## 2 Materials and Methods
### Methods  
#### Calculation of Ecosystem Service Value  
(1) Determination of ESV equivalent factor per unit area. As determined via using the ecosystem service unit area value equivalent factor method to calculate ESV, the equivalent factor of ESV per unit area is 1/7 of the economic value of average grain yield in a 1 \(\mathrm{hm^{2}}\) farmland ecosystem [21; 22; 23]. The average grain price was 1.78 \(\mathrm{CNY/kg}\), and the average grain yield per unit area was 6021.66 \(\mathrm{kg/hm^{2}}\). In order to eliminate the impact of rising prices on food prices, the consumer value index (CPI) was used to modify the ESV equivalent [24] (Formulas (2)-(4)), and, finally, the ESV equivalent factor per unit area of Sichuan Province was determined to be 1561.85 \(\mathrm{CNY/hm^{2}}\). \[DM_{0}=\frac{1}{7}\times G\times\frac{1}{n}\sum_{i=1}^{n}S,i=1,2,3\cdot\cdot\cdot n \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data** & **Years** & **Spatial Resolution** & **Source** \\ \hline Administrative division & 2018 & Vector data & \\ Land use & 2005, 2010, 2015, 2018 & 30 m & [[http://www.resdc.cn/](http://www.resdc.cn/)]([http://www.resdc.cn/](http://www.resdc.cn/)) (19 January 2023) \\ DEM & 2005 & 500 m & \\ NDVI & 2005, 2010, 2015, 2018 & 250 m & [[https://modis.gsfc.nasa.gov/](https://modis.gsfc.nasa.gov/)]([https://modis.gsfc.nasa.gov/](https://modis.gsfc.nasa.gov/)) (20 January 2022) \\ NPP & 2005, 2010, 2015, 2018 & 500 m & \\ Socio-economic & 2005, 2010, 2015, 2018 & Statistical data & [[http://tj.sc.gov.cn/](http://tj.sc.gov.cn/)]([http://tj.sc.gov.cn/](http://tj.sc.gov.cn/)) (26 January 2022) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data resource. Figure 2: Map of Sichuan province. Here, \(DM_{0}\) refers to ESV equivalent factor per unit area (CNY/hm\({}^{2}\)); \(G\) and \(S\) denote the average price of grain in Sichuan Province and the average grain yield in Sichuan Province (kg/hm\({}^{2}\)), respectively; and \(n\) is year of the study period. \[B_{i}=\frac{\text{CPI}}{100} \tag{2}\]  
\[\frac{B}{B_{0}}\times\frac{B_{2}}{B_{1}}\times\frac{B_{3}}{B_{2}}\times\cdots \frac{B_{n}}{B_{n-1}}=\frac{B_{n}}{B_{0}} \tag{3}\]  
\[DM_{0}=DM_{0}\times\frac{B_{n}}{B_{0}} \tag{4}\]  
Above, CPI is the consumer price index, \(B_{i}\) is the CPI of the elimination unit, \(\frac{B_{1}}{B_{0}}\) is the first period of the CPI, and \(\frac{B_{n}}{B_{0}}\) is the current year-on-year fixed base CPI. (2) Correction of ESV coefficient in Sichuan Province  
In this study, the analysis of ecosystem service functions encompassed four primary-level services and eleven secondary-level services. The coefficient representing the value of the ecosystem service function was derived by converting the proportional coefficient using the equivalent factor (Table 2). The calculation formula is shown below  
\[DM_{ij}=c_{ij}DM_{0}{}^{\prime},i=1,2,3\cdots 6;j=1,2,3\cdots 11 \tag{5}\]  
where \(i\) is ecosystem services function type \(i\), and \(j\) is land use type \(j\). The 5 km \(\times\) 5 km grid unit consistent with the landscape ecological risk evaluation was used to calculate the ESV of the grid unit in Sichuan Province. The formula is as follows:  
\[\text{ESVI}=\sum_{i=1}^{11}\sum_{j=1}^{6}\left(A_{j}\times DM_{ij}\right),i=1, 2,\cdots 11;j=1,2,\cdots 6 \tag{6}\]  
Here, \(ESVI\) represents the ESV (CNY) of each grid; \(A_{j}\) and \(DM_{ij}\) refer to the area of land use type (hm\({}^{2}\)) and ESV coefficient of \(i\) ecosystem service function of \(j\) land use type (CNY/hm\({}^{2}\)), respectively; \(i\) is ecosystem services function type I; and \(j\) is land use type \(j\).