Quantifying landscape patterns of urban–rural regional systems: comparing concentric and transect approaches

The urban–rural regional system (URRS)—a mosaic of urban, rural, and transitional areas connected through socioeconomic and ecological processes—constitutes a key spatial domain for the science and practice of landscape ecology and regional sustainability. However, we still lack an adequate understanding of how spatial sampling schemes (e.g., concentric rings vs. transects) and spatiotemporal and thematic scales jointly affect the quantification of spatial patterns across the URRS as an integrated regional landscape. This study was designed to develop a multi-method, multiscale analytical framework for quantifying spatial patterns of URRS and to apply it to three urbanizing regions in the southwestern United States as illustrative case studies. We addressed two questions: 1) What major spatial signatures characterize the spatial patterns of URRS? 2) How can these patterns be effectively quantified? Using the Phoenix, Tucson, and Las Vegas metropolitan regions as case studies, we calculated landscape metrics from annual LULC data from 1985 to 2023, with factorial combinations of spatial sampling schemes, sampling window sizes, and thematic resolutions. Across all three regions, both concentric rings and transects revealed a consistent wave-like spatial signature extending from the urban core to the urban periphery, with a narrow crest of extreme values for patch diversity, fragmentation, shape complexity, and aggregation that expanded outward and flattened over time. Spatial and thematic scales had significant influences on the overall pattern, while sampling window size mainly affected the smoothness of the wave-like profile. Adequate quantification of URRS requires the use of multiple spatial sampling schemes and multiple spatial and thematic scales to capture radial, direction-specific, and system-wide patterns, all of which may be relevant to urban–rural linkages and regional sustainability. Our study provides a transferable methodological framework, supported by a transparent computational workflow and code, to facilitate such analyses.