## Materials and Methods
### Land Use Allocation and Ecosystem Consequences
#### 2.4.1 Land Use Allocation Module  
In this study, we adopted the framework of the conversion of land use and its effects (CLUE), which considers the natural suitability and policy restrictions. Through iterative, all the spatial units (grid cells) would be allocated a certain land use and land cover type [69; 70; 71; 72]. Five types of land use categories (cropland, grasslands, forests, built-up, and bare land) were allocated in the module in APTZNC. In order to simplify the land-use allocation, water bodies' changes were not considered. It was assumed that water areas remain unchanged in representing land-use dynamics. Since (i) according to the actual situation of the study area, the proportion of water is very small, only 0.1%; (ii) research focuses on changes in agricultural land (i.e., arable land, woodland, grassland) and non-agricultural land (i.e., built-up) and their impact on ecosystem functions.  
Equation (1) was adopted to assign a specific land use and land cover type to each spatial unit (grid cell) with the maximum overall suitability:  
\[\begin{split}& LU(r)=LT_{j},\\ & if\max_{j=1,\ldots,5}(F_{site,j}+F_{\text{exp},j}+F_{loss,j}+D_{j} )=F_{site,j}+F_{\text{exp},j}+F_{loss,j}+D_{j}\end{split} \tag{1}\]  
where \(LU(r)\) denotes one land use and land cover type, \(r\) represents the \(rth\) grid cell, and \(LT_{j}\) is the numerical code of land use type, \(LT_{j}=1\), 2, 3, 4, and 5 for arable land, grasslands, forests, built-up, and bare land, respectively. \(F_{site,j}\) is a site occurrence probability (Equation (2)). \(F_{expt,j}\) is the suitability factor (Equations (3) and (4)). \(F_{loss,j}\) is land use stability. \(D_{j}\) is the constants for model interactives. Each land unit (grid cell) will then be assigned a land type that has the maximum suitability and stability, and adjusted by the quantitative demand.  
Binary logistic regression was used to identify the probability of events' occurrence, which could explain the appearance of a specific land use type driven by site conditions. The advantage is that the variables can be either continuous or categorical. \(F_{site,j}\) was computed as follows:  
\[F_{site,j}=\frac{\textit{exp}(a_{j}+\sum_{\xi=1}^{m}b_{j\xi},X_{\xi})}{1+\textit {exp}(a_{j}+\sum_{\xi=1}^{m}b_{j\xi},X_{\xi})}, \tag{2}\]where \(j\) represents the \(j\)th land use type. \(X_{\xi}\) for \(\xi\) from 1 to 9 denotes a series of site variables: socioeconomic variable (population density), geographical, and ecological variables (elevation, slope, average annual temperature, average annual rainfall, cumulative daily mean temperature during the growing season, rainfall during the growing season, average organic matter content of soil and average total nitrogen content of soil). \(a_{j}\) and \(b_{j\xi}\) were regression coefficients.  
\(F_{expt,j}\) was calculated using Equations (3) and (4):  
\[F_{expt,j}=\sum\
olimits_{i=1}^{n}w_{i}f_{i}(x_{i}), \tag{3}\]  
\[f_{i}(x_{i})=\left\{\begin{array}{c}[1+(\frac{x_{i}-x_{0}}{B_{i}})^{2}]^{-1} \\ 1,\text{{otherwise}}\end{array},\right.\quad x_{i}<x_{0}, \tag{4}\]  
where \(w_{i}\) is the weight estimated by the relationship between land use type and the _ith_ socio-economic and ecological conditions \(x_{i}\). \(f_{i}(x_{i})\) is the fuzzy membership function to estimate the site suitability. \(x_{i0}\) and \(B_{i}\) are parameters set up based on empirical experts' knowledge and land classification from Food and Agriculture Organization.  
\(F_{loss,j}\) was used to quantify the stability of land use and land cover change. At least two maps of land use for different time periods were used to calculate the probability that land use type \(i\) converted to land use type \(j\):  
\[F_{loss,j}=\sum\limits_{i=1,\
eq j}^{q}\mu_{ij}, \tag{5}\]  
where \(\mu_{ij}\) is equal to the number of grid cells that converted to land use type \(j\) in the later map divided by the total number of grid cells that the land use type was \(i\) in the earlier map. \(q\) is the number of land use conversion trajectories.