Comprehensive indicators and fine granularity refine density scaling laws in rural-urban systems

Density scaling laws complement traditional population scaling laws by enabling the analysis of the full range of human settlements and revealing rural to urban transitions with breakpoints at consistent population densities. However, previous studies covering all areas, not just cities, have been constrained by the granularity of available rural and urban units, as well as limitations in the quantity and diversity of indicators. This study addresses these gaps by examining Middle Layer Super Output Areas (MSOAs) in England and Wales, incorporating an extensive set of 117 indicators for the year 2021, spanning age, ethnicity, educational attainment, religion, disability, economic activity, mortality, crime, property transactions, and road accidents. Results indicate that the relationship between indicator density and population density is best described by a segmented power law model with a consistent breakpoint (33 ± 5 persons per hectare) for 92 of the 117 indicators. Additionally, increasing granularity reveals further rural to urban transitions not observed at coarser spatial resolutions. Our findings also highlight the influence of population characteristics on scaling exponents, where stratifying dementia and ischaemic heart disease by older age groups (aged 70 and above) significantly affects these exponents, illustrating a protective urban effect.