Phenotypic prediction at different locations and periods
After environmental indices were identified, they were leveraged to predict phenotypic outcomes in different environments (Guo et al., 2020, Li et al., 2022, Li et al., 2021). Here we identified three environmental indices. For any environmental index, we employed the same approach in constructing the model. Firstly, one model was constructed to estimate the magnitude of changes in phenotypic response to each environmental index at the population level by a general linear model (Fig. S6):
\begin{equation} y_{i}=\beta_{0}+\beta_{1}x_{i}+\epsilon_{i}\nonumber \\ \end{equation}
where \(y_{i}\) is the mean SOC for the population in the \(i\)th environment (\(i=1,\ 2\ldots v\)), \(x_{i}\) is the mean values for the environmental index in the \(i\)th environment, \(\beta_{0}\) is the intercept of the linear model, \(\epsilon_{i}\) is the deviation from regression and \(\beta_{1}\) is the slope estimate of the linear model, which indicated the expected trait value change per a one-unit change of the corresponding climatic variant (Li et al., 2022). Subsequently, the other two models are also constructed using the same theoretical framework. Finally, environmental data were retrieved for each location and for each simulated planting date, extracting three environmental indices corresponding to that environment. Subsequently, values of these environmental indices were used as input into separate models, the averaged output values of the three models were calculated, ultimately yielding the predicted phenotypic value.
To predict the SOC when planting 10 days earlier or later than the designated planting period in the established cultivation area and ensure prediction stability, following the above approach, the predicted outcomes computed for planting 9 days early, 10 days early and 11 days early were averaged as the prediction for planting 10 days early. Similarly, the predicted outcomes for planting 9 days late, 10 days late and 11 days late were averaged as the prediction for planting 10 days late (Fig. 3b; Supplementary Table S11). For predicting the trend of SOC variation as a function of planting dates in seven primary B. napus producing regions in the middle and lower Yangtze River, environmental data were obtained for 10 years (2011–2020) (Supplementary Table S13). Daily SOC predictions were conducted from September 10th to October 28th, using the environmental data accumulated over the preceding decade for the prediction on each day (Fig. 3c).