The core part of this study is to use the PCA to identify the main controlling factors on cultivated land variations and use the GWR model to explore how these factors contribute to cultivated land variations. Figure 2 shows an overview of the workflow.

The quantitative change of land use types can be represented by a single land use dynamics model. Therefore, the model can be used to quantitatively analyze the change rate of cultivated land in the the Yangtze River Delta region The specific formula is as follows: K i = U i b − U i a U i a × 1 T i × 100 % (1) where K _i is a dynamic degree that represents the change rate of i-type land use. U _ia and U _ib are the quantities of i-type land use in the first year and last year of the study period, respectively. T _i is the duration of study time. When T _i was set as years, K _i is the annual change rate of i-type land use in the study area (Wang and Bao, 1999).

Utilizing a single variable to analyze a certain problem may cause one-sided conclusions. However, when considering more variables, there is a problem of colinearity among various factors. Therefore, the basic idea of the principal component analysis (PCA) is to achieve the purpose of dimension reduction while preserving as much original information as possible, simplifying the problem, and grasping its main contradiction (He, 2004). The principle is to make a linear change to the original variables that may have colinearity, and then to transform them into new mutually independent variables and rank them according to their variances. The new variable with the larger variance contains more original information, which will be recognized as the more significant variable. According to the variance value, we will find the first principal component, the second principal component, and the third principal component, etc. (Li and Zhang, 2017). In this study, we used the PCA to explore and identify the main controlling factors on the variations of cultivated land in the Yangtze River Delta region.

Before performing geographically weighted regression analysis, the dependent variable should be tested for spatial autocorrelation because the results of whether the dependent variable has a certain degree of gathering in spatial distribution must be taken into consideration (Li J. H. et al., 2020). Therefore, this study used the Moran’s Ⅰ index to test the spatial correlation of the cultivated land area in the characteristic years. This is calculated as follows: I = n ∑ i = 1 n ∑ j = 1 n W i j ( X i − X ¯ ) ( X j − X ¯ ) ∑ i = 1 n ∑ j = 1 n W i j ∑ i = 1 n ( X i − X ¯ ) 2 (2) where W _ij is the space weight function calculated by the Gaussian function. X _i and X _j are the values of X on the corresponding spatial units. X ¯ is the mean value of X, n represents the sum of space units, and i represents the unit.

Compared with the traditional global regression model that only generates one global regression coefficient, the geographically weighted regression (GWR) model can combine the geographic features with the regression model, reflecting the spatial distribution of regression parameters (Qin et al., 2005). Therefore, the GWR model can clearly show the spatial distribution of the regression coefficients of 41 prefecture-level cities in the Yangtze River Delta region. The specific formula is as follows: y i = β 0 ( u i , v i ) + ∑ k = 1 p β k ( u i , v i ) x i + ε i (3)

In this equation, the dependent variable is y _i . (u _i , v _i ) is the coordinate of the sample point i. β k ( u i , v i ) represents the k _th regression parameter on the sample point i. The number of independent variables is p, and x _ik is the value of the independent variable x _k at point i. The random error of this equation is ε_i.

Based on the aforementioned results, we analyzed the spatial distribution of cultivated land and per capita cultivated land area in the selected three characteristic years. As shown in Figure 4, the cultivated land area and per capita cultivated land area distributed more in the north and less in the south of the Yangtze River Delta region. First, the northern part of the Yangtze River Delta region is the main grain-producing area in the middle and lower reaches of the Yangtze River. Meanwhile, the prefecture-level cities with cultivated land above 40 × 10⁴ ha and per capita cultivated land area above 0.05 ha were mainly concentrated in this area. Second, due to the rapid development of urbanization in the central and southern regions of the Yangtze River Delta region, most of the cultivated land area of prefecture-level cities in this region were below 20 × 10⁴ ha. Furthermore, the per capita cultivated area of these cities were also below 0.05 ha. This indicates that the increase in population is causing great pressure on the cultivated land in the central and southern regions.

Through the comparative analysis of the spatial distribution of cultivated land and per capita cultivated land area in various stages and the overall time series, it can be found that there were obvious spatial variation characteristics in them (Figure 5). The cultivated land decreased by 8.2 × 10⁴ ha from 2009 to 2013 in the Yangtze River Delta region (Figure 5A). Of all the cities, 32 cities showed a decreasing trend in cultivated land area, with a total decrease of 1.2 × 10⁵ ha. Furthermore, Suzhou and Nantong of Jiangsu province and Ma’anshan of Anhui province decreased by more than 1.0 × 10⁴ ha of cultivated land area. However, nine cities showed an increasing trend in cultivated land area, which was presented as a scattered distribution in the Yangtze River Delta region, with a total increase of 4.3 × 10⁴ ha. Moreover, only Wuhu City, located in southern Anhui, increased more than 1.0 × 10⁴ ha of cultivated land area, while the increase of cultivated land of the remaining eight prefecture-level cities did not exceeded 1.0 × 10⁴ ha. Compared with the cultivated land change in 2009–2013, the per capita cultivated land area also showed a decreasing trend, with a total decrease of 0.063 ha (Figure 5D). First of all, 35 cities exceeded 0.001 ha, with a total decrease of 0.066 ha. Among these, the reduction of more than 0.002 ha of the per capita cultivated area mostly concentrated in the northern part of the Yangtze River Delta region. Suzhou and Ma’anshan whose cultivated land decreased by more than 1.0 × 10⁴ ha also belong to this area. Only six cities showed that the per capita cultivated land area increased over 0.0001 ha, with a total increase of 0.003 ha. Meanwhile, Wuhu had the largest per capita cultivated land area of 0.0009 ha.

During the time period 2013–2018, the cultivated land in the Yangtze River Delta region decreased by 0.4 × 10⁴ ha, showing less decrease than during the time period 2009–2013 (Figure 5B). Of all the cities, 24 cities showed a decreasing trend in cultivated land area, with a total decrease of 6.4 × 10⁴ ha, while the remaining 17 cities had a total increase of 6.0 × 10⁴ ha. Compared with the time period 2009–2013, more cities showed increased cultivated land area and the spatial distribution was different. Furthermore, the distribution of increased area had extended up to the north of Jiangsu and Anhui provinces. However, the decreasing trend of per capita cultivated land area had become stronger than in the first period in the Yangtze River Delta (Figure 5E). Of all cities, the sum of the per capita cultivated land area of 30 cities had reduced by 0.173 ha. Most of these cities are located in the northern region of the Yangtze River Delta region. Only 10 cities showed an increasing trend of per capita cultivated land area, with a total increase of 0.033 ha. The sum of the decrease was reached 0.14 ha.

During the time period 2009–2018, the cultivated land in the Yangtze River Delta region decreased by 8.6 × 10⁴ ha. Of all the cities, only 14 cities showed an increasing trend, with a total increase of 4.7 × 10⁴ ha (Figure 5C). However, 27 cities had decreased by 1.3 × 10⁵ ha, indicating that the situation of cultivated land resources was not optimistic in the study area. Therefore, exploring the controlling factors on the cultivated land change can effectively coordinate the relationship between cultivated land protection and economic development in order to provide reasonable reference suggestions for the sustainable utilization of cultivated land in the Yangtze River Delta region. As shown in Figure 5F, the relationship between population and cultivated land was very apprehensive in the Yangtze River Delta region. The per capita cultivated land area of most cities had shown a declining trend in 2009–2018, with a total decrease of 0.23 ha. The cities with an increase in per capita cultivated land area presented as a scattered distribution in the study area, with a total increase of 0.027 ha. This indicates that the increased range of the cultivated land area could not adapt to the rapidly increasing population in the Yangtze River Delta region from 2009 to 2018.

The results of the change rate of cultivated land area from 2009 to 2013 have shown a rapid decline in the Yangtze River Delta, with hotspots for reduction occurring in the central and southeast coastal areas (Figure 6A). The dynamic change rate of cultivated land ranged from −2.42% to −0.10%, and the decline of cultivated land was relatively rapid. In the northern part of the Yangtze River Delta region, the cultivated land area was decreased slowly in some agricultural-oriented cities, with a dynamic change rate from −0.09% to 0.00%. However, a few cities had slowly increased cultivated land area, but the increase rate has been slower, below 1%. This indicates that the protection policy of cultivated land was immature, reflecting that the phenomenon of economic development at the expense of cultivated land resources was serious in the Yangtze River Delta region during this period. During the time period 2013–2018, less decline in cultivated land area in the Yangtze River Delta region was seen because of the continuous improvement of the national farmland protection policy, especially for the central and northern cities that rapidly decreased from 2009 to 2013, showing a slower reduction of change rate from 2013 to 2018 (Figure 6B). Moreover, more than 40% of the urban cultivated land area slowly increased, indicating that most cities have gradually realized it is unsustainable to occupy cultivated land for blindly pursuing economic development. During the time period 2009–2018, there were obvious spatial differences in the dynamic rate of cultivated land change in the Yangtze River Delta region (Figure 6C). More than 60% of the cultivated land area has shown a decreasing trend to different degrees, which were mainly distributed in the southern and central regions of Jiangsu and Shanghai. However, the cultivated land has been slowly decreasing in the Anhui province, which includes the northern, central, and southern areas of the Anhui province. More importantly, the slowly increased regions of cultivated land area have shown no spatial aggregation, suggesting that the development situation of cultivated land was not optimistic in the Yangtze River Delta region.

The dynamic change rate of the per capita cultivated land area also showed a decreasing trend in different periods (Figures 6D–F). The dynamic change rate of most cities ranged from −0.99 to 0.00. However, a few cities have shown an increased dynamic rate and a spatial distribution that is scattered in the study area. When comparing Figures 6A–C, the cities with a dynamic change rate of over 0.01% belonged to the slowly increasing region of cultivated land. Moreover, the cities with a dynamic change rate below −1% and above 0.01% had the same spatial distribution, and they showed a scattered distribution as well in the Yangtze River Delta region.

This shows that although the reduction of cultivated land had been controlled by the implementation of the protection policy of cultivated land, the rapid increase of population had threatened the carrying capacity of the cultivated land in the Yangtze River Delta region. Therefore, coordinating the relationship between population increase, economic development, and cultivated land reduction should be a critical task in the Yangtze River Delta region.

We used the method of the principal component analysis to quantitatively analyze the controlling factors by taking the cultivated land area as the dependent variable in the Yangtze River Delta region. Based on the development status of the study area, 12 indicators were selected as independent variables (Table 2), which included three aspects, namely, population, economic development, and agricultural technological progress. Meanwhile, there is no strong correlation between the variables if the related coefficient is less than 0.3, suggesting that the group of influencing factors is unsuitable for the principal component analysis (Xue, 2011). As shown in Table 3, except for X₇, X₁₀, and X₁₁, there were strong correlations among variables. Therefore, the selected independent variables were suitable for the principal component analysis.

The common method that confirms the number of principal components is to select the components with a characteristic value greater than 1 and a cumulative contribution rate more than 85% (Lin and Zhang, 2005). As shown in Table 4, the characteristic values of the first and second components were 10.155 and 1.01, respectively. Meanwhile, the cumulative variance contribution rate of the two components had exceeded 85%, showing that these two components contained all the information of the 12 controlling factors. Therefore, the number of principal components was determined as two.

As shown in Table 5, the first principal component consisted of X₁ (population), X₃ (urbanization rate), X₅ (added value of industry), X₆ (total investment in fixed assets), and X₁₂ (proportion of secondary and tertiary industries). The correlation between these controlling factors and the first principal component was above 0.95, showing the significant effects of population growth and economic development on the change of cultivated land area in the Yangtze River Delta region. The second principal component consists of X₈ (total power of agricultural mechanization) and X₁₀ (consumption of fertilizer), showing significant effects of technological progress on the change of cultivated land area in the Yangtze River Delta region.

Based on the quantitative results of the principal component analysis (Table 5), we selected population (POP), gross domestic product (GDP), and the total power of agricultural mechanization (TPAM) as the independent variables of the GWR model. First, we used Moran’s I to test the spatial autocorrelation of the cultivated land area in 2009, 2013, and 2018. As shown in Figure 7, the cultivated land area of the three characteristic years had spatial agglomeration, which provided a foundation for the construction of the GWR model. Besides, we analyzed the correlation between the selected three independent variables in order to evaluate the possibility of collinearity problem (Table 6). The results showed that the correlation coefficients of the three variables were all less than 0.8 in different characteristic years, indicating that there was no multicollinearity for these indicators. Therefore, the GWR model can be built using these indicators. Moreover, we tested the spatial autocorrelation of the residual error of the GWR model (Table 7), which showed random spatial distribution. Therefore, further regression analysis can be performed on the selected independent and dependent variables using the GWR model.

According to the aforementioned results, we used the spatial kernel function of FIXED for calculation. In addition, we applied the AICc method to determine the optimal bandwidth. It can be found that the values of R² and adjusted R² explained 84%, 84%, and 89% of the variations in 2009, 2013, and 2018, respectively (Table 8). The results had indicated that the GWR model can well simulate the influence of controlling factors on the change of cultivated land resources in the Yangtze River Delta region.

There was a positive correlation between the population and cultivated land (Figures 8A–C), suggesting that the growing population played positive effects in promoting the increase of cultivated land. It showed a stronger impact of population on the cultivated land in the northeast coastal area than in the southwest area, with a higher degree of differentiation in the southeast coastal areas. The spatial distribution of population regression coefficients gradually changed from 2009 to 2013, showing that a greater impact was not only concentrated in the coastal areas but also began to move to the north of the Yangtze River Delta region. Meanwhile, this positive effect also had a strong impact on some cities in the Anhui province. However, the distribution of the regression coefficient of the population showed of high in the north and low in the south in the Yangtze River Delta region from 2013 to 2018. The center of gravity for the spatial regression coefficient moved from the coastal area of the northeast to the inland area of the north in the Yangtze River Delta region. During this time period, the positive impact of the population had gradually extended to some inland cities in the northern Yangtze River Delta region. The perfect medical security system and infrastructure construction of some coastal cities in the Jiangsu province led to a large population moving in. However, it will inevitably raise the cost of living and employment in these cities because urban development reaches a certain degree of saturation, resulting in the population moving to small cities (Wang L. W. et al., 2018).

There was a negative correlation between the GDP and cultivated land area in the Yangtze River Delta region, with significant spatial change (Figures 8D–F). The negative effect of the GDP on the cultivated land area gradually increased from the north to south region to the central to eastern region in 2009, which was especially obvious in the eastern coastal and central regions of the Yangtze River Delta region, attributing to the impact of the macro-control of national policies. For example, the Anhui province put forward the economic development strategy of “developing the Wanjiang River and calling for Pudong” in the 1990s. Furthermore, it also attended the forum of major leaders of the Yangtze River Delta region in 2008 (Zhang et al., 2019), suggesting that the form of regional cooperation and development in the Yangtze River Delta region extended to the Anhui province. The aggregation area of low value located in the coastal area of the Jiangsu province spread southward continually, showing that the restraining effect of the GDP on cultivated land area was continuously increasing in the coastal cities of the Zhejiang province and some inland cities. For example, the National Development and Reform Commission promulgated the “Regional Plan for the Yangtze River Delta” in 2010, a policy document that included eight prefecture-level cities in the Zhejiang province (Liu et al., 2020). Some cities in the Zhejiang province had developed because of the implementation of this policy that enabled the negative effects of the GDP to spread to the southern area of the Yangtze River Delta region from 2009 to 2013. In addition, the negative effects of the GDP also existed from 2013 to 2018, with a stronger effect in the northeast and weaker effect in the southwest.

The regression coefficients of the TPAM region were all positive in the Yangtze River Delta region, suggesting positive effects of TPAM on the cultivated land (Figures 8G–I). In 2009, the center of gravity of the regression coefficient of TPAM gradually moved to the central area of the Yangtze River Delta region. However, spatial distribution of the regression coefficients of TPAM in the Yangtze River Delta region moved from the central area to the southeast coastal area from 2009 to 2013, with a stronger positive effect in the southeast, whereas a weaker one in the northwest. In 2013–2018, the spatial distribution of regression coefficients showed higher values in the south and lower values in the north. The center of gravity for the high-value gathering area moved to the south, mainly getting distributed in the hilly and coastal areas of the Zhejiang province. This phenomenon may be attributed to the investment of agricultural mechanization conducted by the government of the Zhejiang province in 2013 (Gao, 2014). Besides, the Zhejiang province has promoted the development of agricultural mechanization in hills and mountainous areas by renovating scattered and fragmented hilly cultivated land in recent years, leading to a stronger positive impact of this factor.r in the southern area than in the northern area in the Yangtze River Delta region (Liu et al., 2019).