GxE in the MAGIC population
Genotype x environment interaction analysis was carried out after correcting data for micro-environmental heterogeneity and removing outliers. As a first step, variance analysis was conducted with ASReml-R package and the variance components from model (2) used to estimate the proportion of GxE variance (\(\text{prop.}{\sigma^{2}}_{\text{GxE}}\)) and heritability at the whole design level (\(H^{2}\)). Significant GxE was found for every trait and the\(\text{prop.}{\sigma^{2}}_{\text{GxE}}\) varied from 0.15 (for nflw) to 0.68 (for leaf). Although GxE was significant, seven out of the ten measured traits showed a higher proportion of genotypic variance compared to GxE (Supplemental Table 3). The broad-sense heritability of the whole design \(H^{2}\) was largely variable according to the trait, varying from 0.18 (nfr) to 0.77 (flw). Its calculation took into account the residual environment-specific variance which showed different range according to the trait, lowering heritability of traits such as nfr and fset (Supplemental Table 3). Furthermore, \(H^{2}\) at the whole design level was lower than the heritability computed in single environment (Supplemental Figure 3).
Afterwards, the proportion of the GxE that could be predicted by the environmental covariates was assessed following the factorial regression model (4). Across traits, different environmental covariates significantly explained the GxE #(Supplemental Figure 4). Considering only the most significant covariate, from 18% (FW) to 47% (fset) of the GxE (proportion of the sum of squares) could be reliably attributed to the responses of genotypes to climatic parameters measured within the greenhouses. To perform the factorial regression model (4), the most important environmental covariate was first identified for each trait (Supplemental Figure 4). Growth traits, height and leaf were for example mostly affected by the thermal amplitude and maximal temperature, respectively, while yield component traits, FW and nfr were particularly sensitive to the sum of degree day. The vapour pressure deficit (Vpd, kPa) was the most important environmental factor affecting firm, fset and SSC. Flowering time (flw) and nflw were mostly affected by minimal temperatures and relative humidity, respectively. Stem diameter was the only trait for which none of the environmental covariates significantly affected the trait.