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	Shrinking Cities Analysis	Urban Density Gradient Model
Field	Urban Studies	Human Geography
Family	Process / pipeline	Regression model
Year of origin	2014	1951
Originator	Shrinking Cities research network; Haase, Rink, Grossmann, Bernt, Mykhnenko (synthesis)	Colin Clark; Edwin Mills & Richard Muth (theory); Bruce Newling (quadratic form)
Type	Descriptive pipeline for analysing urban population and economic decline, vacancy, and right-sizing	Family of functional models of urban population density as a function of distance from the centre
Seminal source	Haase, A., Rink, D., Grossmann, K., Bernt, M., & Mykhnenko, V. (2014). Conceptualizing urban shrinkage. Environment and Planning A, 46(7), 1519–1534.	Clark, C. (1951). Urban population densities. Journal of the Royal Statistical Society. Series A (General), 114(4), 490–496.
Aliases	Urban Shrinkage Analysis, Urban Decline Analysis, Right-Sizing Analysis, Depopulation Analysis	Urban Density Function, Population Density Gradient, Density-Distance Function, Monocentric Density Model
Related	4	4
Summary	Shrinking cities analysis is the study of cities and neighbourhoods that are losing population and economic activity, tracing the demographic decline, job loss, housing vacancy, and infrastructural over-capacity that follow, and the 'right-sizing' planning responses they provoke. It treats shrinkage not as the temporary failure of a growth path but as a distinct, often persistent urban trajectory requiring its own descriptive tools. The conceptual synthesis by Haase and colleagues in 2014 frames urban shrinkage as a multidimensional process linking population loss, economic restructuring, and changes in the built environment.	The urban density gradient model is the broad family of functional relationships that describe how population density varies with distance from a city's centre. Its canonical member is Colin Clark's 1951 negative-exponential form, but the family also includes Bruce Newling's quadratic-exponential function that permits a density crater at the core, simpler linear and Smeed forms, and the economic micro-foundation supplied by the Muth-Mills monocentric city model. Together these give planners and economists a compact, comparable language for urban spatial structure.