QTL-by-environment analysis (QEI)
Multi-environment forward-backward models were used to assess the significance and the strength of the QTL effects across environments. The QEI analysis was conducted in two steps using the same set of 1345 SNP markers that were also used for linkage mapping analysis. This analysis yielded 28 QEI (only those showing significant interaction) for the 10 traits (Supplemental Table 4). The number of QEI varied from 0 QEI for nfr to 6 QEI for flw. These two traits also demonstrated the lowest and highest \(H^{2}\).
All QEI identified in this step were confronted to the plasticity and genotypic means QTLs using the physical positions of the QTLs and their confidence intervals. Interestingly, this comparison revealed that all the detected QEI were also identified using either genotypic means or plasticity parameters, in the linkage mapping analysis, except two QEI located on the same region of chromosome 6 (flw6.1 and firm6.1). Among the 106 unique QTLs identified on genotypic means, PP and QEI, a notable number of QTLs were specific representing 30 and 32% for plasticity and genotypic means, respectively (Figure 4). Eight QTLs involving five different traits (flw1.1, fw2.1, fw2.2, fw11.2, leaf6.1, nflw11.2, SSC1.2 and SSC9.1) were identified with all the three approaches highlighting their robustness and susceptibility to environmental variation.