In the typical karst area covering basically the natural and socioeconomic backgrounds in the southwest karst region of China, we selected a total of six areas – the town of Beipanjiang in the county of Zhenfeng, the town of Pingle in the county of Anlong, Wangjiazhai small watershed in the city of Qingzhen, Houzhaihe in the county of Puding and the town of Dongtang in the county of Libo in Guizhou – as the study area (Fig. 1). These areas have different topography and combined patterns of land resources, including (1) peak-cluster depressions–canyon; (2) continuous closed peak-cluster depression group; (3) peak-cluster depression–valley combination; (4) open peak-cluster depressions; (5) peak-cluster depressions surrounded by flatland and shallow-peak-cluster depression (Fig. 1). The socioeconomic factors of these six study areas include different types of economic development and road accessibilities that are quite different. The Wangjiazhai is adjacent to the city, and its development is driven by the city. The Houzhaihe area is influenced by the county and town's economic radiation, Huajiang area's development is driven by the poverty-alleviating and KRD control policy and Dongtang is influenced by the national nature reserve. Pingle is in the karst mountain hinterland which is away from town traffic trunk roads, resulting in an area with slow development.

The land use data used in the study, including data on settlements and cropland, come from the interpretation of Advanced Land Observation Satellite (ALOS) images (with a resolution of 10 m × 10 m) in 2010, combined with local agricultural statistics, field surveys distinguishing the characteristics of land use and KRD in 2011 and 2012 and 2.5 m supplementary images (with a resolution of 2.5 m × 2.5 m). The land use/cover types were divided into seven subclasses such as cropland, settlement, road, water, slope cropland, woodland and shrub grassland, by integrating the national standardized land classification scheme and the land use types of the local area. In this paper KRD classification criteria are described in Fig. 2, based on other researchers' work (Huang and Cai, 2007; Yue et al., 2010; Xu et al., 2013; Zhang et al., 2014). The NKRD (no karst rocky desertification) refers to the concentrated and contiguous woodland and the flatland with no land degradation, the PKRD (potential karst rocky desertification) refers to the karst sloping land where the land ecosystem has been degraded slightly, but the percentage of bare rock is less than 30 % and the sloping cropland, shrub grassland may be in a land degradation state of LKRD (light karst rocky desertification), MKRD (moderate karst rocky desertification) or SKRD (severe karst rocky desertification). The distribution maps of land use and KRD land in six study areas were made using a the human–computer interactive interpreting method, and the vector data layers were amended according to the result of the field sampling inspection and investigation in 2010; the interpretation accuracy of sampling patches is more than 90 %. The topography, land use and KRD of these study areas are provided by Fig. 2. The slope gradient is generated by a digital elevation model, digitized according to the topographic map at a 1:10 000 scale.

Because the sloping cropland is still the main driving force of KRD (Li et al., 2015), farmland referred to in this paper is only that with a slope < 6∘; the area of flat cropland with a slope < 6∘ is used to represent land carrying capacity. The ratio of settlements area to the cropland area is used to represent population pressure, for which both data were acquired from ALOS image interpretation. The local agricultural statistics are used to verify the area of flat cropland and slope cropland further.

We consider assessing the land carrying capacity of six study sites according to the area and the spatial distribution of cropland patches. First, if the percentage of arable land resources of the total area is less than 10 %, we consider the study area to have a lack of arable land resources; if not, the study area is rich in land resources. Second, in order to further illustrate the spatial distribution of agglomeration and the fragmentation characteristics of cropland patches at six study sites, we divide the area of cropland patches into eight levels: 1. ≤ 0.1; 2. 0.1–1; 3. 1–5; 4. 5–10; 5. 10–20; 6. 20–50; 7. 50–100; 8. > 100 hm-2, and count the total number and total area of cropland patches of different size levels. Aggregation refers to the tendency of patch types to be spatially aggregated, so, the aggregation index of cropland patches was computed using FRAGSTATS 4.2. For the definitions and full descriptions of these metrics, please see FRAGSTATS 4.2 user's guide.

In the karst peak-cluster depression area, different combinations of small terrain have different proportions of flatland terrain (referred to as depressions in this paper) and form different area proportions of cropland resources. For the six study areas, the flat cropland area is the least at the peak-cluster canyon, in which small and scattered cropland patches are distributed. The area percentage of cropland at the peak-cluster depression–valley combination increases to 10.74 %, and this percentage at peak-cluster depression surrounded by shallow hills area is the highest (Table 1). In terms of the percentage of cropland resources accounting to total area, six study areas can be divided into three types. The continuous deep depressions, shallow depressions and peak-cluster canyon show a shortage of cropland resources; open peak-cluster depression and peak-cluster depression surrounded by shallow hills are comparatively rich in cropland resources and peak-cluster depression–valley is the transitional one between plenty and scanty cropland resources.

The most frequent size of croplands ranges from the groups < 0.1 to 0.1–1 hm2; there are only 17 cropland patches 20 hm2 and the total area of these 17 patches accounts for 67 % of the total cropland area in the peak-cluster depression–valley combination (Fig. 3). This indicates that the cropland is relatively concentrated and contiguous in this kind of landform with characteristics of big patches located in valleys and larger depressions, while small patches are located in small depression centers.

The number of croplands from 0.1–1 to 1–5 hm2 are 162 and 39, and their areas account for 28.24 and 36.12 % of the total cropland area respectively; there are only two patches between 10 and 20 hm2 accounting for 10.10 % of the total cropland area in the continuous deep depressions. The cropland patches with sizes of 0.1–1 hm2 are the most frequent at the shallow depressions areas in Dongtang. There are 37 patches of flat cropland, with a total area of 3.7 hm2, and the largest patch area is up to 0.56 hm2 in the peak-cluster–canyon combination. In the peak-cluster depressions surrounded by shallow hill, the cropland patches between 20 and 50 hm2 account for 35.11 % of the total cropland area. The cropland patches between 20 and 50 hm2 account for 39.68 % of the total cropland area in the open peak-cluster depressions.

According to characteristics of cropland in different sizes and their aggregation, we categorize the cropland spatial distribution of the six study areas into two types as follows: (1) fragmented cropland, including the continuous deep depressions, shallow pond depressions, peak-cluster canyon, in which there are a great number of cropland patches, with mainly 0.1–1 hm2, small and scattered cropland, accounting for a high proportion of the total cropland area; (2) centralized cropland, including peak-cluster depression–valley combination, peak-cluster depression surrounded by shallow hills and open peak-cluster depression. The cropland distribution of this type is relatively concentrated, and cropland patches with large sizes account for a high proportion of the total area.

A significant negative correlation exists between the percentage of cropland area and the percentage of KRD area (Table 2); the correlation coefficient is 0.5394. For continuous depressions, shallow depressions and peak-cluster canyon, the cropland accounts for less than 6 % and the KRD area account for over 50 %. Cropland area in peak-cluster depression–valleys accounts for 10.74 %, but its settlement area exceeds 20.32 %, so the areas over LKRD account for 60 %. Cropland is relatively rich in peak-cluster depressions, surrounded by shallow hills and open peak-cluster depressions. The area over LKRD accounts for 30 %, but the percentage of KRD area of open peak-cluster depressions is larger because of its higher ratio of settlement to cropland. Obviously, KRD is more serious for peak-cluster depressions with higher ratios of settlement area to cropland. The correlation coefficient between this ratio and KRD, MKRD and SKRD is 0.034, 0.5125 and 0.6824 respectively.

In order to reveal the corresponding relation between the change of cropland and the change of KRD around the settlements, furthermore, the settlements of the six study areas are taken as centers to build buffer belts with distances of 0–200, 200–400, 400–600, 600–800, 800–1000 and > 1000 m. Then, the changes of cropland and KRD land percentage in buffer zones of the six study areas are compared. The results show that the cropland decreases as the buffer distance increases. In areas within 400 m buffer distance, the cropland proportion in peak-cluster depressions surrounded by shallow hills is highest. The lowest is the peak-cluster canyon, and its cropland only distributes at this buffer range (Fig. 4). Correspondingly, the proportion of LKRD is highest within 200–400 m buffer distance, and reduces from peak-cluster canyon, continuous deep depressions, shallow depressions and peak-cluster depression valleys in turn.

The proportion of MKRD is highest within 200–400 and 0–200 m buffer distance, and the proportions of peak-cluster depression–valleys and continuous deep depressions are higher than the other four study areas. This proportion of MKRD of shallow depression area is less than 0.1 %.

The highest proportion of SKRD is within 0–200, and then 200–400 m buffer distance at the peak-cluster canyon area. The relatively high proportion of SKRD of peak-cluster depression–valleys is within 0–800 m; but at the open peak-cluster depressions area, this SKRD proportion is relatively high in 800–1000 m buffer distance, where the slope land had been cultivated, now abandoned. The SKRD proportion within 200–400 m buffer distance at the continuous deep depressions is 0.44 % and there is no SKRD in shallow depressions. What are the reasons for this phenomenon? We find that, in the karst mountains, the radius of cultivation is no more than 1000 m. If the ratio of cropland surrounding settlements is lower, then, the slope reclamation, deforestation and other irrational disturbance is more severe, which also leads to more frequent occurrence of KRD.

The analysis above shows that the KRD area and distribution is related to the quantity and distribution of cropland and settlement in the six study areas. Actually this relationship reflects human (settlements)–environment (cropland) interaction. Under the special human–environment relationship in karst peak-cluster depressions, these relationships reflect three scenarios of KRD processes.

The first scenario describes KRD with low land carrying capacity. Small cropland, small population, but population and arable land resources are at a low level of coordination, causing insignificant land degradation (KRD). Shallow depressions are an example of the first scenario. Cropland is small and population pressure exceeds land carrying capacity, which leads to mild or moderate degradation (mainly LKRD or MKRD). Continuous peak-cluster depression is typical in this scenario. The cropland is small, but population pressure exceeds land carrying capacity, causing land degradation (mainly SKRD and MKRD); Huajiang peak-cluster-valley is such an example.

The cropland resource pattern in peak-cluster depression areas is characterized by fertile land concentrated in depressions, and poor land or wasteland distributed on the peak-cluster slopes around the depressions. Although some cropland aggregation effects exist, but not to a great extent, and the scale is small; therefore, the farming radius is still large in this area (Wu et al., 2007). Generally, the gentle farmland forms slightly desertified KRD landscapes; the steep land forms moderately desertified karst rocky landscapes due to slope soil erosion which makes KRD landscape degrade more seriously (Yang et al., 2006).

Based on the above analysis, the present study put forward a theoretical hypothesis: in the peak-cluster depression areas, the proportion of negative terrain (referring to depressions, often cultivated land resources) may determine population distribution, and the realistic population pressure (population density) may determine whether the peak-cluster depression areas will be degraded. We use the percentage of flat cropland of the total area to represent land bearing capacity and the ratio of settlement area to cropland area to represent population pressure. The formation of KRD in the peak-cluster depression areas can be clarified according to the variations of these two indexes (Fig. 5). As the percent of cropland decreases and the percent of settlement dedicated to the croplands increases, the severity of KRD increases. That is to say, the more serious rocky desertification KRD only occurs under the regions of low land carrying capacity and high population pressure where farmers have to take extreme steep reclamation activities. Thus, in the peak-cluster depression areas, low land carrying capacity is the fundamental cause of KRD. In general, the harmony between depression area (flat terrain) and population determines the ecological quality of peak-cluster depression areas.

In Europe, five main quality indices such as climate, vegetation, soils, groundwater and socioeconomic quality are used to estimate the sensitivity to land degradation and desertification (Symeonakis et al., 2014); therefore, the mixture of endogenous (manual agriculture, fuel wood and fodder extraction, land tenure and steep slopes) and exogenous drivers (high rainfall variability, climate change, prolonged drought or heavy rainfall) must be taken into account in the process of combating desertification (De Pina Tavares et al., 2014). Moreover, changing governance and transition towards new political and economic structures have played a key role in shaping today's land degradation in the context of climatic variability (Stringer and Harris, 2014). The eco-environment of karst mountains is fragile and the land degradation is mainly driven by desertification processes. Generally speaking, lithology and soil type and road influence are identified as the leading factors influencing KRD (Xu and Zhang, 2014; Yang et al., 2013). The succession of KRD has had different impacts on soil fertility indicators (Xie et al., 2015); i.e., the genesis of KRD has been attributed to land mismanagement of local households (Wu et al., 2011) and it has been found that climate change accelerates rocky desertification in the karst areas (Xiong et al., 2009). However, it has not been clarified why the local farmers take land mismanagement (Yan and Cai, 2015). The relationships of settlements, cropland and KRD processes at six different peak-cluster depression combination areas are compared. Serious rocky desertification is found in areas with less cultivated land with a slope < 6∘, low land carrying capacity and big population pressure. This phenomenon confirms that the theoretical assumptions we proposed are correct. Therefore, we can assume that the main reason for KRD is population exceeding land carrying capacity in karst mountains of Southwest China; that is to say, low land carrying capacity leads to the conversion of sloping land into croplands, and this is the main driving factor leading to KRD (Ying et al., 2014). KRD is a kind of land degradation that occurs in vulnerable karst dryland socioecological systems (Bisaro et al., 2014; Yang et al., 2011). The nature of KRD in karst mountains is evident by low land carrying capacity and high population pressure.

The correlations between cropland richness, land carrying capacity and KRD can reasonably explain the occurrence of KRD at different scales. This paper can help reveal the cause of KRD formation. Additionally, this paper also pointed out the prevention and control measures of KRD, including increasing land carrying capacity or decreasing population. Revegetation alone is difficult to increase land carrying capacity, but decreasing population in the short term is also difficult, so increasing land carrying capacity is the primary means of controlling KRD.

The inadequacy of the analysis of the ratio of settlement to cropland is a disadvantage. Although studies show that the spatial distribution of settlements can replace population distribution (Niu et al., 2006), the shortcoming of this paper is the use of the settlement area only. Due to some settlements being abandoned in recent years, the changes of settlements and population may not be exactly the same. Therefore, further research should combine the evolution of the population and the livelihoods of farmers to calculate the land carrying capacity. Meanwhile, whether adjacent depressions of settlements are cultivated by farmers was not taken fully into account in some locations; this necessitates further field investigations.