# Predicting Wheat Potential Yield in China Based on Eco-Evolutionary Optimality Principles
## 3 Results
### Trend of the Wheat PY in China  
The response of wheat PW in China to climate change diverges under the two characteristic SSPs, as displayed in Figure 7. The observed outcomes underscore a two-stage trajectory in wheat PY, with a peak projected around 2060. Notably, the incorporation of sowing date optimization aligns with this overarching trend while additionally bolstering PY (5.7%, Figure 7). Substantial increases in PY are anticipated before 2060 within key wheat-producing provinces such as Shandong, Henan, and Jiangsu (Figure 8a and Table 1). Subsequently, a nationwide PY trend of statistically insignificant magnitude is anticipated (Figure 8b). Within the context of SSP370, the majority of regions, with the exception of select nonmain production zones in southwestern China, display insignificant trends. Over this timeframe, sowing date optimization is projected to yield an additional PY of 3.7%. Subsequently, from 2061 to 2100, a substantial PY enhancement is foreseen due to the concurrent benefits stemming from both optimized sowing dates and elevated CO\({}_{2}\) concentrations.  
Figure 6: Prediction of optimized wheat sowing date. **(a,b)** represent the sowing date variation from 2021 to 2060 and 2061 to 2100 under SSP 126, respectively; **(c,d)** represent the sowing date variation from 2021 to 2060 and 2061 to 2100 under SSP 370, respectively. The grid with significant variation trend is labeled with the black points. A positive value in this figure represents an advance of the sowing date.  
Figure 8: Prediction for wheat PY in China. (**a**,**b**) represent the PY variation from 2021 to 2060 and 2061 to 2100 under SSP 126, respectively; (**c**,**d**) represent the PY variation from 2021 to 2060 and 2061 to 2100 under SSP 370, respectively. The grid with significant variation trend is labeled with the black points.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Province**} & \multicolumn{2}{c}{**SSP126**} & \multicolumn{2}{c}{**SSP370**} \\ \cline{2-5}  & **2021–2060** & **2061–2100** & **2021–2060** & **2061–2100** \\ \hline Henan & 0.72 \(\pm\) 0.06\% *** & \(-\)0.02 \(\pm\) 0.10\% & 0.07 \(\pm\) 0.12\% & 0.74 \(\pm\) 0.19\% ** \\ Shandong & 0.45 \(\pm\) 0.15\% ** & \(-\)0.03 \(\pm\) 0.15\% & 0.16 \(\pm\) 0.15\% & 0.30 \(\pm\) 0.18\% * \\ Hebei & 0.43 \(\pm\) 0.18\% * & 0.04 \(\pm\) 0.24\% & 0.20 \(\pm\) 0.18\% & 0.25 \(\pm\) 0.12\% * \\ Jiangsu & 0.17 \(\pm\) 0.02\% *** & 0.01 \(\pm\) 0.02\% & 0.04 \(\pm\) 0.03\% & 0.22 \(\pm\) 0.04\% ** \\ Anhui & 0.20 \(\pm\) 0.03\% *** & 0.00 \(\pm\) 0.04\% & 0.03 \(\pm\) 0.04\% & 0.23 \(\pm\) 0.05\% ** \\ Sichuan & 0.09 \(\pm\) 0.02\% ** & \(-\)0.03 \(\pm\) 0.04\% & 0.00 \(\pm\) 0.02\% & 0.06 \(\pm\) 0.03\% * \\ Shannxi & 0.13 \(\pm\) 0.002\% ** & \(-\)0.02 \(\pm\) 0.03\% & 0.04 \(\pm\) 0.03\% & 0.11 \(\pm\) 0.03\% * \\ \hline \hline \end{tabular} Note: Significance: *** is \(p\) \(<\) 0.001, *** is \(p\) \(<\) 0.01, *** is \(p\) \(<\) 0.05.  
\end{table}
Table 1: Annual variation of wheat PY in main production provinces. Only seven production provinces are listed. The rank of the table represents the wheat production. We use the average PY during 2011 to 2020 as the benchmark.  
Figure 7: Prediction for relative variation of total wheat PY in China. We use the average PY during 2011 to 2020 as the benchmark. Dashed line represents the annual wheat PY, thick line represents the PY trend after smoothing. Two simulation configurations, with and without the optimizing sowing date, are represented by two colors.