**2. Materials and Methods**

## *2.1. Overview of the Study Area*

Karst landforms are a variety of surface and underground forms created by the longterm dissolution of soluble rocks by water. Due to the rugged terrain, thin soil, and shortage of surface water resources in karst landform areas, ecological fragility is prominent, the response to the interference of outside factors is weak, ecological restoration is difficult, and the population carrying capacity is low. The types of small-scale landforms in the karst mountainous areas of China are diverse, and there are heterogeneities in human activities and the natural conditions of different landforms; this results in differences in the land-use structures and their spatial patterns in different landform types [29]. According to the main landform types of karst mountainous areas in southwestern China, four typical townships in Guizhou Province with different landform types (Longchang with a karst mid-mountain landform, Liuguan with a karst basin landform, Xianchang with a karst trough valley landform, and Minxiao with a karst low hilly landform) were selected as the research areas (Figure 1). The altitude of Longchang with a karst mid-mountain landform is between 1283 and 2581 m, and the terrain relief is large. The altitude of Liuguan with a karst basin landform is between 1226 and 1382 m, the terrain in the central and eastern parts of this town is relatively flat, and there are low mountains in the southern and northern parts of the town. The altitude of Xianchang with a karst trough valley landform is between 758 and 1283 m, the central part of the town is a flat valley, and the eastern and western parts are high-altitude mountains. The altitude of Minxiao with a karst low hilly landform is between 758 and 1283 m. The town is located near the Fanjingshan Nature Reserve. In addition, as typical ecologically fragile areas in western China, the four selected towns belong to China's important ecological restoration areas, and the Grain for Green Project has been continuously implemented in this area for more than 20 years. Moreover, under the influence of poverty alleviation and resource development, the economy of karst mountainous areas has developed rapidly, and the per capita income reached 1715 USD/year by the end of 2020. However, compared with eastern China, the karst mountainous areas are still economically underdeveloped and suffer serious population loss [30].

**Figure 1.** The locations of the four selected towns in karst mountainous areas. (**a**) Longchang, (**b**) Liuguan, (**c**) Xianchang, (**d**) Minxiao.

#### *2.2. Data Sources and Processing*

Two types of high-resolution remote sensing data from 2010 and 2020 were collected in this study, including SPOT remote sensing images (from March to November 2010) with a 5 m spatial resolution and Pleiades remote sensing images (from April to October 2020) with a 1 m spatial resolution. Image preprocessing was performed via geometric correction, image registration, image mosaic, and cutting. Due to the fuzzy boundaries between landuse types in the remote sensing images, it would be difficult for computer classification methods (such as supervised or unsupervised classification methods) to obtain good classification results. Therefore, the artificial visual interpretation of remote sensing images was adopted in this study. The detailed steps were as follows. First, the interpretation indicators of various land-use types were established via preliminary image interpretation and field investigation. Then, the images in 2010 and 2020 were visually interpreted, and the land use was divided into seven types: cultivated land, forestland, shrub-grassland, built-up land, roads, water bodies, and unused land (Figure 2). Finally, 400 field points were selected to evaluate the accuracy of the classification results. After the accuracy test, the mapping accuracy was found to exceed 89.16%, which indicates that the classification results were good and met the accuracy requirements of land data. Elevation data with a resolution of 30 m were downed from the platform of the Geospatial Data Cloud, Computer Network Information Center, Chinese Academy of Sciences (http://www.gscloud.cn, accessed on 18 August 2022). The slope analysis tool in ArcGIS software was used to generate slope data based on the elevation data, and the slope data were divided into five gradients via the quantile method (Table 1).

**Figure 2.** The distribution of land-use types. (**a**) Longchang in 2010,(**b**) Longchang in 2020, (**c**) Liuguan in 2010, (**d**) Liuguan in 2020, (**e**) Xianchang in 2010, (**f**) Xianchang in 2020, (**g**) Minxiao in 2010, (**h**) Minxiao in 2020.


**Table 1.** The slope classification of the karst mountainous areas.

#### *2.3. Methods*

2.3.1. Land-Use Change Matrix

In this study, the land-use change matrix is introduced to reflect the dynamic process of the reciprocal transformation between the areas of various land-use types at the beginning and end of a certain period. Its formula is as follows:

$$S\_{ij} = \begin{bmatrix} S\_{11} & S\_{12} & \dots & S\_{1n} \\ S\_{21} & S\_{22} & \dots & S\_{2n} \\ & \vdots & \vdots & \vdots \\ S\_{n1} & S\_{n2} & \dots & S\_{nn} \end{bmatrix} \tag{1}$$

where *Sij* represents the area converted from land-use type *i* to land use type *j*, *n* is the number of land-use types, and *i* and *j* represent the land-use types before and after the conversion, respectively.

#### 2.3.2. Calculation Method of the Non-Agriculturalization of Cultivated Land

In this study, land-use types other than cultivated land are defined as non-cultivated land-use types (namely, forestland, shrub-grassland, built-up land, roads, water bodies, and unused land). Because forestland, shrub-grassland, water bodies, and unused land are crucial to the ecological environment, these land-use types are collectively referred to as ecological land in this article. Similarly, built-up land and roads are land-use types formed by human activities and have become the main space of human life. Therefore, they are collectively referred to as living land. Based on the preceding analysis, in this study, the non-agriculturalization of cultivated land is defined as the conversion of cultivated land into non-cultivated land-use types. It is composed of two parts: (1) the conversion of cultivated land into ecological land (forestland, shrub-grassland, water bodies, and unused land), and (2) the conversion of cultivated land into living land (built-up land and roads). Based on the data, the rate of conversion of cultivated land to non-cultivated land is calculated as follows:

$$N\_{\mathfrak{c}} = W\_{\mathfrak{i}} / G\_{\mathfrak{j}} \times 100\% \tag{2}$$

$$N\_l = L\_i / G\_j \times 100\% \tag{3}$$

$$N = N\_{\rm f} + N\_{\rm l} \tag{4}$$

where *N* represents the rate of conversion from cultivated land to non-cultivated land, *Ne* is the rate of conversion from cultivated land to ecological land (forestland, shrub-grassland, water bodies, and unused land)*, Nl* is the rate of conversion from cultivated land to living land (built-up land and roads), *Wi* is the area of cultivated land converted to ecological land from 2010 to 2020, *Li* is the area of cultivated land converted to living land from 2010 to 2020, and *Gj* is the area of cultivated land in 2010.

The area of cultivated land converted to non-cultivated land is calculated by the spatial analysis tool in ArcGIS. In addition, to achieve the clear spatial expression of the non-agriculturalization of cultivated land, the spatial pattern of the non-agriculturalization of cultivated land from 2010 to 2020 was presented by using the grid tool in ArcGIS.

#### 2.3.3. Calculation Method of Landscape Ecological Risk

The calculation model of landscape ecological risk is established by considering the landscape disturbance index and landscape loss index. The landscape disturbance index represents the degree of external disturbance to different landscapes, which is calculated by the landscape separation index, dominance index, and fragmentation index. The landscape loss index represents the loss degree of landscape types under the interference of various factors.

$$dI\_i = bC\_i + cF\_i + aD\_i \tag{5}$$

$$C\_i = n\_i / A\_i \tag{6}$$

$$F\_i = 0.5 \sqrt{\frac{n\_i}{A}} / \frac{A\_i}{A} \tag{7}$$

$$D\_i = 0.25 \times (n\_i/N + m\_i/M) + 0.5 \times A\_i/A \tag{8}$$

where *Ci* represents the landscape fragmentation degree, *Fi* is the landscape separation degree, *Di* is the landscape dominance degree, and the values of *a*, *b*, and *c* are, respectively, assigned as 0.5, 0.3, and 0.2 according to the expert scoring method. Moreover, *Ni* and *N* are, respectively, the numbers of patches in landscape *i,* and all landscape types, *Ai* and *A* are, respectively, the patch areas in landscape *i* and all landscape types, and *Mi* and *M* are, respectively, the number of grids in landscape *i* and the total number of grids.

$$\mathcal{R}\_i = \mathcal{U}\_i \times \mathcal{Q}\_i \tag{9}$$

where *Ui* represents the landscape disturbance index, and *Qi* is the landscape vulnerability index. According to experts' experience, water bodies and unused land are the most vulnerable to external disturbances and have a vulnerability index of 5. Built-up land and roads are stable and have a vulnerability index of 1. Finally, cultivated land, shrubgrassland, and forestland have vulnerability indexes of 4, 3, and 2, respectively.

Based on the area ratio of various landscape types in each grid, the calculation model of the landscape ecological risk index is established as follows:

$$ERI\_i = \sum\_{i=1}^{n} \frac{A\_i}{A} \times R\_i \tag{10}$$

where *ERIi* represents the landscape ecological risk index, *Ai* is the area of landscape *i*, *A* is the area of all landscape types, and *Ri* is the landscape loss index of landscape *i*.

The grid tool in ArcGIS software was used to divide Longchang, Liuguan, Xianchang, and Minxiao into 167, 157, 148, and 160 grids, respectively. Then, the landscape ecological risk index of each grid was calculated to obtain the risk value of the sample center, and the spatial pattern map of landscape ecological risk was generated by using the spatial interpolation tool in ArcGIS software. The landscape indices (*Ni*, *N*, *Ai*, and *A* in Equation (10)) required for landscape ecological risk calculation were obtained by Fragstats 4.2 software.

2.3.4. Correlation between the Non-Agriculturalization of Cultivated Land and Landscape Ecological Risk

The global and local Moran's indices were introduced to analyze the spatial correlation between the non-agriculturalization of cultivated land and landscape ecological risk. The global Moran's index was used to determine the correlation between the nonagriculturalization of cultivated land and landscape ecological risk in the whole research area. The local Moran's index was used to identify the distribution of the types of spatial agglomeration between the non-agriculturalization of cultivated land and landscape ecological risk in local areas (i.e., within the demarcated grid).

$$I = \frac{\sum\_{i=1}^{n} \sum\_{j=1}^{n} \mathcal{W}\_{ij} (\boldsymbol{\chi}\_{i} - \overline{\boldsymbol{\pi}}) (\boldsymbol{\chi}\_{j} - \overline{\boldsymbol{\pi}})}{\sum\_{i=1}^{n} \sum\_{j=1}^{n} \mathcal{W}\_{ij} \sum\_{i=1}^{n} \left(\boldsymbol{\chi}\_{i} - \overline{\boldsymbol{\pi}}\right)^{2}} \tag{11}$$

$$I\_i = \frac{\left(\mathbf{x}\_i - \overline{\mathbf{x}}\right)}{\mathbf{S}^2} \sum\_{j=1}^n \mathcal{W}\_{ij} (\mathbf{x}\_j - \overline{\mathbf{x}}) \tag{12}$$

where *I* and *Ii* are, respectively, the global and local Moran's indices, and *Xi* and *Xj* are, respectively, the values of the non-agriculturalization of cultivated land and landscape ecological risk in spatial units *i* and *j*. Moreover, *x* is the average value of the non-agriculturalization of cultivated land and landscape ecological risk of all spatial units, *Wij* is the spatial weight, and *S*<sup>2</sup> is the variance of the non-agriculturalization of cultivated land and the landscape ecological risk value of each spatial unit.

A value of *I* greater than 0 indicates that there is a positive spatial correlation between the two variables. The larger the value, the more obvious the spatial agglomeration. A value of *I* less than 0 indicates a negative spatial correlation. If the value of *I* is equal to 0, there is no correlation between the two variables. According to the calculation results of *Ii*, the agglomeration types of the study area were divided into high-high, low-low, high-low, low-high, and not significant areas.
