Empirical validation
After the completion of the initial analysis and model building,
empirical validation experiments were carried out. Specifically, a
subset of 50 inbred lines, consisting of 25 high-plasticity lines and 25
low-plasticity lines, was grown in Wuhan (114° 21′E, 30° 28′N) and Ezhou
(114° 42′E, 30° 21′N) on three different planting dates in 2022
(Supplementary Table S4). For any environmental index, we employed the
same approach in constructing the model. First, one model was
constructed to estimate the magnitude of changes in phenotypic response
to each environmental index at the individual level by joint regression
analysis (Guo et al., 2023) (Fig. S9; Supplementary Table S3):
\begin{equation}
Y_{\text{ij}}=u_{i}+\beta_{i}I_{j}+\delta_{\text{ij}}\nonumber \\
\end{equation}where \(Y_{\text{ij}}\) is the line mean of the \(i\)th line in the\(j\)th environment (\(i=1,\ 2\ldots v\); \(j=\ 1,2\ldots n\));\(u_{i}\) is the mean of the \(i\)th line across all environments;\(\beta_{i}\) is the regression coefficient that measures the response
of the \(i\)th line to environmental input; \(I_{j}\) is the
environmental mean, expressed as the mean of all lines in the \(j\)th
environment; and \(\delta_{\text{ij}}\) is the deviation from
regression. After that, the other two models are also constructed using
the same theoretical framework. Subsequently, environmental data were
collected from NOAA and USNO (Supplementary Table S14) and separately
used as input for these three models to predict the SOC of the 50 lines.
The final predicted value for each line was the average output from
these three models. Finally, the accuracy of the model was evaluated by
examining the correlation between the predicted and observed values of
each inbred line, measured as Pearson’s correlation coefficients (Fig
4b, c).