Spatiotemporal Interaction Between Rural Settlements and Cultivated Land in Karst Mountainous Area, China

Settlements and cultivated land are important production and living spaces in promoting rural revitalization. However, few studies have explored the relationship between rural settlements and cultivated land from spatiotemporal interaction perspective. This paper analyzed the spatiotemporal conversion and the interactive mechanism between rural settlements and cultivated land in a karst mountainous area (Qixingguan District of Guizhou Province) with fragile ecological environment in China during 2009–2018. The results showed that the expansion of rural settlements and the loss of cultivated land coexisted in Qixingguan District. Only 2.68% of the new cultivated land was reclaimed from rural settlements, whereas 85.45% of the new rural settlements occupied cultivated land. Six spatial expansion modes of rural settlements when occupying cultivated land were identified. Among these six modes, the area of the edge-expansion & along traffic roads (EA) mode accounted for 52.75%. The occupation by rural settlements made the cultivated land landscape more fragmented. The area ratio index of cultivated land to rural settlements (ARICR) of Qixingguan District averaged 18.75 in 2009 and 17.21 in 2018, respectively. The ARICR reduced in all township administrative regions. Cultivated land with suitable slope condition for farming or without rocky desertification was more likely to be occupied by rural settlements. The probability of cultivated land occupied by rural settlements increased with the decrease of the distance to traffic roads, towns, and old rural settlements. The better the economic and social development of the township administrative regions, the more the ARICR decreased, while the richer the agricultural resources and the better the rural development of the township administrative regions, the less the ARICR decreased. The optimal reconstruction path of rural settlements, the comprehensive conservation path of cultivated land and the urban-rural integration development path in karst mountainous area were proposed. The findings would contribute to our understanding of the spatiotemporal interaction between rural settlements and cultivated land, and would provide a theoretical basis for promoting the coordinated development of rural man-land relationship and rural revitalization in karst areas.


Introduction
Rural decline has become a global issue (Liu and Li, 2017), and the world's countryside is in urgent need of revitalization. Rural settlement and cultivated land provide space for agricultural production and rural living, and are two important land types that reflect rural man-land relationship (Qu et al., 2019). The growing global population and consumption have brought a sharply increasing demand for food (Tilman et al., 2011;Davis et al., 2016). We face the challenge of achieving global food security and environmental sustainability (Foley et al., 2011), and the quantity and quality of cultivated land are closely related to food security (Li and Yan, 2012;Liu et al., 2020;Cheng et al., 2022b). However, cultivated land loss resulting from urban and rural expansion occurs around the world (Brown et al., 2005;Francis et al., 2012;Xi et al., 2012;Deng et al., 2015;Liu et al., 2015). Numerous studies argue that urban expansion is the major driving force behind the loss of cultivated land (Batisani and Yarnal, 2009;D' Amour et al., 2017). However, the occupation of rural settlements also contributes greatly to the loss of cultivated land (Long et al., 2007;Rosell et al., 2017), and rural settlements are more likely to occupy high-quality cultivated land (Gude et al., 2006;Conrad et al., 2015;Ju et al., 2018), affecting the sustainability of agriculture and threatening long-term food security (Li and Song, 2019). However, in contrast to urban studies, the previous studies have paid less attention to the effects of rural settlements occupation on cultivated land.
After the reform and opening up, a large flow of ruralto-urban migration has occurred in China, resulting in large-scale rural depopulation (Zhang and Song, 2003;Liu et al., 2013;Li W S et al., 2020). China's rural population decreased from 810 million to 560 million during 2000-2018 (National Bureau of Statistics, http://www. stats.gov.cn/), while the total area of rural settlements was increasing Song and Liu, 2014;Zhu et al., 2020), and a series of issues including 'hollow village' emerged (He et al., 2019). Optimal reconstruction of rural settlements has become a key issue in rural revitalization (Kong et al., 2021;Zhou T et al., 2021). The scattered, extensive, and disorder expansion of rural settlements have occupied a large amount of cultivated land (Tian et al., 2007;Cao et al., 2017;Wang J et al., 2018). The illegal occupation of cultivated land to build houses is still prevalent in rural China (Zhou Y et al., 2021). Although the Chinese government has always attached great importance to the protection of cultivated land and has implemented a series of policies, the cultivated land is facing the loss of quantity and the degradation of quality (Kong, 2014;Wu et al., 2017;Chen et al., 2018). The management of rural settlements expansion is crucial for cultivated land protection (Xi et al., 2012).
The bidirectional conversion between rural settlements and cultivated land is a normal phenomenon in rural land use change. Understanding the relationship between cultivated land and rural settlements is of great significance to agricultural production and rural development in the context of global rural revitalization. Previous studies have often focused on the quantitative contribution of the occupation of rural settlements to the loss of cultivated land (Su et al., 2011;Ju et al., 2018;Wang J et al., 2018;Li and Song, 2019). Some studies have also explored the spatial relationship between rural settlements and cultivated land (Guan et al., 2012;Wu et al., 2019;Luo et al., 2020). For example, the area ratio index is used to reflect the spatial distribution relationship between cultivated land and rural settlements (Ma et al., 2018;Wu et al., 2019). However, there are few in-depth discussions on the spatiotemporal interaction between rural settlements and cultivated land. Some related studies focused on the spatiotemporal interaction based on large-scale statistical data and remote sensing data on national scale Qu et al., 2019) and economically developed areas (Long et al., 2009), but there is still a lack of patch-scale research based on the vector data, which can accurately identify the dynamic changes of rural settlements with fragmentation characteristics.
The karst region of southwestern China is one of the largest continuous karst regions in the world . It is a typical ecologically-fragile region, with widespread rocky desertification (Tang et al., 2022). The population density in this area is 1.5 times of the average population density in China, and more than 2 times of the theoretical maximum population density in the karst area (Karst Rocky Desertification Bulletin, China https://www.mnr.gov.cn/dt/ywbb/201812/t20181217_ 2379630.html). The strained man-land relationship plays a critical role in the spread of rocky desertification (Jiang et al., 2014;Wang et al., 2019). Due to the lack of high-quality cultivated land, farmers here are forced to cultivate a large number of slope land for their livelihoods, which aggravates water and soil erosion, and produces new rocky desertification . Meanwhile, the economic development of the karst region is backward, especially in rural karst region Yang et al., 2021). Therefore, the karst region is the key and difficult area of rural revitalization in China, and it is urgently to formulate targeted revitalization strategies for such typical areas.
This paper analyzed the spatiotemporal interaction between rural settlements and cultivated land in a karst mountainous area (Qixingguan District) of China. The study attempts to address the following issues: 1) What are the spatiotemporal changes of rural settlements and cultivated land in the karst mountainous area? 2) What is the interaction relationship between rural settlements and cultivated land at the patch and administrative scale? 3) What factors drive these changes and relationships? The research results can provide a theoretical basis and method support for the optimization of settlement space layout and the sustainable utilization of cultivated land of typical regions in the context of rural revitalization.

Overview of the study area
Qixingguan District (27°03′N-27°46′N, 104°51′E-105°5 5′E) of Bijie City is located in the northwest of Guizhou Province, China. The total area is 3410.98 km 2 , of which cultivated land accounts for about 40% (Fig. 1). The terrain of the Qixingguan District is high in the west and low in the east, with an average altitude of 1511 m. The karst landscape is widely distributed in Qixingguan District. The fragile ecological environment and special geological conditions lead to the scarcity of high-quality cultivated land, backward rural develop-ment and tense man-land relationship (Yang et al., 2021;. Qixingguan District is an important political, economic, cultural, and transportation center in the northwestern Guizhou. In March 2020, Qixingguan District successfully got rid of poverty. In 2021, the per capita disposable income of urban residents was 39 384 yuan (RMB), and that of rural residents was 12 625 yuan (RMB) (the People's Government of Qixingguan District, Bijie City, http://www.bjqixingguan.gov.cn/). The socioeconomic development has promoted the rapid expansion of settlements and aggravated the conflict between settlements and cultivated land.

Data sources and preprocessing
The vector and raster data used in this study were provided by the Qixingguan District Bureau of Natural Resources. The vector data include the land use and land cover (LULC) data in 2009 and 2018 and township boundaries of Qixingguan District (1: 10 000). According to the land classification criteria in the Technical Specification for the Second National Land Survey (TD/T 1014(TD/T -2007, cultivated land (including dry land, paddy land and irrigated land) and rural settlements were extracted from LULC data, and the remaining LULC types were reclassified into garden land, forest land, grassland, transportation land, water and con- Qingshuipu H eg ua nt un F a n g z h u X ia o ji c h a n g C e n g ta i Datun Z h u c h a n g Xiaoba Q in g c h a n g L i a n g y a n Changchunbao Y a n g j i a w a n Q ia n x i T ia n k a n Tianbaqiao Longchangying 0 100 km 50 0 20 km 10 Liucangban D a x i n q i a o b a n S a n b a n q i a o b a n Shixiban G u a n y in q ia o b a n

Conversion relationship calculation
This study focuses on the conversion relationship between rural settlements and cultivated land and other LULC types. A LULC change matrix of Qixingguan District from 2009 to 2018 was constructed. Then, for each LULC type, the percentage of 'conversion loss to' or 'conversion gain from' in relation to the total 'loss or gain' conversion of rural settlements or cultivated land was calculated according to Equation (1).
where i is rural settlements or cultivated land; j is a LULC type other than LULC type i; P loss (i), j is the percentage taken by LULC type j in the total 'conversion loss' of rural settlements or cultivated land; S ij is the area converted from type i to j; S i* is the total area of type i in 2009; S ii is the area of type i that did not change during the study period. P gain (i), j is the percentage taken by LULC type j in the total 'conversion gain' of rural settlements or cultivated land; S ji is the area converted from type j to i; S *i is the total area of type i in 2018.

Kernel density estimation (KDE)
Kernel density estimation (KDE) is a non-parametric estimation method used to estimate an unknown probability density function (Brunsdon, 1995;Peng et al., 2016). The KDE estimates the value of the probability density of a raster pixel using neighborhood analysis based on the distance decay function. The higher the estimated value of probability density, the greater the distribution density of the research object (Hai et al., 2013). In this study, The KDE was used to identify the spatial distribution characteristics of the patches where rural settlements and cultivated land were converted to each other (Dong et al., 2022). The smoothness of the KDE result map is affected by the output raster size and search radius (Wu et al., 2019). After many experiments, the output raster size was finally determined to be 100 m, and the search radius was 5 km.

Landscape pattern analysis and expansion mode identification
Landscape indexes are the quantitative expression of landscape pattern information, reflecting landscape structural composition and spatial configuration (Zhou et al., 2018;Li J H et al., 2020). According to the structural characteristics of landscapes in the karst mountainous area, the number of patches (NP), the patch density (PD), the largest patch index (LPI), the landscape shape index (LSI), the mean patch size (MPS), the area-weighted mean patch fractal dimension (AWMPFD) and the aggregation index (AI) were used in this study. The cultivated land patches occupied by rural settlements during the study period were restored to the existing cultivated land landscape in 2018, and the changes of landscape indexes before and after restoration were compared to explore the impact of cultivated land occupied by rural settlements on the overall cultivated land landscape pattern.
In addition, this study also quantitatively identified the spatial expansion modes of rural settlements when occupying cultivated land through the Landscape Expansion Index (LEI). Different from the conventional landscape indexes, LEI not only reflects the spatial pattern of landscape, but also contains the dynamic change process information of landscape pattern . In this study, the buffer around the target patch was used in the calculation of the LEI  (Equation (2)).
where LEI is the landscape expansion index of a new rural settlement patch that have occupied cultivated land; A 0 is the area of the intersection between the buffer zone of a new rural settlement patch and the old rural settlement patches; A v is the difference between the area of the buffer zone and A 0 . The range of LEI is [0, 100). When LEI = 0, the expansion mode of the patch is outlying; when LEI is (0, 50), the expansion mode of the patch is edge-expansion; when LEI is [50, 100), the expansion mode of the patch is infilling .
The buffer distance has a great impact on LEI. Jiao et al. (2015) believed that a very small buffer distance in LEI may lead to an overestimation of the outlying patch, and the buffer distance needs to be set in geographic context. Therefore, considering the scattered distribution of rural settlements, the buffer distance in this study was set as 50 m.
In addition, when identifying the expansion modes, we also considered the relationship between the new rural settlement patches and the traffic roads. If the new rural settlement patches that have occupied cultivated land are located within 50 m of the traffic roads, the expansion mode is along traffic roads, otherwise, the expansion mode is not along traffic roads.

Area ratio index of cultivated land to rural settlements (ARICR)
At the administrative scale, the area ratio index of cultivated land to rural settlements (ARICR) was used to explore the spatial distribution and temporal changes of the quantitative relationship between cultivated land and rural settlements in the Qixingguan District (Gan et al., 2015;Ma et al., 2018;Wu et al., 2019) (Equation (3)).
where S C is the total area of cultivated land in the township administrative region, and S R is the total area of rural settlements in the township administrative region. The larger the ARICR, the richer the cultivated land resources in the township administrative region, and the less strained the man-land relationship.

Binary logistic regression
Binary logistic regression is one of the most used meth-ods for modelling data when the outcome variable is dichotomous (Yu et al., 2017;Buya et al., 2020). At the patch scale, the number of patches reclaimed from rural settlements to cultivated land was very small, it does not meet the requirements of constructing a quantitative model. Therefore, this study only explored the natural and location conditions of cultivated land that was more easily occupied by rural settlements. We analyzed the relationship between whether cultivated land was occupied by rural settlements and its natural and location conditions using binary logistic regression. In this study, the dependent variable (Y) denotes whether the cultivated land was occupied by rural settlements or not. When Y = 1, it means that the event of cultivated land being occupied by rural settlements occurred, and when Y = 0, it did not occur.
where p is the probability of the event occurring in the range [0, 1]. p/(1-p) is the probability of an event occurring divided by the probability of the event not occurring (Odds). Logarithmic transformation is performed on Odds to obtain a linear model of the logistic regression model (Equation (5)).
The random sampling was used in this study. We extracted an equal number of samples from the cultivated land occupied by rural settlements and the existing cultivated land in 2018 to ensure that the dependent variables Y = 1 and Y = 0 have roughly the same prediction accuracy (Xie and Li, 2008;Shu et al., 2021). The driving factors 'slope conditions' and 'rocky desertification types' are the disordered categorical variables. According to soil and water conservation science, cultivated land with a slope degree > 15° is not suitable for farming because it is easy to cause soil erosion (Yu and Hu, 2003). Therefore, we divided the factor 'slope conditions' into two categories: slope degree > 15° is 'unsuitable slope condition for farming', and slope degree < 15° is 'suitable slope condition for farming'. The reference object in the regression model is 'suitable slope condition for farming'. The factor 'rocky desertification types' was also divided into 'no rocky desertification' and 'rocky desertification', with 'no rocky desertification' as a reference object. For location factors, we used the near tool of ArcGIS to calculate the distance between the cultivated land and the elements such as traffic roads and old rural settlements. Then the distance was divided into different distance ranges according to equal spacing. Considering the actual situation of the study area, when dividing the distance range, the spacing of the distance to the traffic roads and the old rural settlements was set to 100 m, the spacing of the distance to the waters and the towns was set to 200 m, and the spacing of the distance to the cities was set to 500 m. By assigning values to different distance ranges of 1, 2, 3..., we converted the continuous variables into ordered categorical variables.
The model test includes a multicollinearity test between independent variables and a validity test of model results. Variance inflation factor (VIF) was used to test the multicollinearity of the independent variables. When VIF < 10, it indicates that there is no multicollinearity (Cheng et al., 2022a). The model results were tested by Hosmer-Lemeshow (HL) index. When the HL index is not statistically significant, the model fits well.

Optimal parameters-based geographical detectors (OPGD)
The geographical detector is a set of statistical methods that detect spatial heterogeneity and reveal the driving force behind it. The core idea of it is that if an independent variable has an important influence on a dependent variable, the spatial distribution of the independent and dependent variables should be similar (Wang et al., 2010;Wang and Hu, 2012). At the administrative scale, the optimal parameters-based geographical detectors (OPGD) model was used to explore the driving mechanism of the changes in the ARICR (Song et al., 2020;Zhang et al., 2022). The OPGD model can select the best combination of discretization method and the break number for each geographical continuous variable (Song et al., 2020). It solves the subjective selectivity of discretization (Mamattursun et al., 2022). In this study, we mainly used the factor detector, the core part of geographical detector, to explore which driving factors were more important. Considering previous studies and the accessibility of statistical data at the township level, 16 factors were selected from four aspects (Table 2). Agricultural development is reflected by the quantity of cultivated land resources, grain yield and the proportion of agricultural workers to rural practitioners. Rural development is reflected by the proportion of villages with cable TV, the construction of rural roads, the scale of rural settlements and population, as well as the changes of the rural labor resources, which are all important factors in achieving quality rural development. Social development of the townships is reflected by the development of educational, medical and business service facilities. Economic development is reflected by the average nighttime light index, the total output value of industrial enterprises, the land urbanization rate and the rural-urban development divide Li Hongbo et al., 2014;Zhang and Cui, 2015;Liu et al., 2019). The 16 factors were the independent variables, and the change of the ARICR of the township administrative regions was the dependent variable.

Spatiotemporal conversion between cultivated land and rural settlements
From 2009 to 2018, in Qixingguan District, the total 'conversion loss' area of cultivated land was 44.13 km 2 , and the total 'conversion gain' area of cultivated land was 3.69 km 2 ; the total 'conversion loss' area of rural settlements is 0.68 km 2 , and the total 'conversion gain' area of rural settlements area is 4.19 km 2 . We used Sankey diagram to illustrate the direction of 'loss or gain' conversion of rural settlements and cultivated land (Fig. 2). Over the period from 2009 to 2018, the expansion of cities and towns and the construction of traffic roads were the main reasons for the loss of rural settlements and cultivated land. More than 40% of the lost cultivated land was occupied by cities and towns, and more than half of the lost rural settlements were occupied by transportation land. Conversion between rural settlements and cultivated land was also frequent. For the new cultivated land, the contribution of rural settlements was only 2.68%. For the new rural settlements, the contribution of the cultivated land was as high as 85.45%. The results of KDE show the spatial distribution characteristics of the mutual conversion patches between rural settlements and cultivated land. The higher the density value, the greater the distribution density of the mutual conversion patches in the area. The number of patches converted from cultivated land to rural settlements was large. The distribution density of the patches converted from cultivated land to rural settlements in the southeastern Qixingguan District was higher than that in other regions, and the range of high-density areas was the largest. There are also some high-density areas in the southwestern Qixingguan District. Overall, the conversion of cultivated land to rural settlements in the southern Qixingguan District was more intense than that in the northern part (Fig. 3a). The number of patches converted from rural settlements to cultivated land was very small and the area was much smaller than that of patches converted from cultivated land to rural settlements, with only a small area of high-density distribution in the southwest of Qixingguan District (Fig. 3b).
Landscape pattern analysis shows that the occupation of rural settlements had a negative impact on the landscape pattern of cultivated land. We firstly calculated the landscape indexes of the existing cultivated land in 2018, then calculated the landscape indexes again after restoring the cultivated land patches occupied by rural settlements. The results show that (Table 3), after including the cultivated land patches occupied by rural settlements, the value of NP, PD and LSI of cultivated land landscape decreased, and the value of MPS and LPI increased, indicating that the fragmentation degree of the cultivated land landscape decreased and the patch shape was more regular. The value of AWMPFD and AI increased, indicating that the cultivated land landscape is less disturbed by human activities and the landscape is more concentrated. Therefore, the occupation of rural settlements made the cultivated land landscape more fragmented.
There were six spatial expansion modes of rural settlements when occupying cultivated land in  (Fig. 4). The EA mode had the largest proportion of area, followed by the OA mode;   Notes: NP is the number of patches, PD is the patch density, LPI is the largest patch index, LSI is the landscape shape index, MPS is the mean patch size, AWMPFD is the area-weighted mean patch fractal dimension, AI is the aggregation index the area proportion of the IA mode is the smallest. In summary, more than half of the cultivated land occupied by rural settlements was distributed near the old rural settlements and the traffic roads in Qixingguan District. At the administrative scale, the occupation of cultivated land by rural settlements occurred in all township administrative regions, and the area is large (Fig. 5a). But only a few township administrative regions had cultivated land reclaimed from rural settlements, and the area is small (Fig. 5b). The ARICR reveals the dynamic relationship between rural settlements and cultivated land in Qixingguan District at the administrative scale. Firstly, if only focused on the quantity of cultivated land, the cultivated land resources in Qixingguan Dis-trict were relatively rich. The ARICR averaged 18.75 in 2009 and 17.21 in 2018. Secondly, the value of the ARICR of all township administrative regions in 2018 was lower than that in 2009 (Fig. 5c), indicating that the cultivated land resources became scarce, and the conflict between man and land gradually emerged. Third, the administrative regions with a large reduction in the ARICR were the three subdistricts in the Urban District, the townships of Lishu and Xiaoba near the Urban District. The northeast and the southwest of Qixingguan District had little changes in the ARICR.

Factors influencing the conversion between rural settlements and cultivated land
The multicollinearity test was made before modeling the The results showed that the VIF values of all independent variables were less than 10, indicating that the problem of collinearity between independent variables is not serious. So, all independent variables can be included in the logistic regression model ( Table 4). The prediction accuracy of the final logistic regression model was 64.7%. The significance of the HL index is 0.32, which is greater than 0.05 and statistically insignificant, indicating that the fitting effect of the model is very good.

Wladχ 2
The statistic represents the relative weight of each driving factor in the model. The larger the value, the more significant the influence of the driving factor on the probability of event occurrence. The occurrence ratio (OR) represents the change in the multiple of event occurrence ratio for each additional unit of the driving factors, which can be used to understand the influence of driving factors on event occurrence probability.

Waldχ 2
According to statistic, the influence degree of these driving factors from big to small is: distance to old rural settlements > distance to towns > slope conditions > rocky desertification types > distance to waters > distance to cities > distance to traffic roads. Except for 'distance to traffic roads', the significance level of the other six factors is lower than 0.01. The values of these six factors of the cultivated land patches occupied by rural settlements are visualized in Fig. 6. Although the modes of rural settlements when occupying cultivated land show that most of the occupied cultivated land was distributed near traffic roads (Fig. 4), the importance of the factor 'distance to traffic roads' in the results of logistic regression was very small. This may be because most of the cultivated land in the study area, whether occupied by rural settlements or not, was distributed near the traffic roads. About 53% of the cultivated land in Qixingguan District was distributed within 100 m from the traffic roads, and about 77% of the cultivated land was distributed within 200 m from the traffic roads. Therefore, when exploring the conditions under which cultivated land was more likely to be occupied by rural settlements, the factor 'distance to traffic roads' was not significant. Among the natural factors, the probability of cultivated land with a suitable slope condition for farming being occupied by rural settlements was 1.44 times higher than that with an unsuitable slope condition for farming (OR = 0.694). The probability of cultivated land without rocky desertification being occupied by rural settlements was about 1.53 times higher than that of cultivated land with rocky desertification (OR = 0.652). That is, cultivated land with superior natural conditions was more likely to be occupied by rural settlements in Qixingguan District. Among the cultivated land occupied  by rural settlements, 42.06% was with unsuitable slope condition for farming and only 15.60% was with rocky desertification. The cultivated land and rural settlements in the karst mountainous area were in fierce competition for land with superior natural conditions. Among the location factors, the coefficients β of the three factors of 'distance to traffic roads', 'distance to towns' and 'distance to old rural settlements' in the logistic regression model are negative, indicating that with the decrease of distance to traffic roads, distance to towns and distance to old rural settlements, the probability of cultivated land occupied by rural settlements increased ( Table 4). As the distance between the cultivated land and the nearest traffic roads, towns or old rural settlements decreased by one level, that is, the distance to the traffic roads decreased by 100 m, the distance to the towns decreased by 200 m, and the distance to the old rural settlements decreased by 100 m, the probability of cultivated land being occupied by rural settlements would increase by about 1.11 times (OR = 0.897), 1.03 times (OR = 0.969) and 2.00 times (OR = 0.499), respectively. The coefficients β of the two factors of 'distance to waters' and 'distance to cities' are positive, indicating that the closer the distance to waters and cities, the less the probability of cultivated land being occupied by rural settlements.

Driving mechanism at the administrative scale
The factor detector reveals the relative importance of driving factors with a Q statistic. The larger the Q value is, the stronger the influence of the factor on the changes of the ARICR is. According to calculation results of factor detector, all factors passed the significance test (P < 0.01). The factor that had the greatest influence on the changes of the ARICR is the 'rural-urban development divide' (Q value = 0.89), and the factor that had the least effect is the 'number of rural populations' (Q value = 0.47). Overall, the influence of economic development on the changes of the ARICR is the largest, followed by social development and agricultural development, and the influence of rural development is relatively low (Fig. 7).
Pearson correlation analysis was performed on the 16 factors, and the results are shown in Table 5. Among the factors of agricultural development, the 'proportion of cultivated land' and the 'proportion of agricultural workers' were positively correlated with the changes of the ARICR, while the 'grain yield per unit area' was negatively correlated. All factors of rural development were positively correlated with the changes of the ARICR. Meanwhile, all factors of social development and economic development were negatively correlated with the changes of the ARICR.
The results of the OPGD and pearson correlation ana-  lysis show that the factors representing agricultural development that had the greatest influence on ARICR is the 'grain yield per unit area'. The higher the grain yield per unit area of the township administrative region, the more the ARICR decreased. Cultivated land and agricultural workers are important resources for agricultural development, and the more abundant the resources of cultivated land and agricultural workers in the township administrative region, the less the ARICR decreased.
The Q values and pearson correlation coefficients of each factors representing rural development are small, and their effects and linear correlations on the changes of the ARICR were weak. In contrast, the factors representing social and economic development had strong effects and negative correlations on the changes of the ARICR. This suggests that better social and economic development of the township administrative regions resulted in more reduction of ARICR. The Q values and pearson correlation coefficients for both 'land urbanization rate' and 'rural-urban development divide' are large, indicating that these two factors contributed the most to the decrease in ARICR.

Policy and planning effects on the conversion between cultivated land and rural settlements
Policies to promote economic and social development increase the risk of cultivated land being occupied by rural settlements. In recent years, a series of policies such as China's western development strategy, Guizhou Province's powerful industrial province strategy and targeted poverty alleviation, as well as the realization of X 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 Fig. 7 Results of the factor detector of the driving factors at the administrative scale in Qixingguan District of Bijie City, Guizhou Province Note: ** indicates that correlation is significant at the 0.01 level opening expressways in all counties have made the economy and society of Qixingguan District developed rapidly. In 2009, the urbanization rate of Qixingguan District was 34.95% and the regional GDP was 10.15 billion yuan (RMB), and in 2018, the urbanization rate was 51.49% and the regional GDP was 38.00 billion yuan. In 2020, Qixingguan District successfully eliminated poverty. The rapid development of the economy and society has increased the demand for construction land. In addition, when food security was not received enough attention, people often choose to use construction land with more economic benefits to occupy cultivated land in the face of tight land resources and economic development needs. The results were the rapid expansion of construction land including rural settlements and the rapid reduction of cultivated land. Therefore, the ARICR of all township administrative regions decreased in Qixingguan District during 2009-2018. The reclamation of rural settlements into cultivated land is mainly promoted by policies and planning. Qixingguan District began to implement the policy 'linking the increase of land for urban construction with the reduction of land for rural construction' in 2011, and tried to combine it with poverty alleviation relocation in 2016. These measures to some extent promoted the reclamation of rural settlements into cultivated land. Recently, Qixingguan District has actively explored innovative ways to realize the economical and intensive utilization of land resources, and has made a series of achievements in land remediation projects, the construction of high-standard basic farmland, topsoil stripping and reusing projects and the development and utilization of urban inefficient land. It was awarded as a model county for economical and intensive use of land resources in 2016. However, these results of the quality improvements cannot be reflected in land use data, resulting in less rural settlements reclaimed to cultivated land in Qixingguan District between 2009 and 2018.
Regional planning would influence the spatial layout and dynamics of rural settlements and cultivated land. Planning would affect the development direction of a region. In Qixingguan District, the six subdistricts in the Urban District, and the townships of Yachi, Changchunbao, Salaxi and Haizi have a larger area of urban, and are the focus of regional urban development and long-term planning. According to the Qixingguan Regional Rural Construction Plan (2017-2035, the three townships of Haizijie, Yachi and Bazhai and the six subdistricts in the Urban District were designated as the central urban area of Bijie City and assumed comprehensive functions. The two townships of Salaxi and Yanzikou were designated as the key towns of the region and undertook the function of central service place. The content of the plan fully showed that the economic and social development of these towns was better than that of other towns, and they also undertook more functions of regional development. Therefore, Yachi and Salaxi were the two townships with the largest area of cultivated land converted into rural settlements.

Interactive mechanism between rural settlements and cultivated land
As a typical karst mountain area, the interactive mechanism between rural settlements and cultivated land in Qixingguan District had regional characteristics. Previous studies have shown that rural settlements are more likely to occupy high-quality cultivated land (Gude et al., 2006;Conrad et al., 2015;Ju et al., 2018). The results of this study also prove that cultivated land with a suitable slope condition for farming and no rocky desertification was more likely to be occupied by rural settlements. More than 50% of the cultivated land with a suitable slope condition for farming and more than 80% of the cultivated land without rock desertification were occupied by rural settlements in Qixingguan District from 2009 to 2018. It is fully demonstrated that the rural settlements and cultivated lands in karst mountainous area compete fiercely for the land with superior natural conditions. The natural environment with the extensive sloping cultivated land and serious rocky desertification makes the land resources suitable for farming or living in karst mountainous area scarce, which is the fundamental factor restricting the spatial distribution of rural settlements and cultivated land in this area.
Better location conditions often represent the ability to receive more economic, policy and other development resources radiation and better exchange of goods, labor and other supplies. So rural settlements tended to occupy cultivated land closer to towns, traffic roads and old rural settlements. Towns are generally the center of political, economic, cultural and life services in rural areas, with strong agglomeration functions. Rural settlements gradually close to the town, relying on road connections to form an organic system of villages and towns, which is the basis for the formation of townships. Meanwhile, the Qixingguan District is rich in water resources, when expanding settlements, people here were more concerned with avoiding floods than the convenience of water intake (Zhou et al., 2013), so they tended to build settlements farther away from the waters.
Although the closer to the cities also represents better development conditions, the cultivated land here may be more occupied by the expanding cities. Urbanization and economic development have an important impact on the reduction of cultivated land, increasing the pressure on cultivated land (Deng et al., 2015) while providing a good economic basis for the expansion of rural settlements. The cultivated land was facing the double pressure of being occupied by urban and rural settlements. The results of the exploration of the driving mechanism at the administrative scale also indicate that the higher the land urbanization rate and larger the urban-rural development divide, that is, the better the economic and social development of the township administrative regions, the more the ARICR decreased. More than half of the lost cultivated land in Qixingguan District has been converted to cities, towns and rural settlements. Notably, the Urban District is an important support for the economic development of Qixingguan District (Yang et al., 2021). The regions near the Urban District were easily affected by the radiation of development of the Urban District. Therefore, the three subdistricts in the Urban District and the townships of Lishu and Xiaoba around the Urban District had become hotspots for the reduction of the ARICR. The area of the cultivated land occupied by rural settlements was the most in the Yachi near the Urban District. The northeastern part of Qixingguan District had a backward location and economic conditions, where the conversion between cultivated land and rural settlements was not intense, and the ARICR did not change much. The southwest part of Qixingguan District was rich in cultivated land resources and was a typical agricultural area. The expansion of rural settlements was less, and there were many rural settlements reclaimed as cultivated land.
At the administrative scale, the township administrative regions with more agricultural resources, namely cultivated land and agricultural workers, have a greater the proportion of agriculture in the setup of production. Such regions may be the traditional agricultural areas with a strong dependence on cultivated land and are less likely to occupy cultivated land. Meanwhile, agricultural income was limited. So farmers in these areas did not have sufficient economic capacity to expand settlements (Yang et al., 2015). Abundant agricultural resources had a positive effect on maintaining a high ARICR in Qixingguan District. Grain yield per unit area reflects the agricultural production capacity of township administrative regions. The township administrative regions with higher grain yield per unit area can meet the grain demand with less cultivated land, making it possible to reduce the area of cultivated land used for food security in the regions (Wang et al., 2022). Rural development was positively correlated with the changes of the ARICR. ARICR decreased less in the township administrative regions with good rural development. The traditional Chinese rural areas have the characteristics of closedness and stability, with less communication with the outside and slow changes of their own. It can be found through statistics that the changes of cultivated land and rural settlements in the township administrative regions with better rural development in Qixingguan District are small, resulting in less reduction of ARICR. And rural areas affected by urban development would change their own development. Rising non-farming wages and the opportunity costs of farming have contributed to a massive loss of rural labor and the abandonment of cultivated land (Liao et al., 2021). The reduction of cultivated land was higher in the township administrative regions where the number of rural labor resources decreased, resulting in a large decrease in ARICR.

Optimization path for rural settlements and cultivated land in karst mountainous area
According to the correlation characteristics and interactive mechanism between rural settlements and cultivated land in karst mountainous area, we proposed the targeted optimization path in karst mountainous area (Fig. 8).
The first is the optimal reconstruction path of rural settlements. Effective village planning should be designed and practically promoted. The development of rural settlements must be guided by village planning. The number, scale, and layout of rural settlements should be adjusted at the macro level. The spatial distribution characteristics of cultivated land and rural settlements in karst mountainous area and their interaction should be fully considered in the planning. This study found that the expansion of rural settlements is more likely to occur in places closer to the old rural settlements and towns. Thus, new rural settlements can be built in an orderly, intensive, and compact way through the guidance of village planning and land remediation projects. Rural depopulation in karst mountainous area is serious, and the rural population in Qixingguan District decreased by more than 140 000 from 2009 to 2018. Meanwhile, the area of rural settlements is increasing, and the land use efficiency of rural settlements is low. Therefore, comprehensive land consolidation should be carried out within rural settlements to revitalize rural stock land. The idle and abandoned homesteads should be reclaimed or reused in time, and the exit system of rural homesteads should be improved. Meanwhile, the same attention should be paid to the protection of traditional characteristic villages.
The second is the comprehensive conservation path for the quantity, quality and ecology of cultivated land. Although the quantity of cultivated land in Qixingguan District is relatively rich, the cultivated land with suitable slope condition for farming and without rocky desertification accounted for only 22.43%. Expanding rural settlements and urban also greatly threaten the high-quality cultivated land. The high population density in this area forced more slope land to be cultivated, which aggravated rocky desertification and formed a vicious circle. Vulnerable karst is not suitable for high-intensity agricultural development . Therefore, returning the cultivated land with unsuitable slope condition for farming or with rocky desertification to forest and grassland in karst mountainous area should be realized as early as possible in order to protect the ecological environment. At the same time, agriculture based on forage grass and woody crops and ecotourism can be developed combined with regional characteristics . Sufficient food production can be ensured through high-standard cultivated land construction projects on cultivated land with good natural conditions and location conditions. Strengthen-  ing land use control is also necessary. New rural settlements should make more use of wasteland and bad land rather than high-quality cultivated land. Dynamic equilibrium of the total cultivated land system also needs to be improved to comprehensively maintain and improve the production, ecological and living functions of agricultural ecosystems, and realize the protection of the quantity, quality and ecology of the cultivated land. The last is the urban-rural integration development path. In 2018, the rural population of Qixingguan District accounted for 57.86% of the total population, and the population urbanization rate was only 42.13%. Rural revitalization in the karst mountainous area needs to be combined with the urbanization process. In 2006, the policy of 'linking the increase of land for urban construction with the reduction of land for rural construction' was enacted in China (Yu et al., 2018). However, during the study period, the reduction of cultivated land in Qixingguan District was mainly due to the occupation of urban land, and the proportion of new cultivated land reclaimed from rural settlements was also small. Therefore, we should continue to strengthen the control of the phenomenon of construction land occupying cultivated land and promote the reclamation of rural settlements. The policy of 'linking the increase of land for urban construction with the reduction of land for rural construction' can be combined with poverty alleviation relocation projects, guiding people to concentrate from remote and unlivable rural settlements to nearby towns, and reducing the number of rural populations and villages. Abandoned rural settlements need to be reclaimed into forest land or cultivated land. The reduction of population pressure can facilitate the recovery of the karst ecosystem. The development of small towns, key towns and central villages in karst mountainous area should be strengthened. Taking small towns as the center, each village can be connected through the road network to establish a characteristic town and village system in karst mountainous area. The deep integration of the rural economy and urban economy can be promoted through urban radiation, providing an economic foundation for rural revitalization .

Conclusions
With the rapid development of the economy and the continuous expansion of urban, the conflict between rur-al settlements and cultivated land has become increasingly serious. Based on land use vector data, we analyzed and identified the spatiotemporal conversion characteristics and interactive mechanism between rural settlements and cultivated land in a karst mountainous area (Qixingguan District) with fragile ecological environment and scarce land resources. From 2009 to 2018, the expansion of rural settlements and the loss of cultivated land coexisted in Qixingguan District. The occupation of rural settlements was an important reason for the decrease of cultivated land and made the cultivated landscape more fragmented. The cultivated land occupied by rural settlements was mainly located near the old rural settlements and the traffic roads. The ARICR of all township administrative regions in Qixingguan District in 2018 was lower than that in 2009, and the man-land relationship became strained. The conversion between rural settlements and cultivated land was more frequent in the southern Qixingguan District with better economic and social development than that in the northern region. The interactive mechanism of rural settlements and cultivated land in Qixingguan District had the regional characteristics. Restricted by the natural environment, the competition between rural settlements and cultivated land was fierce for the land with suitable slope condition for farming and without rocky desertification. Cultivated land closer to towns, roads and old rural settlements was more likely to be occupied by rural settlements due to better location conditions. The better the economic and social development of the township administrative regions, the more the ARICR decreased, while the richer the agricultural resources and the better the rural development of the township administrative regions, the less the ARICR decreased. The cultivated land in the administrative regions with better urban development was under double pressure from the expansion of urban and rural settlements, and the ARICR decreased obviously. The optimal reconstruction path of rural settlements, the comprehensive conservation path of cultivated land and the urban-rural integration development path in the karst mountainous area were proposed. The findings would provide a decision-making basis for optimizing the spatial layout of cultivated land and rural settlements in karst mountainous area, and would provide a theoretical basis for promoting the coordinated development of the rural manland relationship and rural revitalization in karst areas.