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.