Phenotypic plasticity
Three different parameters of plasticity were estimated using the Finlay-Wilkinson regression (3) and a factorial regression (4) models.
In model (3), \(y_{\text{ij}}\) is the phenotype (average values per environment and genotype) and \(\mu\) the general intercept. \(G_{i}\)and \(E_{j}\) are the effects of the MAGIC line i and environmentj , respectively and \(\beta_{i}\) represents the regression coefficient of the model. It measures individual genotypic sensitivity to the environment.
\(y_{\text{ij}}=\ \mu+G_{i}+\beta_{i}xE_{j}+\varepsilon_{\text{ij}}\)(3)
Environments are described here as an index that represents the ‘quality’ of the environment (i.e. the average performance of all genotypes in a given environment). The \(\varepsilon_{\text{ij}}\) are the error terms including the GxE and\(\varepsilon_{\text{ij}}\ \)~ N (0, σ2R). From model (3), three parameters were estimated: (i) the genotypic means that is equivalent to the sum (\(\mu+G_{i}\)) representing the average performance of a genotype considering all environments; (ii) he \(\beta_{i}\) terms (slope), corresponding to genotypic responses to the environments and the variance (VAR) of the\(\varepsilon_{\text{ij}}\) terms that is a measurement of non-linear plasticity (Kusmec et al., 2017). All these parameters were used then to characterize the genotypes according to their individual performance and their stability in the MAGIC-MET design. For every trait, reaction norms were then computed from the model (3).
The factorial regression model (4) was further applied to describe the GxE through the genotypic response to the different environmental covariates (Tmin°, Tmax°, Tm°, Amp.Th°, Vpd, RH and SDD). The environmental covariates defined from the daily recorded climatic variables in the greenhouses were used for this purpose. For each trait, the most significant environmental covariate (p-value significant at α = 5%) was first identified – by testing successively the significance of each single covariate – and used as an explanatory variable represented by \(\text{Cv}_{j}\) in model (4).
\(y_{\text{ij}}=\ \mu+G_{i}+E_{j}+\alpha_{i}x\text{Cv}_{j}+\varepsilon_{\text{ij}}\)(4)
The \(\alpha_{i}\) terms of the model were extracted and considered as a third plasticity parameter (SCv). They represent genotypic sensitivities to the most impacting environmental covariate for each trait. This measurement of plasticity is of interest as it allows identifying the direction and the intensity of each MAGIC line’s sensitivity to a meaningful environmental covariate. Throughout the rest of the document, the ‘slope’ and ‘VAR’ estimated from the Finlay-Wilkinson model and the ‘SCv’ from the factorial regression model will be considered as plasticity phenotypes – all of these parameters being trait-specific.