Slope Structure Evolution and Spatial Competition Mechanisms Among Urban, Agricultural, and Ecological Spaces in China

Abstract

Rapid urbanization and stringent ecological protection policies in China have reshaped spatial competition among urban, agricultural, and ecological spaces. However, existing studies often overlook how this competition evolves across different slope structures. To address this, this study establishes a fine-scale analytical framework using H3 hexagonal grids and slope spectrum analysis to investigate slope structure evolution and spatial competition patterns from 1990 to 2023. The results reveal a distinct topographic stratification: urban space dominates low-slope regions (<6°) but exhibits a pervasive “upslope expansion” trend, with its average slope increasing from $1.81°$ to $2.07°$, equivalent to an annualized increase of approximately $0.008°{\mathrm{yr}}^{-1}$; agricultural space characterizes the transition zones (6–$15°$), showing an “upslope migration” in the Southeastern Hills associated with urban expansion pressure in low-slope areas; and ecological space functions as a stable barrier in steep terrains (>15°) but faces encroachment in transition zones. Furthermore, cluster analysis identifies significant regional heterogeneity aligned with China’s macro-topography, including “low-slope agglomeration” in the Eastern Plains, “interwoven upslope” patterns in the Southern Hilly Regions, and ecological dominance in the Western Highlands. Association analysis using GeoDetector and Multiscale Geographically Weighted Regression (MGWR) indicates that competition intensity is most strongly associated with human activity factors, especially human footprint and nighttime lights ($q>0.29$), which show the highest explanatory power among the examined factor groups. The interaction between human activity and elevation further shows relatively high explanatory power ($q=0.41$), suggesting that spatial competition is more pronounced where intensive human activities overlap with topographic constraints. Crucially, this study challenges the traditional flat-projection planning model. We propose a transition to “three-dimensional topographic regulation,” advocating differentiated management strategies—such as strict “slope redlines” for urban-agricultural transition zones—to mitigate intensifying spatial conflicts in complex terrains and safeguard agricultural sustainability.

1. Introduction

The United Nations’ 2030 Agenda for Sustainable Development establishes 17 Sustainable Development Goals (SDGs), serving as a comprehensive framework for global sustainability [1]. Within this framework, the interactions among Goal 2 (Zero Hunger), Goal 11 (Sustainable Cities and Communities), and Goal 15 (Life on Land) are characterized by a complex interplay of synergies and trade-offs [2,3,4]. Along with the unprecedented pace of global urbanization, urban areas are expanding rapidly, particularly in regions subject to resource and topographic constraints. Such expansion frequently encroaches upon agricultural and ecological spaces, exacerbating land-use conflicts that pit urban development against food security and ecological conservation [5]. Consequently, elucidating and quantifying the competitive dynamics among urban, agricultural, and ecological spaces along natural gradients through robust spatial indicators is imperative. This is not merely an abstract exercise in optimizing spatial development patterns, but is fundamentally tied to safeguarding regional food security and implementing rigorous agricultural land management [6,7]. In topographically constrained environments where highly productive flat arable land is naturally scarce, understanding the precise trajectories of these spatial shifts is essential to preventing agricultural displacement onto fragile terrains [8].

Topographic slope serves as a decisive natural constraint governing the spatial distribution and expansion trajectories of diverse land-use types [9]. Conventionally, a distinct vertical stratification exists: urban space clusters in low-slope regions [10,11,12], agricultural space occupies gentle-to-moderate gradients [13,14], while steep terrain is predominantly retained as ecological space [15,16]. However, in recent years, urban expansion has increasingly encroached onto higher-slope terrains [12,17], thereby challenging this traditional topographic equilibrium. This phenomenon of climbing uphill not only reconfigures the slope structure of land use but also is associated with novel competitive dynamics, intensifying ecological vulnerability in fragile mountainous environments. However, the barrier effect of topography is not uniform across regions. In areas with strong development demand, improved transportation infrastructure, or high land values in lowlands, slope constraints may be partly overcome through engineering investment and land development pressure, leading to upslope urban expansion [9,12,17]. In contrast, in regions with weaker development pressure or stricter ecological regulation, steep terrain may remain a stronger barrier to urban and agricultural expansion. Therefore, slope should be understood not only as a physical constraint, but also as a terrain-related condition whose effect varies with socioeconomic development, infrastructure investment, and land-use policy [18].

At the global scale, urban expansion has shown a measurable tendency to move toward steeper terrain, especially in rapidly urbanizing regions where flat land is increasingly scarce [9,17,19]. Global and regional land-use studies have also shown that urban expansion can directly and indirectly reduce natural areas and biodiversity-related land resources [5,20]. In mountain regions, hillside cultivation, farmland abandonment, and ecological restoration are closely related to terrain constraints and socioeconomic transformation, especially in European and Mediterranean mountain systems [21,22,23,24]. These studies provide useful comparative evidence for understanding agricultural marginalization and land-use transitions in topographically constrained regions. Meanwhile, landscape ecology and soil conservation studies have emphasized that topographic gradients are closely linked to erosion risk, ecological management, and ecosystem-service provision, providing a broader basis for slope-related ecological zoning [25,26,27]. Methodologically, hexagonal grids have been increasingly used in ecological and urban spatial analysis because of their relatively uniform neighborhood structure and reduced directional bias compared with square grids [28,29]. These international studies provide important comparative references, but most of them examine urban expansion, agricultural transition, ecological conservation, or grid-based spatial analysis separately. Few studies have integrated urban, agricultural, and ecological spaces into a unified slope-spectrum framework to examine how tripartite spatial competition varies along topographic gradients.

Previous studies have extensively investigated the interrelationships among urban, agricultural, and ecological (UAE) spaces across multiple scales, which can be categorized into three primary research streams:

(1) Quantification of spatial substitution dynamics based on land-use change detection. Utilizing methods such as transition matrices, change-patch interpretation, and urban expansion trajectory analysis, these studies quantitatively reveal the encroachment of urban space onto agricultural and ecological spaces, as well as the spatiotemporal characteristics of these displacements [20,30]. This research highlights the spatial coupling between the expansion of urban space in fringe areas and the loss of agricultural space, uncovering typical urbanization-driven conversion patterns that are particularly pronounced in rapidly urbanizing regions such as East and South Asia. (2) Structural evolution of urban fringes or peri-urban transition zones. By leveraging remote sensing monitoring, spatial metrics, and boundary-detection algorithms, this stream conducts in-depth analyses of boundary dynamics, expansion pathways, and transformation processes among UAE spaces [31,32,33,34,35,36]. This line of research emphasizes the frontier characteristics of urban growth, elucidating phenomena such as spatial squeeze and fragmented encroachment, thereby highlighting the pivotal structural role of boundary zones in shaping the tripartite competition. (3) Trade-offs and synergies from the perspectives of ecosystem services and policy regulation. Moving beyond traditional physical pattern analysis, this research shifts focus to how different spaces interact and complement each other in providing ecosystem services (e.g., food production, water conservation, and biodiversity maintenance), offering theoretical support for integrated spatial governance [26,27,37,38,39]. Concurrently, scholars assess these dynamics through the lens of land-use conflicts and institutional intervention, analyzing how regulatory frameworks–such as urban growth boundaries, farmland protection, and ecological redlines–intervene in and reshape the relationships among the three spatial domains [40,41].

Despite these advancements, current research remains constrained by several critical limitations. First, the analytical granularity is often too coarse to capture fine-scale spatial heterogeneity, as reliance on administrative boundaries frequently obscures localized topographic variations (the Modifiable Areal Unit Problem). Second, while spatial substitution is well documented, the structural evolution of land-use competition along natural gradients—specifically slope—is seldom explicitly quantified. Third, the comprehensive integration of spatial patterns and associated factors of this tripartite competition remains insufficient at the national scale. In addition, existing international studies provide valuable evidence on slope-related urban expansion, mountain agricultural transition, ecological conservation, and grid-based spatial analysis, but a unified framework for comparing the slope-dependent competition among UAE spaces remains underdeveloped.

China provides a representative case for examining this issue because rapid urbanization, strict cropland protection, ecological restoration, and strong topographic differentiation coexist within a single national land system. Given the intensifying spatial squeeze among urban, agricultural, and ecological spaces across topographic gradients, it is imperative to develop a fine-scale analytical framework that can identify where productive agricultural land is being displaced toward more constrained terrain. Although slope-spectrum analysis has been applied to individual land-use types, such as cropland slope change [42], few studies have simultaneously characterized the slope structures of urban, agricultural, and ecological spaces using a consistent fine-scale spatial unit. Moreover, while the competitive dynamics among these spaces have been widely examined through transition matrices and spatial metrics, the topographic-gradient dimension of this competition has not been systematically quantified at the national scale. Therefore, to address these gaps, this study integrates the H3 hexagonal grid system and slope spectrum analysis to systematically investigate the slope structure evolution and spatial competition patterns and associated factors of UAE spaces in China from 1990 to 2023. Specifically, the objectives of this study are to: (1) construct slope structure indicators using fine-scale H3 grids to capture the topographic dependence of agricultural, ecological, and urban spaces; (2) quantify the spatial competition intensity and identify the upslope displacement patterns of agricultural and urban spaces; and (3) utilize GeoDetector and Multiscale Geographically Weighted Regression (MGWR) models to examine the factors associated with the spatial differentiation of this competition. The innovation of this study is mainly reflected in three aspects. First, it represents one of the early attempts to adapt H3 hexagonal grids to slope-spectrum construction, providing a consistent fine-scale spatial unit for comparing slope structures across regions. Second, it extends the slope-structure indicator system developed in our previous work [13] to the simultaneous characterization of urban, agricultural, and ecological spaces at the national scale. Third, it develops a topography-sensitive analytical framework for interpreting how tripartite spatial competition is differentiated across low-slope, transition-slope, and steep-slope terrains.

2. Materials and Methods

2.1. Research Area

China, characterized by a vast territory and complex topography, exhibits a distinct three-step staircase terrain descending from west to east (Figure 1, all maps in this article are based on the approval number GS (2024) 0650 for China’s map shpfile, with data sourced from the National Geoinformation Public Service Platform). The landscape is dominated by mountains, plateaus, and hills, which collectively account for approximately 69% of the total land area [43], creating a highly heterogeneous foundation for land-use patterns. Governed by the interplay of topographic constraints, hydrothermal gradients, and uneven population distribution, China’s land-use structure shows pronounced regional differentiation.

In recent decades, rapid urbanization and industrialization have precipitated the accelerated expansion of urban space, particularly in resource-constrained regions where flat terrain is scarce. Consequently, cities are increasingly encroaching onto steeper slopes, a phenomenon that significantly alters the regional land-use structure and threatens ecological security. Statistics indicate that China’s urban space (construction land) expanded from $2.48\times {10}^7\mathrm{ha}$ in 1984 to $4.09\times {10}^7\mathrm{ha}$ in 2019, reflecting an average annual growth rate of 1.45% [44]. Driven by this massive demographic pressure and continuous urbanization, the demand for urban space is expected to remain inelastic in the foreseeable future. This trend will inevitably exacerbate the tripartite competition and spatial conflicts among urban, agricultural, and ecological spaces, making China an ideal study area for investigating slope-dependent land-use dynamics.

2.2. Data Sources

2.2.1. Urban–Agricultural–Ecological Space

Urban–agricultural–ecological space refers to a functional zoning approach based on land-use functions, which is closely linked to specific land-use types. This study employs the China Land Cover Dataset (CLCD) [45], which provides consistent, high-temporal-resolution land-use data across China from 1985 to 2023 [44,46]. The CLCD has been widely used in various research fields, including land-use change detection, ecological and environmental monitoring, and sustainable development assessments [47,48,49]. For this study, we selected the time series data from 1990 to 2023 and maintained the original 30-m resolution to ensure analytical robustness and comparability. Based on the land-use classification provided by the CLCD, this study integrates the categories into three major types: urban space, agricultural space, and ecological space (

Table 1. Urban–agricultural–ecological space classification system.

Category	CLCD Land-Use Type
Urban space	Impervious
Agricultural space	Cropland
Ecological space	Forest, Shrub, Grassland, Water, Snow/Ice, Barren, Wetland

). Urban space mainly refers to built-up land, corresponding to the Impervious class in CLCD, and serves as the core carrier of economic, social, and cultural activities. Agricultural space is represented by cropland, which is primarily devoted to food production and agricultural development. Although cropland also provides ecological services as a managed ecosystem, it is classified as agricultural space in this study according to its dominant production function. Ecological space consists of forests, grasslands, water bodies, and other natural protection areas, functioning as ecological barriers and playing a vital role in environmental regulation. This classification framework enables a more effective characterization of the spatiotemporal evolution of land with different functions across China, thereby providing essential data support for subsequent analyses.

2.2.2. Digital Elevation Model (DEM) and Slope Calculation

Topographic data were derived from the NASADEM global digital elevation model (DEM). With a spatial resolution of approximately 30 m (1 arc-second), NASADEM provides significant improvements in vertical accuracy and data completeness by reprocessing original SRTM data and incorporating auxiliary data to fill voids [50]. The slope gradient was calculated on the Google Earth Engine (GEE) platform. To facilitate the subsequent construction of the slope spectrum, the continuous slope values were discretized into integer units by truncating to $1°$ intervals. Finally, to ensure spatial consistency across multiple datasets, all raster layers were reprojected into the Albers Conic Equal Area projection, consistent with the CLCD dataset.

2.2.3. Potential Driving Factors for UAE Space Changes

To explore the potential factors associated with the spatiotemporal dynamics of UAE space, this study considered a set of driving factors encompassing natural, climatic, and anthropogenic dimensions. To avoid an overly fragmented predictor system, these variables were organized into two broad groups: natural environmental factors and human activity factors. The natural environmental group includes topographic, vegetation, hydrological, and climatic variables, whereas the human activity group includes nighttime light, road network density, and human footprint. These factors were selected based on data availability, theoretical relevance, and their documented roles in shaping land-use patterns in previous studies.

Table 2. Datasets and potential driving factors used for analyzing the competition of Urban–Agricultural–Ecological (UAE) spaces.

Category	Variable	Abb.	Dataset	Format	Res.	Source
Natural environmental factors	Soil water erosion	SWE	Soil Water Erosion Dataset	Raster	30 m	[51,52]
	Vegetation Index	NDVI	Landsat/Sentinel series	Raster	30 m	GEE processing
	Elevation	ELE	NASADEM	Raster	30 m	[50]
	Relief degree	RDL	Derived from NASADEM	H3 Grid	Res 5	Derived from NASADEM
	Slope	SLP	Derived from NASADEM	Raster	30 m	Derived from NASADEM
	Topographic position	TPI	Derived from NASADEM	H3 Grid	Res 5	Derived from NASADEM
	Water network	WND	Drainage Density Dataset	Raster	1 km	[53]
	Mean temperature	TMP	Monthly temp dataset	Raster	∼1 km	[54]
	Mean precipitation	PRE	Monthly precip dataset	Raster	∼1 km	[54]
Human activity factors	Night-time light	NTL	DMSP and VIIRS dataset	Raster	∼1 km	[55]
	Road network density	RND	OpenStreetMap	H3 Grid	Res 5	OpenStreetMap
	Human Footprint	HAF	Human Footprint dataset	H3 Grid	1 km	[56]

Note: Abb. = Abbreviation; Res. = Resolution; H3 Grid Res 5 indicates the fundamental analytical unit at resolution 5 in the H3 system.

summarizes the datasets, variables, types, resolutions, and sources employed in the analysis. All datasets were acquired at their original spatial resolutions and then harmonized to a common grid-based analytical framework. To ensure the accuracy of area-based statistics, the Albers Conic Equal Area projection consistent with the CLCD dataset was used as the reference projection. Raster layers generated in Google Earth Engine were first processed under the WGS 84 coordinate system and then reprojected to the same Albers Conic Equal Area projection for spatial consistency. Finally, all variables were aggregated to H3 Resolution 5 cells using the zonal statistics and spatial aggregation tools in QGIS.

2.3. Methods

The methodological framework of this study is designed to systematically quantify the spatiotemporal evolution and competition of Urban–Agricultural–Ecological (UAE) spaces across China from 1990 to 2023. The research logic follows four primary stages: (1) Space Reconstruction: Reclassifying multi-period land-use data into three functional spaces (Urban, Agricultural, and Ecological); (2) Multi-scale Spatial Unit Construction: Employing the H3 hexagonal grid system (Resolution 5) as the fundamental analytical unit to ensure spatial consistency and computational efficiency in large-scale topographical analysis; (3) Slope Structure Quantification: Utilizing the “slope spectrum” theory to derive a series of indicators (e.g., T-value, ULS, and SCI) for characterizing the topographic niches of UAE spaces; and (4) Competition and Driving Mechanism Analysis: Identifying competition types and employing the Multiscale Geographically Weighted Regression (MGWR) model to explore the spatial heterogeneity of dominant driving factors. The overall workflow is illustrated in Figure 2.

2.3.1. H3 Hexagonal Grid System

We adopted the H3 hierarchical geospatial indexing system [57] as the foundational framework for our grid-based slope-spectrum analysis. Compared with traditional administrative boundaries and quadrilateral grids, the H3 hexagonal lattice offers superior spatial isotropy, uniform neighborhood relationships, and a strict parent–child hierarchical structure. These properties significantly enhance the reliability of large-scale spatial comparisons, data aggregation, and multi-resolution analyses.

Determining an appropriate analytical scale is critical for capturing topographic heterogeneity without introducing statistical noise. Therefore, we evaluated three candidate H3 resolutions representing distinct spatial grains: Level 4 (coarse, average area $\approx 1770{\mathrm{km}}^2$), Level 5 (intermediate, ≈253 km²), and Level 6 (fine, ≈36 km²) [58]. For each resolution, we tessellated China, independently reconstructed the land-use–slope spectra, and recalculated the five core slope-structure indicators (T-value, ULS, PaP, SMA and PaT; detailed in Section 2.3.2) across agricultural, ecological, and urban spaces.

The suitability of these candidate resolutions was assessed through a dual-aspect evaluation framework. First, we evaluated the completeness of the slope-spectrum information within individual grid cells. This involved calculating the slope-spectrum span (the difference between the maximum and minimum slope degrees with non-zero areas) and the spectrum dispersion (the total number of populated $1°$ slope bins from $0°$ to $90°$). Additionally, we quantified the spatial presence ratio of each functional space, the rate of missing indicator values, and the proportion of cells exhibiting low dispersion. Together, these metrics helped navigate the trade-off between the risk of over-aggregation (loss of detail) at coarser scales and insufficient spectrum continuity (local fragmentation) at finer scales. Second, we assessed the cross-scale ordinal stability of the slope-structure indicators by leveraging the H3 parent–child topology. Using Level 6 as the finest baseline unit, we traced each cell to its corresponding Level 5 and Level 4 parent cells. Multi-resolution indicator sequences were constructed by matching the values across these three levels. We then computed Spearman rank correlation coefficients for the L4–L5, L5–L6, and L4–L6 pairs. High Spearman coefficients indicate that the relative spatial distribution (rankings) of the indicators is robustly preserved across different grid resolutions.

Ultimately, the suitable analytical resolution was determined by synthesizing these two dimensions: maximizing slope-spectrum completeness to mitigate local fragmentation, while ensuring strong ordinal stability to prevent information degradation from over-aggregation.

2.3.2. Slope Spectrum Analysis Framework

To systematically characterize the topographic distribution of UAE spaces, this study adopts and extends the slope spectrum analysis method(Figure 3). While conventional applications often focus on singular land-use types (e.g., cropland), we expand this framework to simultaneously compare the vertical stratification of multiple functional spaces.

Conceptually, the slope spectrum functions analogously to a histogram in image processing: just as a histogram visualizes the frequency distribution of pixel values (e.g., brightness or color intensities), the slope spectrum quantifies the relative share of land area distributed across successive slope intervals [59]. In this study, we discretized slope values into $1°$ intervals (bins). Within each interval, the area proportion of each land-use category was calculated to construct continuous distribution curves (the detailed slope spectrum extraction results for the studied years: 1990, 1995, 2000, 2005, 2010, 2015, 2020, and 2023, are available in Supplementary Data S1). Crucially, a “background terrain slope spectrum” (representing the natural slope distribution of the entire study area) was generated as a baseline. By benchmarking specific land-use spectra against this background baseline, we can effectively evaluate the topographic selectivity–identifying whether specific spaces exhibit preference or avoidance behaviors toward certain gradients [42].

To systematically quantify the structural characteristics of urban, agricultural, and ecological spaces across slope gradients, this study established a system of five Slope Structure Indicators [13] (

Table 3. Slope structure indicators for UAE spaces.

Indicator	Abbreviation	Description
Slope intersection	T-value	The slope at which the slope spectrum of a spatial category intersects the regional background slope spectrum, representing the critical point where its distribution shifts from dominance on gentle slopes to steeper slopes.
Upper Limit of Slope	ULS	The slope threshold at which the cumulative area of a spatial category reaches 95% of its total area, reflecting its upper adaptive boundary to slope conditions and its potential expansion limit.
Peak Area Proportion	PaP	The percentage of the spatial category’s area corresponding to the peak value of the slope spectrum.
Slope at Maximum Area	SMA	The slope class corresponding to the maximum proportion of a spatial category, indicating the slope most intensively occupied.
Proportion above T-value	PaT	The share of the spatial category’s area located on slopes steeper than the T-value, characterizing the extent of high-slope occupation pressure.

).

Specifically, to capture the expansion trends of different spatial categories into steep terrain, we defined the Slope Change Index (SCI). This index measures the temporal shift in the distribution of a given spatial category above a specific slope threshold (t). The SCI is derived by calculating the difference in the Proportion above Threshold (PaT) between two time points. The formula for calculating $PaT$ at time j is expressed as:

$${\mathrm{PaT}}_j={\displaystyle \frac{A_j(>T)}{A_j}}\times 100\%,$$

(1)

where $A_j(>T)$ is the area of the spatial category at time j located on slopes steeper than the threshold T, and $A_j$ is the total area of the spatial category at time j. Subsequently, the SCI is defined as the difference between the PaT values at time j and time i, as follows:

$$\mathrm{SCI}={\mathrm{PaT}}_j-{\mathrm{PaT}}_i.$$

(2)

In this formula, ${\mathrm{PaT}}_j$ is the proportion of the spatial category located on slopes steeper than T at time j, and ${\mathrm{PaT}}_i$ is the corresponding proportion at time i. A positive SCI value (SCI $>0$) indicates an increased proportion of the spatial category in steeper-slope areas, reflecting an upslope expansion trend. Conversely, a negative SCI value (SCI $<0$) suggests a shift toward gentler slopes, reflecting a downslope contraction pattern.

2.3.3. Analysis of Competition Patterns

To systematically elucidate the spatial mechanisms of land-use transformation, we developed a slope-gradient-based competition analysis framework using the H3 hexagonal grid system. This framework integrates four key analytical dimensions: quantification of net area changes, identification of dominant competition relationships, assessment of competition intensity, and detection of the competitive dominance slope.

(1)

Net Change Calculation and Dominant Type Identification

First, we calculated the net area change in the three functional spaces–urban, agricultural, and ecological–within each H3 grid cell between 1990 and 2023. These changes are denoted as follows:

• $\Delta Are{a}_{\mathrm{urban}}$: Net change in urban space area;
• $\Delta Are{a}_{\mathrm{agri}}$: Net change in agricultural space area;
• $\Delta Are{a}_{\mathrm{eco}}$: Net change in ecological space area.

The land-use category exhibiting the largest absolute change (i.e., $\max \left(\right|\Delta Area\left|\right)$) within a grid cell is identified as the Dominant Type. Its dynamic status is determined by the sign of the change: a positive value indicates expansion, while a negative value indicates contraction.

(2)

Identification of Dominant Competition Relationships

To characterize the primary mode of spatial replacement, we compared the absolute changes of all three categories. The two categories with the greatest absolute changes were identified as the primary interacting pair. This relationship is denoted as Type X vs. Type Y, representing the dominant trade-off within the grid. For instance:

• Urban vs. Agricultura: Signifies that the reciprocal transformation between urban and agricultural spaces dominates the local land-use dynamics (typically implying urban encroachment on farmland).
• Ecological vs. Urban: Indicates that the tension between ecological conservation and urban development is the primary driver of land-use change.

(3)

Assessment of mean annual competitive intensity

To quantify the overall magnitude of land-use reconfiguration and capture the regional heterogeneity of spatial conflicts, we defined the mean annual competitive intensity (MACI). This index measures the gross annual intensity of spatial reconfiguration among urban, agricultural, and ecological spaces within each grid cell, rather than the unique area of land conversion. The MACI is calculated as follows:

$$\mathrm{MACI}={\displaystyle \frac{|\Delta Are{a}_{\mathrm{urban}}|+|\Delta Are{a}_{\mathrm{agri}}|+|\Delta Are{a}_{\mathrm{eco}}|}{N}}$$

(3)

where $|\Delta Are{a}_{\mathrm{urban}}|$, $|\Delta Are{a}_{\mathrm{agri}}|$, and $|\Delta Are{a}_{\mathrm{eco}}|$ represent the absolute net area changes of urban, agricultural, and ecological spaces, respectively; and N represents the duration of the study period (in years), which is 33 years (1990–2023) in this study. MACI is explicitly designed to quantify the gross spatial flux and the overall intensity of structural reorganization within a given grid cell. Thus, the simultaneous retention of coupled gain–loss responses accurately reflects the cumulative magnitude of spatial competition among UAE spaces. A higher MACI value indicates a more intense annual fluctuation in land-use structure, reflecting a “hotspot” of spatial competition.

(4)

Competitive dominance slope

Finally, to pinpoint the specific topographic gradients where land-use competition is most concentrated, we defined the competitive dominance slope (CDS). The CDS identifies the specific slope interval ($1°$ bin) within each grid unit that accounts for the maximum aggregate intensity of land-use conversion. It is calculated as:

$${\mathrm{CDS}}_g=\underset{s\in S}{\arg \max }\sum _{c\in \{\mathrm{urban},\mathrm{agri},\mathrm{eco}\}}\left|\Delta Are{a}_{g,s,c}\right|$$

(4)

where ${\mathrm{CDS}}_g$ represents the slope class within grid g experiencing the most intense land-use change; S is the set of all slope classes; and $\Delta Are{a}_{g,s,c}$ denotes the net area change in land-use category c (urban, agri, or eco) at slope class s within grid g.

2.3.4. Analysis of Driving Mechanisms

To comprehensively elucidate the driving forces underlying the spatial differentiation of land-use competition, this study combines the Optimal Parameters Geodetector (OPGD) and Multiscale Geographically Weighted Regression (MGWR).

(1)

Optimal Parameters Geodetector (OPGD)

The Geodetector is a statistical tool used to detect spatial stratified heterogeneity and reveal the driving factors behind it [60]. However, the traditional Geodetector requires manual discretization of continuous variables (e.g., precipitation, GDP), which often introduces subjectivity. To address this, we employed the OPGD model implemented in the GD R package [61]. OPGD automatically selects the optimal combination of discretization methods (e.g., natural breaks, quantile, geometrical interval) and the number of intervals to maximize the explanatory power (q-statistic).

The core metric, the q-statistic, quantifies the extent to which factor X explains the spatial variance of the dependent variable Y (MACI). It is calculated as:

$$q=1-{\displaystyle \frac{{\sum }_{h=1}^L{N}_h{\sigma }_h^2}{N{\sigma }^2}}$$

(5)

where $h=1,\dots ,L$ represents the strata of factor X; $N_h$ and N are the number of units in stratum h and the entire study area, respectively; and ${\sigma }_h^2$ and ${\sigma }^2$ denote the variances of Y within stratum h and the entire area. The q value ranges from $[0,1]$. A higher q indicates a stronger explanatory power. Additionally, the Interaction Detector was used to assess whether two factors work independently or interact to enhance their influence on land-use competition.

(2)

Multiscale Geographically Weighted Regression (MGWR)

While OPGD identifies global dominant factors, it does not reveal the spatial non-stationarity of these relationships. To capture local variations, we employed the MGWR model [62]. Unlike the classical Geographically Weighted Regression (GWR), which assumes a constant bandwidth (spatial scale) for all variables, MGWR allows each covariate to operate at a distinct spatial bandwidth. This improvement effectively captures the multi-scale nature of land-use processes—some factors operate locally (small bandwidth), while others operate regionally or globally (large bandwidth).

The MGWR formula is expressed as:

$$y_i={\beta }_0(u_i,v_i)+{\displaystyle \sum _{j=1}^k}{\beta }_{b{w}_j}(u_i,v_i)x_{ij}+{\epsilon }_i$$

(6)

where $y_i$ is the dependent variable at location $(u_i,v_i)$; ${\beta }_0$ is the intercept; ${\beta }_{b{w}_j}$ represents the local regression coefficient for the j-th variable at location i, calibrated using a specific bandwidth $b{w}_j$; $x_{ij}$ is the value of the j-th explanatory variable; and ${\epsilon }_i$ is the error term. By generating variable-specific bandwidths, MGWR provides a robust estimation of how natural and human factors differentially shape land-use competition across China.

3. Results

3.1. Slope Distribution Characteristics of Urban–Agricultural–Ecological Spaces in China (National Scale)

To capture the overall dynamics at the national scale, we conducted a statistical analysis of urban, agricultural, and ecological spaces in China from 1990 to 2023. The results reveal distinct slope evolution patterns for the three land-use types (Figure 4). Urban space exhibited a clear uphill trend, with the average slope increasing from $1.81°$ in 1990 to $2.07°$ in 2023. Agricultural space showed a fluctuating pattern: the mean slope initially rose from $4.14°$ and peaked at $4.18°$ in 2003, before declining slightly to $4.09°$ by 2023. In contrast, ecological space remained relatively stable between 1990 and 2008, fluctuating around $11.85°$, but thereafter experienced a marked increase, reaching its maximum of $11.97°$ in 2023.

Figure 5 illustrates the slope spectrum distributions of urban, agricultural, and ecological spaces in China from 1990 to 2020 at 5-year intervals. Overall, land resources are predominantly distributed on slopes below $5°$, accounting for 48.8% of the total land area. Consequently, the slope distributions of urban, agricultural, and ecological spaces are strongly constrained by the topographic background, exhibiting similar patterns.

A pronounced peak is observed in the [$1°$, $2°$) interval across all three land-use types. With increasing slope, the curve of urban space declines most steeply and intersects with the background terrain around 4–$4.5°$. Agricultural land shows a moderate decline and intersects with ecological space at approximately $6°$. Notably, the turning point for ecological space occurs at $6°$, indicating its competitive disadvantage on slopes below this threshold, where its proportion decreased from 44.11% in 1990 to 43.55% in 2023. In contrast, agricultural land consistently maintained dominance below $6°$, with its share exceeding 79% of total cropland throughout the 30-year period. Urban space exhibited the narrowest range of advantageous slopes, being highly concentrated below $4°$. However, its share also declined, from 92.38% in 1990 to 88.94% in 2023.

In addition, given the large national scale, the slope spectra of cropland and ecological space exhibit only minor temporal differences, with slight variation confined to the 0–3° range, while the rest of the curves are nearly overlapping. By contrast, the slope spectral curves of urban space show a clear temporal evolution. From 1990 to 2023, the slope distribution of urban land underwent notable changes, with the maximum proportion decreasing by approximately 3.04%, indicating an intensified trend of urban expansion onto steeper terrain in recent years. These findings suggest that both urban and agricultural land in China have been extending toward higher-slope regions, particularly during the last decade, when the intensity of development in steeper areas has increased.

At the same time, we examined the changes in both area and proportion of the three land-use types across slope intervals from 1990 to 2023. The results (Figure 6) show that, within the study period, urban space expanded markedly in the low-slope interval $[0°,5°)$, while cropland and ecological land experienced evident contraction in this range.

3.2. Slope Spatial Distribution Characteristics Based on the H3 Grid

3.2.1. Multi-Resolution Sensitivity and Selection of H3 Resolution

The multi-resolution sensitivity analysis first showed clear scale-dependent differences in slope-spectrum completeness among H3 Levels 4, 5, and 6 (

Table 4. Slope-spectrum completeness statistics across H3 resolutions.

Space	Statistic	L4	L5	L6
Agricultural	Presence ratio (%)	86.34	78.39	68.69
	Mean dispersion	32.59	27.52	23.21
	Mean span	34.57	28.97	24.41
	Low-dispersion cells (%, ≤20 bins)	34.54	44.53	50.12
Ecological	Presence ratio (%)	99.68	99.78	98.82
	Mean dispersion	55.06	47.15	39.58
	Mean span	55.09	47.17	39.54
	Low-dispersion cells (%, ≤20 bins)	6.62	16.03	26.54
Urban	Presence ratio (%)	76.09	65.70	52.79
	Mean dispersion	25.77	19.42	13.00
	Mean span	27.85	21.53	14.82
	Low-dispersion cells (%, ≤20 bins)	41.06	58.47	81.75

). Level 4 generally produced broader and more dispersed slope spectra, suggesting a higher risk of aggregating heterogeneous terrain conditions within large grid cells. In contrast, Level 6 provided finer spatial detail but increased the proportion of fragmented or low-dispersion cells, especially for agricultural and urban spaces. Level 5 showed an intermediate condition, retaining more slope-spectrum information than Level 6 while reducing the over-aggregation risk associated with Level 4.

The Spearman rank correlation analysis further indicated that the five slope-structure indicators generally maintained moderate to high ordinal stability across adjacent H3 resolutions (

Table 5. Spearman rank correlations of slope-structure indicators across H3 resolutions.

Space	Indicator	L4–L5	L5–L6	L4–L6
Agricultural	T-value	0.686	0.666	0.462
	ULS	0.906	0.928	0.881
	PaP	0.668	0.665	0.450
	SMA	0.767	0.805	0.716
	PaT	0.563	0.599	0.412
Ecological	T-value	0.825	0.732	0.685
	ULS	0.923	0.940	0.870
	PaP	0.889	0.867	0.792
	SMA	0.805	0.842	0.744
	PaT	0.833	0.833	0.732
Urban	T-value	0.676	0.666	0.455
	ULS	0.810	0.801	0.724
	PaP	0.606	0.623	0.371
	SMA	0.662	0.657	0.561
	PaT	0.589	0.627	0.438

). Correlations between L4–L5 and L5–L6 were generally higher than those between L4–L6, suggesting that scale effects existed but did not fundamentally alter the relative spatial ranking of the main indicators. Ecological space showed the highest stability, agricultural space showed moderate to high stability, and urban space was more scale-sensitive. Among the indicators, ULS and SMA were relatively stable, whereas T-value, PaP, and PaT were more sensitive to grid resolution. Overall, H3 Level 5 provided a practical compromise between the over-aggregation risk of Level 4 and the local fragmentation risk of Level 6, and was therefore selected as the analytical resolution for the subsequent H3-based slope-spectrum analysis.

3.2.2. Overall Trend of Slope Change

Based on the SCI index results for 1990–2023, the slope distributions of urban, agricultural, and ecological spaces have all undergone significant changes (Figure 7). For urban space, positive SCI values are mainly distributed in the eastern and northeastern regions of China, indicating that urban expansion has tended to extend from low-slope areas toward adjacent higher-slope terrain. However, the overall magnitude of urban upslope change is mostly low to moderate, and negative SCI values are observed in parts of southwestern and northwestern China, suggesting localized downslope adjustment or contraction in steeper areas.

For agricultural space, positive SCI values are more widely distributed than those of urban space, especially in eastern, southern, and northeastern China. This pattern indicates that cropland-based agricultural space has also shifted toward relatively steeper terrain in many regions. Compared with urban space, agricultural SCI shows a broader and more continuous spatial pattern, suggesting that agricultural upslope adjustment is not limited to urbanized areas but also occurs in hilly and transitional terrain zones. Negative SCI values are mainly found in parts of southwestern China and northwestern China, reflecting localized reductions of agricultural space on steeper slopes.

Ecological space exhibits a different pattern. High positive SCI values are mainly concentrated in mountainous and hilly regions, including southwestern China, the Loess Plateau, the Qinling region, and the Changbai Mountains, where ecological space is closely associated with complex terrain and steep slopes. In contrast, eastern coastal regions, the Northeast Plain, the North China Plain, and the middle and lower reaches of the Yangtze River Plain generally show lower or negative SCI values, indicating that ecological space in these low-slope regions has experienced relatively limited upslope change or has remained concentrated in flatter areas.

By counting the number of grid cells with SCI > 0 in each period, we assessed slope changes over time. The results show that, from 1990 to 2023, the proportion of urban-space grids with SCI > 0 increased from 40.20% (10,062 of 25,028) in 1990–2000 to 60.83% (15,224 of 25,028) in 2010–2020, reaching 60.22% over the entire 1990–2023 period, indicating a sustained “climbing-up” trend. For agricultural space, the proportion of grids with SCI > 0 rose from 46.52% (15,091 of 32,441) to 52.50% (17,031 of 32,441), with 52.16% of grids showing slope increases during 1990–2023, reflecting relatively modest overall changes. In ecological space, the share of grids with SCI > 0 decreased from 38.44% (16,052 of 41,755) to 36.07% (15,059 of 41,755), and 34.15% of grids exhibited slope increases over 1990–2023, also indicating a relatively small magnitude of change.

3.2.3. Characteristics of Change Patterns

Using the Theil–Sen median trend estimator and the Mann–Kendall significance test [63], we assessed the PaT trends of urban, agricultural, and ecological spaces from 1990–2023 (Figure 8). Urban space exhibits a predominantly increasing trend, with upward grids accounting for 66.82% (8446 significantly and 7467 non-significantly increasing), mainly concentrated in the North China Plain (Beijing, Tianjin, Hebei, Shandong) and the Northeast Plain (Liaoning, Jilin). Significant decreases (3136 grids) occur primarily in Yunnan and parts of Gansu, Ningxia, and Shaanxi. Agricultural space shows 55.82% upward grids (5391 significantly and 11,666 non-significantly increasing), with increases clustered in the southeastern hilly–mountainous provinces (Fujian, Guangdong, Guangxi) and decreases in the Yunnan–Guizhou Plateau and parts of the Loess Plateau. Ecological space exhibits the opposite pattern, with only 43.22% upward grids (3389 significantly and 9547 non-significantly increasing) and widespread decreases, especially in southeastern China, while increases appear mainly in the Loess Plateau.

The Getis–Ord Gi* [64] results reveal clear and temporally consistent hot–cold spot patterns of slope-change dynamics across urban, agricultural, and ecological spaces from 1990–2023 (Figure 9). Urban space exhibits persistent and expanding hot-spot clusters in the North China Plain and the eastern coastal region, reflecting a continued shift of urban development toward higher-slope terrain, while cold spots are mainly distributed in Yunnan and parts of northwestern China. Agricultural space shows a contrasting dual pattern, with hot spots concentrated in the southeastern hilly–mountainous provinces (Fujian, Guangdong, Guangxi) and cold spots prevailing in the Yunnan–Guizhou Plateau and parts of the Loess Plateau, consistent with ecological restoration and cropland adjustment. Ecological space displays the opposite spatial structure, with extensive cold spots in southeastern China and pronounced hot spots in the Loess Plateau and northern dryland regions, indicating increasing slope tendencies associated with long-term vegetation recovery. Across the four subperiods, these spatial clusters gradually strengthen and become more coherent after 2000, highlighting the growing influence of urbanization, agricultural restructuring, and ecological engineering on China’s slope-change patterns.

3.2.4. Upper Limit Slope (ULS) Dynamics

From 1990 to 2023, ULS showed distinct patterns across land-use types (Figure 10). Urban areas mostly experienced increases of 1–$6°$, indicating expansion onto steeper slopes, with larger rises (>$7°$) in the Yunnan–Guizhou Plateau near the Yunnan–Guizhou–Guangxi junction. Decreases were limited, mainly in Yunnan and parts of Gansu, Ningxia, and Shaanxi (1–$6°$). Agricultural areas exhibited increases in southeastern hilly regions (Fujian, Jiangxi, Guangxi, Guangdong, Hunan), reflecting intensified cultivation on moderate slopes, while substantial decreases occurred in the Yunnan–Guizhou Plateau, eastern Tibet, Sichuan, and parts of the Loess Plateau, due to cropland retreat and ecological restoration. Ecological areas remained largely stable, with minor changes only in scattered regions of eastern China, indicating that ecological land largely retained its original slope ranges.

3.3. Slope Structure Transition of Urban, Agricultural, and Ecological Spaces

The spatial distributions of the five slope structure indicators in 2023 reveal pronounced contrasts among urban, agricultural, and ecological spaces (Figure 11). Urban areas are characterized by a concentration of low-slope values across all indicators (T-value, PaT, SMA, PaP, and ULS), forming continuous belts in eastern China. These patterns indicate that urban development remains highly dependent on gentle terrain, while localized increases in PaT and ULS suggest emerging expansion toward steeper slopes.

Agricultural areas present a more heterogeneous structure, with moderate to high-slope values widely distributed across the southeastern hilly regions and the Yunnan–Guizhou Plateau. High PaT and PaP patches reflect intensive cultivation in complex terrain, whereas lower SMA and ULS values in southwestern China indicate cropland retreat from steep slopes due to land consolidation and ecological restoration.

Ecological space exhibits the most distinct and stable pattern. High values of T-value, PaP, SMA, and ULS are continuously distributed across the Qinghai–Tibet Plateau, Hengduan Mountains, and Loess Plateau, demonstrating a strong dependence on steep terrain. The consistency among indicators underscores the structural stability of ecological land, with only scattered variations in eastern China. Overall, the three land-use systems show clear slope-based differentiation: low-slope dominance in urban areas, multi-slope complexity in agricultural regions, and high-slope prevalence in ecological landscapes.

To identify the characteristic slope structure types of urban, agricultural, and ecological spaces, we performed K-means clustering [65] separately for the three land-use systems using five slope structure indicators (T-value, PaT, SMA, PaP, and ULS). Prior to clustering, all indicators were subjected to missing-value removal and Z-score standardization to eliminate scale differences and ensure comparability across variables.

Using the 1990 dataset as the baseline, all slope-structure indicators were first standardized before clustering. To ensure temporal comparability, the standardization parameters were fitted using the 1990 dataset and then applied to the 2023 dataset. For each land-use system, clustering solutions with k values ranging from 2 to 15 were evaluated using silhouette coefficients. The results support the final cluster numbers used in this study, with $k=4$ for urban space, $k=3$ for agricultural space, and $k=2$ for ecological space, corresponding to silhouette coefficients of 0.4010, 0.5029, and 0.4589, respectively.

For the 1990 clustering, K-means was implemented with 20 random initializations (n_init = 20) and a fixed random seed (random_state = 42). The solution with the lowest within-cluster sum of squares among the repeated initializations was retained. The cluster centers derived from the 1990 results were then extracted and used as the initial centroids for the 2023 clustering, with n_init = 1. This initialization strategy was used to reduce interannual category-label drift caused by independently trained models and to improve the temporal consistency and comparability of clustering outcomes. Using the same standardization parameters and fixed initial centroids, the 2023 dataset was subsequently classified.

To construct integrated slope structure types, the clustering results of the three land-use systems were combined in the order of urban–agricultural–ecological space (e.g., a combination code of 0–0–1 represents urban cluster 0, agricultural cluster 0, and ecological cluster 1). As the number of combined categories is relatively large, only the 14 dominant types with the largest spatial extents were selected for detailed analysis. The spatial distribution of the 2023 clustering results is presented in Figure 12.

Overall, the slope structures of the tripartite spaces primarily exhibit two typical patterns: “high agglomeration on low slopes” and “dispersion on gentle slopes”. Specifically, urban space is dominated by the U1 (U1 represents the first slope-structure type of urban space, with similar notation applied to agricultural and ecological spaces) and U2 categories, concentrated predominantly in low-slope areas below $6°$, with some expansion into gentle slopes of 16–$20°$. Agricultural space is similarly dominated by the A1 and A2 categories but exhibits a broader range of low-slope agglomeration (mainly below $8°$), extending up to $12°$ in certain regions; notably, the A0 category shows a relatively uniform distribution within the 0–$16°$ range, attenuating gradually with increasing slope. Ecological space, characterized mainly by E0 and E1 categories, displays a relatively balanced distribution across low and gentle slopes (0–$30°$) but still retains distinct agglomeration characteristics in low-slope sections.

Associated with topographic constraints and UAE spatial competition patterns, the slope structures demonstrate distinct spatial differentiation across regions:

1.

The Eastern Plains exhibit a distinct low-slope agglomeration characteristic (Dominant Types: 110, 111). In the Northeast Plain, North China Plain, and the Middle-Lower Yangtze Plain, both urban (U) and agricultural (A) spaces are highly concentrated in low-slope tiers below $6°$. This pattern reflects intense spatial overlap and competition between construction land and cropland in flat regions, while ecological space (E) is largely squeezed to peripheral low slopes (Type 110) or distributed relatively evenly below $30°$ (Type 111).

2.

The Southern Hilly Regions display mixed characteristics of “interwoven 011 and 001” types. Compared with the plains, although urban space in this region remains aggregated on low slopes, its utilization range ascends to approximately $12°$. Meanwhile, agricultural space further expands into higher slope zones, with the upper limit of distribution (e.g., A0 category) reaching $25°$, reflecting the trend of “uphill farming” under topographic constraints.

3.

Central and Southwest China (Loess Plateau, Sichuan Basin, Yunnan-Guizhou Plateau) are dominated by the “001” type. In these regions, the spatial pattern is consistent with a displacement process in which the dominance of urban space in low-slope areas is associated with agricultural space occupying higher gradients. As a result, agricultural space shows a relatively uniform distribution in areas below $16°$. Consequently, ecological and agricultural spaces exhibit a clear complementary relationship, with ecological space occupying a dominant position in steep areas greater than $16°$.

4.

The Northwest and Qinghai-Tibet Regions exhibit “absolute ecological dominance” (Dominant Types: NN0, NN1). The slope structure of the Qinghai-Tibet Plateau is almost entirely controlled by natural topography, where ecological space maintains absolute dominance. In other parts of the Northwest, restricted by climate and water resources, ecological and agricultural spaces show a “trade-off” competitive relationship (Types N21, N01). This indicates that in regions with harsh natural conditions, ecological space maintains absolute dominance regardless of terrain flatness.

From 1990 to 2023, the transformation of slope structures across different spatial types exhibited a scattered distribution pattern nationwide (Figure 13).

Among all transformed grids (excluding the Urban-Agricultural co-change zone), urban space underwent the most significant slope structure changes, accounting for 47.33% (5371 grids) of the total variations. Specifically, the transition to the U1 type was dominant (3162 grids, 27.87% of total), concentrated mainly in rugged terrains such as Southwest China, the Loess Plateau, and the mountainous areas of Northeast China, reflecting a trend of urban agglomeration towards low-slope valleys. The remaining urban transformations were primarily towards the U0 category (approximately 19.47% of total), clustered in the hilly regions of Eastern China, indicating a trend of urban expansion climbing upslope.

The transformation of agricultural space followed, dominated by the shift to the AN category (cropland retirement/abandonment), which accounted for 12.36% (1402 grids) of the total and was mainly located in the Qinghai-Tibet Plateau. This was followed by the transition to the A2 type (1353 grids, 11.92%), distributed primarily in the Shandong Peninsula, the southeastern edge of the Qinghai-Tibet Plateau, and parts of Inner Mongolia. The conversion to the A1 type was concentrated in the Loess Plateau and the border region of Yunnan, Guizhou, and Guangxi provinces.

Ecological space transformation was relatively minor, accounting for only 3.97% (450 grids) of the total changes. These transitions were primarily towards E0 and E1 categories, scattered across various provinces in Eastern China.

3.4. Spatial Competition Among Urban, Agricultural, and Ecological Spaces

3.4.1. Classification of Spatial Competition Types

During the study period, most H3 grid cells exhibited distinct trade-offs among urban, agricultural, and ecological spaces, although some cells involved only two land-use types or remained stable. To characterize the dominant competitive processes, the land-use category with the most significant expansion was defined as the dominant type. Furthermore, the two categories experiencing the greatest magnitude of change were used to define the primary competition mode. Applying these criteria, all grid cells were classified into seven spatial competition types (including stable areas), as illustrated in Figure 14a.

The results indicate that the study area is primarily characterized by Urban–Agricultural competition (UrEx–AgCo, 15.08% of valid grids) and Ecological–Agricultural competition. In these notations, “Ex” and “Co” denote the expansion and contraction of the corresponding spaces, respectively. The Ecological–Agricultural competition comprises two subtypes: AgEx–EcCo (29.35%) and EcEx–AgCo (27.15%).

Geographically, the UrEx–AgCo type is concentrated in the Northeast Plain and the North China Plain—specifically Tianjin, Hebei, Shandong, Henan, northern Anhui, and Jiangsu—indicating a spatial transition from agricultural to urban space. In contrast, Ecological–Agricultural competition exhibits regional heterogeneity: the EcEx–AgCo type is prevalent in Central China, whereas the AgEx–EcCo type is mainly distributed in the southeastern hilly regions, as well as parts of Northeast and Northwest China.

Using the SCI index, we analyzed the slope changes in the dominant expansion type (defined by the largest area increase) within each H3 grid cell (Figure 14b). The results demonstrate distinct spatial differentiation across China. In the eastern and central plains, urban and agricultural expansions are characterized by a shift towards lower slopes (UrEx–LS, AgEx–LS). In contrast, agricultural expansion towards higher slopes (AgEx–HS) is prominent in the mountainous Southwest. In the Northwest, ecological expansion exhibits both slope stability (EcEx–ST) and a trend towards higher slopes (EcEx–HS), whereas the Qinghai–Tibet Plateau remains largely stable (NC). The Northeast also exhibits urban and agricultural expansions shifting towards lower slopes. Overall, expansions towards lower slopes are concentrated in the eastern plains, while expansions towards higher slopes are primarily found in the Southwest and Northwest, indicating a clear spatial association between terrain conditions and the differentiation of urban, agricultural, and ecological expansion patterns.

The spatial distribution of the Competitive Dominance Slope (CDS) exhibits pronounced regional heterogeneity, following a distinct “East-Low, Southwest-High” gradient (Figure 14c). Low-slope CDS (0–5°) prevails across the Northeast Plain, North China Plain, and the Middle-Lower Yangtze Plain (including provinces such as Heilongjiang, Hebei, Shandong, and Jiangsu). This pattern reflects that land-use competition is predominantly confined to low-gradient terrains, primarily involving cropland and built-up areas. Medium-slope CDS (6–15°) clusters in the central hilly regions and the mountainous Southwest (e.g., Hubei, Hunan, Chongqing, and Guizhou), indicating intensified interactions among urban, agricultural, and ecological spaces. High-slope CDS (>16°) is mainly observed in the Yunnan-Guizhou Plateau, the periphery of the Sichuan Basin, and the southern Qinling-Daba Mountains, signifying an expansion trend into mid-to-high slope terrains. Conversely, high-altitude regions such as the Qinghai-Tibet Plateau exhibit low CDS values, attributable to limited anthropogenic interference.

3.4.2. Competition Intensity Analysis

The spatial distribution of the Mean Annual Competitive Intensity (MACI) across China from 1990 to 2023 demonstrates pronounced regional heterogeneity (Figure 15). High-intensity zones ($\mathrm{MACI}>0.8$) are primarily clustered in the eastern and southeastern coastal provinces (e.g., Jiangsu, Zhejiang, Guangdong, Shandong) and the Sichuan Basin (Sichuan, Chongqing). In these regions, rapid urbanization and economic development have propelled frequent transitions among urban, agricultural, and ecological spaces. Conversely, low competitive intensity ($\mathrm{MACI}<0.15$) prevails across vast areas of western and northeastern China (e.g., Xinjiang, Qinghai, Ningxia, Inner Mongolia, Heilongjiang), where topographic constraints and lower population pressure contribute to relatively stable spatial patterns.

Regarding temporal dynamics, the 1990–2000 period saw competitive intensity largely confined to the North China Plain and coastal urban agglomerations, corresponding to the initial phase of rapid urban expansion. From 2000 to 2010, competition intensified and diffused westward, particularly along major urban corridors and within mountainous basins, indicating escalated interactions among agricultural, urban, and ecological spaces. During the 2010–2020 interval, competitive pressure further penetrated central and southwestern regions (e.g., Hunan, Guizhou, Guangxi, Yunnan), signifying the encroachment of urban and agricultural spaces onto sloped terrains. Overall, the trajectory of spatial competition in China exhibits a progressive westward expansion, highlighting the growing prominence of trade-offs among urban, agricultural, and ecological spaces in slope-constrained environments.

3.4.3. Explanatory Factors Associated with Spatial Competition

Before calculating the GeoDetector q-statistics, the optimal parameter-based geographical detector (OPGD) procedure was used to discretize the continuous explanatory variables. Specifically, five candidate discretization methods were tested, including equal interval, natural breaks, quantile, geometric interval, and standard deviation methods, with the number of intervals ranging from 4 to 10. For each explanatory variable, the discretization method and interval number that maximized the q-statistic were selected. Therefore, the reported q-statistics should be interpreted as explanatory power values obtained under the OPGD-selected discretization schemes.

The GeoDetector results (Figure 16) indicate that human activity factors, as a group, showed higher explanatory power for the spatial differentiation of competition intensity among UAE spaces than natural environmental factors. Among the individual variables, the Human Activity Footprint (HAF, $q=0.31$), Nighttime Light intensity (NTL, $q=0.29$), and Road Network Density (RND, $q=0.23$) exhibited relatively high explanatory power, suggesting that human activity intensity, economic development, and transportation accessibility were closely associated with the spatial variation of land-use competition intensity.

In comparison, natural environmental factors showed more differentiated but generally lower explanatory power. Topographic variables such as Elevation (ELE, $q=0.20$) and Terrain Relief (RDL, $q=0.11$) provided moderate explanatory information, whereas climatic and hydrological variables, such as temperature, precipitation, and drainage density, showed weaker explanatory power. Overall, the OPGD results suggest that the spatial differentiation of competition intensity was more strongly associated with human activity factors, while natural environmental factors provided background constraints. These q-statistics depend on the selected discretization schemes and should be interpreted as explanatory associations rather than direct causal effects.

The interaction detector analysis (Figure 17) reveals that the combined explanatory power of factor pairs consistently exceeds that of individual factors, indicating significant bivariate and nonlinear enhancement. The most prominent interaction occurs between HAF and ELE ($q=0.41$). This result indicates that the interaction between HAF and ELE yields a combined explanatory power that exceeds either factor individually, suggesting that topographic and human activity factors jointly structure spatial competition patterns. Relatively high interaction explanatory power is also observed for HAF ∩ NTL ($q=0.37$) and HAF ∩ NDVI ($q=0.37$), indicating close spatial associations among human activity intensity, urban development, and ecological conditions. Furthermore, substantial interactions such as NTL ∩ ELE ($q=0.38$) and RND ∩ ELE ($q=0.35$) indicate that socioeconomic activities and topographic conditions are jointly associated with spatial competition patterns. Overall, the interaction between human activity and topography shows the strongest explanatory power for the spatial variation of slope-related land-use competition.

To further elucidate the spatially varying associations between explanatory factors and MACI from 1990 to 2023, Multiscale Geographically Weighted Regression (MGWR) was employed (Figure 18). The MGWR model was fitted using a distance-band neighborhood type, a bisquare local weighting scheme, and scaled explanatory variables. Variable-specific bandwidths were selected using the gradient search procedure, with AICc used to evaluate the bandwidth search history. The final model was obtained at the fourth bandwidth-search iteration. The MGWR model yielded an adjusted $R^2$ of 0.646, showing only a modest improvement over the traditional GWR model (0.643), while achieving a lower AICc (43,830.14 < 43,854.63). However, the main contribution of MGWR lies not in the marginal improvement in model fit, but in its ability to reveal the spatial heterogeneity of factor–competition relationships. The selected bandwidths ranged from 381.20 km to 383.28 km, suggesting that most variables operated at a broadly regional scale of approximately 382 km. Because these bandwidths are relatively similar across variables, the MGWR results are interpreted cautiously as evidence of spatially varying associations rather than as proof of strong multi-scale differentiation among explanatory factors.

The local coefficient patterns indicate that human activity factors, especially NTL, RND, and HAF, generally show positive local associations with MACI in eastern and densely developed regions. This suggests that the spatial differentiation of competition intensity in these areas is closely related to urbanization intensity, infrastructure accessibility, and human activity pressure. This pattern corresponds to the “Low-Slope Agglomeration” mode identified in Section 3.3, where urban and agricultural spaces are concentrated in limited low-slope areas.

In contrast, natural environmental factors show more heterogeneous coefficient patterns in western plateau, southwestern mountainous, and southern hilly regions. Topographic, climatic, vegetation, and erosion-related variables exhibit alternating positive and negative local coefficients, suggesting that their associations with MACI vary across geomorphological contexts. This pattern is broadly consistent with the “Interwoven Upslope,” “Urban-Valley/Agri-Slope,” and “Ecological Dominance” modes described in Section 3.3, where land-use competition is associated not only with human activity intensity but also with terrain accessibility, ecological background, and climatic conditions.

Overall, MGWR complements the OPGD results by translating overall explanatory relationships into geographically explicit local associations. While OPGD identifies the overall explanatory power and interaction relationships of different factors, MGWR further indicates that human activity factors are more closely associated with competition intensity in lowland and urbanized regions, whereas natural environmental factors show more spatially heterogeneous associations in plateau, hilly, and mountainous regions. These findings suggest that slope-related land-use competition is associated with the combined role of human activity intensity and environmental constraints, although the MGWR results should be interpreted as spatially varying associations rather than causal effects or strong evidence of distinct multi-scale processes.

4. Discussion

4.1. Competition Patterns and Spatiotemporal Evolution of UAE Spaces: A Slope Structure Perspective

The fine-scale analysis based on H3 grids reveals distinct structural disparities in the occupation of slope gradients by urban, agricultural, and ecological spaces, presenting a typical pattern of slope-dependent spatial competition. Regarding urban space, the period from 1990 to 2023 was primarily characterized by the encroachment of urban space onto agricultural space. This trend was predominantly observed in plain area grids, whereas competition between urban and ecological spaces appeared in only a minority of hilly grids. Concurrently, the Slope Structure Index ($SCI$) indicates a discernible trend of upslope urban expansion in the North China Plain and Northeast China. Metrics such as the Upper Limit Slope ($ULS$) demonstrate that urban space retains significant dominance in high-accessibility slope gradients (0–$6°$). Furthermore, the Competitive Dominance Score ($CDS$) confirms that the competitive advantage of urban space is strictly concentrated within this range. These observations corroborate findings from numerous studies regarding urban expansion climbing uphill in China [12,20,66]. However, distinct from regional-scale studies, this H3 grid-scale analysis reveals that shifts in competitive advantage are spatially more discrete and exhibit more pronounced structural heterogeneity. Additionally, multi-temporal trend statistics highlight the spatial migration of urban expansion hotspots: from 1990 to 2000, “upslope urban expansion” clusters were concentrated in the Yangtze River Delta; from 2000 to 2010, they shifted to the Beijing-Tianjin-Hebei region and the southeastern coastal areas (e.g., Zhejiang, Fujian, and Taiwan); and from 2010 to 2020, a trend of concentration towards inland urban agglomerations was observed.

In contrast, the competition for agricultural space is mainly characterized by the agriculture-ecology nexus, with agricultural expansion concentrated mainly in southern China. Indices such as $SCI$ and $ULS$ in the Southeastern Hills region show varying degrees of upward shift. This suggests that agricultural space in this region is associated with an upslope migration trend under the combined context of urban growth pressure and food-security demand, which may increase spatial pressure on ecological space in slope transition zones. This finding aligns with existing literature on the cultivated land moving uphill phenomenon [42,67]. Interestingly, a divergent trend is observed in Southwest China (e.g., Yunnan and Guizhou), where agricultural space tends to expand towards lower slope gradients. The $CDS$ indicates that slope-based competition in this region is concentrated in the 11–$25°$ range. Ecological space maintains dominance in high-slope regions ($>15°$). Its expansion is primarily concentrated in Central China, forming a belt-shaped distribution extending from Inner Mongolia, Northern Hebei, Shanxi, Shaanxi, Ningxia, and Gansu to Sichuan. Within this region, ecological space shows a tendency to expand towards higher slopes, with the $CDS$ of competitive slopes mostly situated above $11°$. Unlike urban and agricultural spaces, the “upslope movement” of ecological space between 1990 and 2023 formed distinct cold and hot spots, exhibiting distribution characteristics contrary to those of the other two spaces.

Overall, this study proposes a tripartite slope-dependent competition framework for interpreting the spatial differentiation of urban, agricultural, and ecological spaces along topographic gradients. This framework consists of three interrelated components: (1) low-slope urban dominance, where urban space is concentrated in accessible low-gradient terrain; (2) transition-slope agricultural occupation and upslope displacement, where agricultural space occupies intermediate gradients and shows signs of movement toward more constrained terrain; and (3) steep-slope ecological stability, where ecological space remains relatively dominant in high-gradient areas. This framework extends previous studies that primarily discussed competitive relationships based on total area change, transition matrices, or spatial proximity [68], by introducing topographic gradients as an explicit analytical dimension. It therefore offers a more comprehensive topography-sensitive perspective for interpreting tripartite spatial competition patterns among urban, agricultural, and ecological spaces.

4.2. Comparative Advantages of H3 Grids over Traditional Statistical Units and Scale Effects in Slope-Spectrum Competition Analysis

The appropriate selection of a statistical unit is critical for the reliability of large-scale spatial analysis. Currently, research on spatial patterns still predominantly employs administrative divisions as statistical units [42,69]. However, administrative boundaries inherently lack physiographic coherence. Their substantial heterogeneity in area, shape, and internal topography makes them highly susceptible to the Modifiable Areal Unit Problem (MAUP) [70], thereby masking the spatial heterogeneity inherent in slope structures. In this sense, the H3 grid system should not be understood as completely eliminating MAUP, but rather as reducing the inconsistencies introduced by irregular administrative boundaries and providing a more standardized spatial framework for comparison. For instance, due to the averaging effect of coarse administrative units, prior research tended to systematically underestimate the degree of urban climbing in regions with mixed terrain. Localized upslope expansion was often diluted by the dominant flat areas within large administrative boundaries, thereby obscuring the widespread nature of this phenomenon. In stark contrast, our fine-scale H3 grid analysis reveals that the “upslope urban expansion” phenomenon is widespread across the majority of urban spaces (60.83%) during similar periods, lacking clear spatial continuity or regional concentration. This suggests that macro-level conclusions drawn from administrative scales often result in obscuring fine-scale realities through over-generalization. Furthermore, traditional slope-spectrum studies often construct spectra using coarse administrative units, which limits analysis to statistical frequency distributions and precludes effective cluster or similarity analysis. By leveraging H3 grids to construct and cluster slope structure factors, our study successfully captured the detailed spatial differentiation of slope structures. Nevertheless, the choice of H3 resolution still introduces scale-dependent aggregation effects. A coarse resolution may over-aggregate heterogeneous terrain conditions within a single cell, whereas a fine resolution may fragment continuous slope gradients and generate cells with insufficient internal slope-spectrum information. Therefore, Resolution 5 should not be interpreted as a universally optimal scale or as being immune to MAUP effects.

Compared with conventional regular square grids, the isotropic geometry of H3 hexagonal grids helps reduce directional bias, which may help slope-spectrum statistics more consistently represent terrain-related spatial patterns [71]. In square grids, slope gradient changes may be constrained by grid orientation, and their neighborhood structure exhibits distinct North-South/East-West biases [72]. This may contribute to the artifactual truncation of terrain-related spatial processes—such as low-slope agricultural expansion or urban sprawl along valleys—at grid boundaries, consequently affecting the stability of competitive patterns and key metrics (e.g., T, $PaP$, and $ULS$). Moreover, the H3 grid system possesses a strict hierarchical structure that facilitates robust multi-scale nested analysis. This feature is useful for assessing the consistency of competition among urban, agricultural, and ecological spaces across scales, partly addressing the limitations of administrative divisions (which lack hierarchy) and common grids (which lack natural nesting capability). However, identifying the universally “optimal” grid scale remains a complex challenge due to regional topographic variations. Future work will focus on establishing an adaptive multi-scale framework to systematically identify appropriate H3 resolutions that balance computational efficiency with the preservation of micro-scale topographic details.

4.3. Limitations and Future Perspectives

Although this study utilizes the H3 grid and slope-spectrum framework to systematically characterize the slope structure and competition patterns and associated factors of urban–agricultural–ecological spaces, several limitations remain that merit attention in future research.

First, the identification of competitive relationships is subject to uncertainties inherent in land-use classification products. The land-use data employed in this study were derived from large-scale products (CLCD). While the overall accuracy is robust, misclassification persists as a challenge in complex mountainous terrains, particularly regarding the confusion between shrubland and cropland, or the misidentification of urban bare land. This issue of “spectral mixture,” which has been noted in existing literature [45,73], may introduce uncertainty into the precise identification of competitive advantage slopes. Following previous studies on the evolution of urban–agricultural–ecological spaces in China [16], this study adopts agricultural space as a key component of the UAE spatial framework. However, because the CLCD classification system was used, agricultural space in this study was operationally represented by the Cropland class. Therefore, the results related to agricultural space should be interpreted primarily as reflecting cropland-based agricultural space, rather than all forms of productive agricultural land use. Other agricultural uses, such as orchards, managed pastures, and permanent crops, may not be fully captured by this classification scheme. In addition, crop-specific slope suitability and climate-induced shifts in crop growth conditions were not explicitly considered, because the CLCD dataset does not distinguish among crop types. This restrictive definition and the potential shrubland–cropland confusion may influence the robustness of several derived indicators. For example, SCI may be affected if cropland is inconsistently classified across years, because temporal classification errors could alter the estimated direction or magnitude of agricultural upslope displacement. ULS and PaT may be more sensitive to such uncertainty because both indicators depend on the upper-slope tail of the agricultural slope spectrum; misclassifying high-slope cropland as shrubland could underestimate the upper slope boundary and the proportion of agricultural space above the T-value, whereas misclassifying shrubland as cropland could overestimate high-slope agricultural occupation.

Second, the selection of spatial scale serves as a trade-off that may influence the interpretability of competitive patterns. This study adopted the Level 5 H3 grid to balance computational efficiency with the continuity of the slope spectrum. However, competitive patterns are often scale-dependent (i.e., the Modifiable Areal Unit Problem), and a single fixed scale may not optimally represent diverse topographic regions. This suggests that future work should establish a multi-scale H3 analysis framework to enhance the robustness of results through cross-scale comparison.

Finally, the quantitative attribution of slope structure dynamics requires further deepening. This study is based on an observational spatial analysis framework. Although GeoDetector and MGWR are useful for identifying explanatory power, spatial associations, and geographically varying relationships, they do not establish causal direction or fully rule out potential confounding and reverse causality. Therefore, the relationships identified in this study should be interpreted as associations between UAE spatial competition and related human activity, topographic, climatic, and ecological factors, rather than as direct causal effects. Establishing causal mechanisms would require further analyses based on natural experiments using exogenous policy shocks, such as the timing of ecological redline designations or changes in farmland protection quotas, as sources of exogenous variation; panel data models with unit fixed effects to control for time-invariant confounders; or agent-based and process-based simulation models to test whether the observed spatial patterns can emerge from hypothesized causal mechanisms. In this sense, the main contribution of this study is descriptive and associational: it maps the slope-dependent spatial structure of UAE competition and identifies its related spatial correlates at the national scale. While this study initially sought to directly model the primary drivers of slope structure evolution, the lack of granular data on institutional factors—specifically the quantitative representation of policy enforcement intensity, land consolidation projects, and ecological protection redlines—constrained the predictive power of direct models. Consequently, this study adopted an alternative strategy by discussing influencing factors through the indirect perspective of “spatial competition intensity.” Future research could further integrate refined policy databases and Coupled Human and Natural Systems (CHANS) models, incorporating high-precision explanatory variables to improve the capability of causal identification regarding slope structure dynamics.

5. Conclusions

This study establishes a fine-scale analytical framework by integrating the H3 hexagonal grid system and slope spectrum analysis to quantitatively investigate the evolution of slope structures and the spatial competition among urban, agricultural, and ecological (UAE) spaces in China from 1990 to 2023. By treating topographic gradients not only as physical constraints but also as operational indicators of land-use competition, this study provides quantitative evidence for identifying agricultural spaces under slope-related pressure and for supporting food-security-oriented agricultural land management. The main conclusions are as follows:

• Topographic Stratification and Agricultural Upslope Pressure: At the national scale, UAE spaces exhibit a distinct slope-based stratification. Urban space is concentrated in the high-accessibility lowlands ($<6°$), agricultural space mainly occupies transitional slopes (6–$15°$), and ecological space dominates steeper terrains ($>15°$).However, this structure has changed over time. The average slope of urban space increased from $1.81°$ to $2.07°$, indicating that urban expansion has gradually extended into more topographically constrained areas. More importantly, 52.16% of agricultural grid cells showed positive SCI values, suggesting that agricultural space has experienced measurable upslope displacement. This result indicates concrete pressure on arable land, especially in regions where flat and highly productive farmland is scarce. Therefore, cropland protection should prioritize low-slope and high-productivity agricultural areas, while agricultural expansion into steeper slopes should be carefully evaluated to avoid productivity decline and ecological degradation.
• Regional Heterogeneity and Differentiated Agricultural Land Management: Based on K-means clustering, China’s slope structure patterns can be categorized into four distinct modes aligning with aligned with macro-geomorphological conditions:
  • The “Low-Slope Agglomeration” mode in the Eastern Plains (intense urban-agri conflict),where urban–agricultural competition is concentrated in flat areas and calls for strict protection of high-quality lowland cropland;
  • The “Interwoven Upslope” mode in the Southern Hilly Regions (agri-ecological tension),where agricultural and ecological spaces are closely intertwined and where agricultural expansion on steep slopes should be monitored and regulated;
  • The “Urban-Valley/Agri-Slope” complementary mode in the Southwest, where valley-based urban development and slope-based agricultural use require coordinated spatial zoning;
  • The “Ecological Dominance” mode in the Qinghai-Tibet Plateau, where ecological conservation should remain the primary management priority.
  These regional differences suggest that agricultural land management should not rely on a uniform slope threshold alone. Instead, slope-based regulation should be combined with regional land-use functions, cropland quality, and ecological sensitivity.
• Human Activity Association and Topographic Constraint: The GeoDetector and MGWR results indicate that the spatial differentiation of competition intensity is more strongly associated with human activity factors, such as Human Activity Footprint and Nighttime Lights, than with natural factors alone. The interaction between Human Activity Footprint and elevation showed relatively high explanatory power ($q=0.41$), suggesting that spatial competition becomes more pronounced where intensive human activities overlap with strict topographic constraints. This finding highlights the need to identify priority management zones where urban expansion, cropland displacement, and ecological vulnerability occur simultaneously.

Overall, this study shows that the spatial competition among UAE spaces has direct implications for cropland protection and food-security-oriented land management. Areas with positive agricultural SCI values, especially those located in hilly regions and transitional slope zones, should be treated as early-warning zones for cropland displacement. Policy responses should move beyond general “strict slope redlines” and adopt differentiated strategies, including protecting high-quality cropland in low-slope areas, controlling disorderly agricultural expansion on steep slopes, monitoring agricultural cells with continuous upslope movement, and coordinating ecological restoration with agricultural production in slope-constrained regions. These findings provide a quantitative basis for balancing urban development, cropland protection, and ecological conservation in mountainous and hilly areas.