated into a new tool, IIIVmrMLM.QEI, designed for effective QEI identification. Simulation studies demonstrated that 3VmrMLM-fixed showed significantly higher powers than existing fixed-SNP-effect methods (MLM and EMMAX) because it takes into account all the possible effects and controls for all the possible polygenic backgrounds. 3VmrMLM-random and 3VmrMLM-fixed exhibited superior combination power to 3VmrMLM-MEJA. In the re-analysis of