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).