2.2.2. Socioeconomic Data

Socioeconomic data, including the yields of major farm crops (YMFC), the gross output value of farming (GOVF), the gross domestic product (GDP), the permanent resident population (PRP) and the employment in agriculture were obtained from the Guizhou statistical yearbook (2001–2021) (http://stjj.guizhou.gov.cn/ accessed on 4 April 2022). In addition, we derived the grain prices from 2001 to 2020 from the "The National Compilation of Cost-benefit data of Agricultural Products" as a reference (Table 1).


**Table 1.** Data sources for assessing cultivated land resources value.

#### *2.3. Methods*

#### 2.3.1. Cropland Resources Value Accounting Framework

To make a scientific evaluation of the value of cropland resources, we established three accounting accounts [34]: the physical quantity account, the conditional account, and the monetary account [35–38]. Among them, the physical quantity account was used to reflect the changes in the number and scope of cultivated land in the study area from 2000 to 2020, and to provide necessary data for value accounting, while the quality account was used to record the quality status of cultivated land in the study area. Since it is obvious that the value of cropland varies along the quality status, there will be significant differences in crop yield and ecological function. Finally, the monetary account includes two parts. One is the direct value, also called the use value or the commodity value, which is the value that is formed by people's direct harvesting, which is the output value of agricultural products provided by cropland resources. This part can be calculated by the market price method, because agricultural products can directly enter circulation as commodities [39]. The other part is the indirect value, which refers to the ecological service ability of cropland resources as a part of the natural environment when they exist in a natural way, as well as the value of natural resource assets that are used to meet human spiritual, cultural, and moral needs, and social development [40] (Table 2).

**Table 2.** Indicators for assessing cultivated land resources value.


The direct value is the gross output value of various grains, tubers, oil crops, vegetables, and other crops in Guizhou Province. The indirect value is the sum of the value equivalent for each ecological function. The annual cropland resources value is the direct value plus the indirect value.

$$V\_T = V\_D + V\_{ID} \tag{1}$$

$$V\_T = \sum\_{i=1}^{n} V\_{Di} \tag{2}$$

$$V\_{ID} = \sum\_{i=1}^{n} V\_{IDi} \tag{3}$$

In the formula, *VT* is the total monetary value of cropland resources, *VD* is the gross output value, and *VID* is the total value equivalent of cropland ecological function.

#### 2.3.2. Landscape Index

Cropland fragmentation refers to the fragmentation, dispersion, and size of the cultivated land due to natural or human factors, and the area of each cultivated land is relatively small, showing a decentralized and disorderly pattern, which is a long-term dynamic process [41–43]. For the karst mountain areas, the high mountains and deep valleys lead to obvious cutting terrain, and cultivated land can only be distributed on gentle slopes or small flat land. Therefore, the degree of cultivated land fragmentation is a very typical quality evaluation index in karst areas and plays a decisive role in the realization of the value of cultivated land resources [44,45].

Research on the impact of cultivated land fragmentation on the landscape scale of cultivated land can directly reflect changes in cultivated land fragmentation. In this study, we used the open-source Python library to compute landscape metrics, and the following six indicators were selected to measure the cultivated land landscape [46]:

• Patch Density (PD)

This indicator refers to the number of cultivated land patches per unit area in the study area, and it has an important impact on biological protection, material, and energy distribution. This index reflects the situation in which the concentrated and contiguous cultivated land is divided into small patches, which directly reflects upon the connotation of cultivated land landscape fragmentation [47].

$$\text{PD} = n/A \tag{4}$$

*n* is the number of the patches; *A* is the total area.

• Edge Density (ED)

This is an index that is used to analyze the shape of land patches, revealing the degree of cropland segmentation, as well as being a direct reflection of the degree of cultivated land fragmentation. The greater the edge density, the higher the degree of cultivated land division, and the more scattered the layout [48].

$$\text{ED} = \text{P}/A \tag{5}$$

*P* is the total perimeter of all cropland patches; *A* is the total area.

• Fragmentation Index of Patch Numbers (FN)

The patch size is the most basic spatial feature and it directly affects the mechanization level of agricultural production. As such, this index is used to measure the degree of fragmentation of the landscapes.

$$\text{FN} = (\text{N} - 1) / MPS \tag{6}$$

*MPS* is the mean patch size; *N* is the number of cropland patches.

• Area-Weighted Mean Shape Index (AWMSI)

Since an irregular shape leads to a reduction in the actual planting area within the total area, the farming production cost per unit area will be increased. However, with an increase in the patch size, the impact caused by the irregular shape will gradually weaken. Considering this phenomenon, AWMSI is taken to be one of the indicators to measure the degree of the cultivated landscape.

$$\text{AMWSI} = \sum\_{i=1}^{n} \left[ \left( \frac{0.25 P\_i}{\sqrt{a\_i}} \right) (a\_i / A) \right] \tag{7}$$

*n* is the number of cropland patches; *Pi* is the perimeter of the patches; *ai* is the area of the patches; *A* is the total area of cropland.

• Fragmentation Shape Index (FS)

This index is used to reflect the internal combination of cultivated land patches. The distribution of cultivated land patches becomes more scattered as the index increases. Additionally, the internal combination simultaneously becomes more complex.

$$\text{FS} = 1 - 1/MSI \tag{8}$$

$$MSI = \sum\_{i=1}^{n} (0.25P\_i / \sqrt{a\_i}) / N \tag{9}$$

*MSI* is the mean shape index; *ai* is the patch area; *Pi* is the perimeter of the patch; *N* is the number of cropland patches.

• Aggregation Index (AI).

This index reflects the degree of patch agglomeration within the landscape type. When the value is larger, the landscape is composed of a few large patches, and when the value is smaller, the landscape is composed of many small patches [49].

$$\text{AI} = \frac{\varepsilon\_i}{\max\\_\varepsilon\_i} \times 100\tag{10}$$

$$\max \underline{x}\_i = \begin{cases} 2n(n-1), & m=0\\ 2n(n-1) + 2m - 1, & m \le n\\ 2n(n-1) + 2m - 2, & m > n \end{cases}, \quad \left(m = A\_i - n^2\right) \tag{11}$$

*ei* is the number of edges that the patches have in common; max\_*ei* is the maximum number of edges that the patches have in common; *Pi* is the perimeter of the patch; *n* is the edge length of the largest integer square that does not exceed the total area of the cropland area.

#### 2.3.3. Revisions of the Ecological Value Equivalent Factors

Costanza et al. proposed the principle and method of ecosystem service value estimation [50], but their methods were criticized because they resulted in the ecological value of the cultivated land being significantly low. Therefore, Chinese researchers such as Xie Gaodi revised Costanza's assessment framework based on China's economic situation, land use, and vegetation types, and developed an assessment method for China's ecosystem service value based on the unit area value equivalence factor [51–53] (Appendix A). As the ecological function value consequently varies with the internal structure and external form of ecosystem, constantly changing within different regions or different periods, we conducted two revisions to obtain the final ecosystem service value equivalent of Guizhou [54]:

1. Previous studies have shown that the ecosystem function is positively correlated with NPP and precipitation. As such, we used two temporal and spatial factors (NPP and precipitation) to modify the ecosystem service value equivalent table of China for each year.

$$F\_i = \begin{cases} \ \ R\_i \times F\_{n1} \\ \ R\_i \times F\_{n2} \end{cases} \tag{12}$$

*Fi* refers to the unit area value equivalent of the ecological service function for each year; *Pi* refers to the NPP regulation factor; *Ri* refers to the precipitation regulation factor; *Fn*<sup>1</sup> represents the value equivalent per unit area of China for gas regulation, climate regulation, environmental purification, nutrient conservation, and biodiversity maintenance; and *Fn*<sup>2</sup> represents the value equivalent of China's unit area of hydrological regulation function.

2. According to Costanza's research, the economic value of ecological service value equivalent factors is 54 USD/hm2 (1997). Combined with China's grain production income, Chinese scholars have calculated that the economic value of an ecological service value equivalent factor in China is 449 CNY/hm2 (58.5 USD/hm<sup>2</sup> in 2007), using the shadow land rent method. However, the price index and grain yield vary interannually, and so to reflect the indirect value change of cultivated land resources more accurately, we revised the economic value by year to form the final economic value of the ecological function, to make it suitable for the study area [55].

$$E\_{Vi} = \frac{1}{\mathcal{T}} \sum\_{i=1}^{n} \frac{m\_i p\_i q\_i}{M} \tag{13}$$

*EVi* refers to the economic value of an ecological service value for equivalent factors of cropland resources in each year; *mi* refers to the area of crops; *pi* refers to the average price of crops; *qi* represents the output of agricultural products; *n* represents the types of crop products.
