## 2 Data and Methods
### Methods
#### 2.3.2 Driving Factors Analysis Method for the Landscape Aggregation Degree of Cultivated Land  
Some scholars have discussed the driving factors of cultivated land fragmentation [46; 67; 68], but few have studied the driving factors of the change of landscape aggregation degree of cultivated land. In this study, AI (aggregation index) is used to represent the landscape aggregation degree of cultivated land. Generally, the factors affecting the change of landscape aggregation degree of cultivated land are diverse, including nature, economy, society, policy, agricultural science and technology. Among them, economic development, industrial restructuring, urbanization, agricultural science and technology level, policy, and natural factors are the main impacting factors [65; 68; 69]. Since natural factors are relatively stable in a short period of time, and policy factors are difficult to be quantified and have a certain degree of contingency. Therefore, this paper mainly considers four aspects of economic development, industrial restructuring, urbanization and agricultural science and technology. According to the actual situation of Shanghai, 15 indicators that may affect the change of arable land landscape aggregation degree are selected. We choose per capita gross domestic product, rural disposable income per capita, newly increased fixed assets and gross output value of agriculture to measure the economic development of Shanghai. To measure the adjustment of Shanghai's industrial structure by gross industrial output value, the proportion of tertiary industry, and the proportion of agricultural workers. The \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Acronym** & **Name** & **Formula** & **Definition** \\ \hline AI & Aggregation index & \(AI=\sum\limits_{i=1}^{n}\left(\frac{\pi_{i}}{\pi_{i}\pi_{i}}\right)P_{i}*(100)\) & \(g_{ii}\) is the number of similar adjacent patches of the corresponding landscape type; \(P_{i}\) is the area ratio of type patches \\ MNN & Mean nearest distance & \(MNN=\frac{\sum_{i=1}^{n}m_{i}(d_{ij})}{\pi_{i}}\) & \(d_{ij}\) is the distance between patches \(i\) and \(j\), \(m_{i}\) is the number of type patches with the closet distance \\ DIVISION & Landscape division index & \(DIVISION=1-\frac{\pi_{i}}{\sum_{j=1}^{n}\left(\frac{\pi_{j}}{\Delta}\right)^{2}}\) & \(a_{ij}\) is the area of patch \(ij\), \(A\) is the total number of landscape grids \\ CONNECT & Connectance index & \(CONNECT=\left[\frac{\pi_{i}^{n}d_{ij}}{\pi_{i}\left(\frac{\pi_{j}}{\Delta}\right) ^{2}}\right]*(100)\) & \(c_{Ri}\) is the number of connections between patch \(i\) and patch \(k\) related to patch type \(i\); \(m_{i}\) is the number of patches \(i\) \\ COHESION & Path cohesion index & \(\left[1-\frac{\sum_{i=1}^{n}\Gamma_{ij}}{\sum_{j=1}^{n}\Gamma_{ij}/\sqrt{n}} \right]*\left[1-\frac{\sum_{i=1}^{n}\lambda}{\lambda}\right]^{-1}*(100)\) & \(p_{ij}\) is the perimeter of patch \(ij\), \(a_{ij}\) is the area of patch \(ij\); \(A\) is the total number of landscape grids \\ SPLIT & SPLIT index & \(SPLIT=\frac{\Delta^{2}}{\sum_{j=1}^{n}\zeta_{j}}\) & \(A\) is the total landscape area; \(a_{\sharp}\) is the area of patch \(ij\) \\ \hline \hline \end{tabular} Note: Type \(i\) represents the landscape type of cultivated land, while patch \(ij\) represents the patch of cultivated land.  
\end{table} 
Table 4: The calculation formula and definitions of landscape structure indexes. urbanization of Shanghai is measured by an increase in urban resident population, the proportion of construction land area, the investment in real estate development, the length of road and green land area. The agricultural science and technology level of Shanghai is measured by the total power of agricultural machinery, consumption of chemical fertilizers and consumption of pesticides. The research methods of driving force analysis of cultivated land landscape aggregation degree include correlation analysis, principal component analysis, and multiple linear regression analysis.