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Urban population scaling of resource use, creativity metrics, and humanbehaviors has been widely studied. These studies have not looked in detail atthe full range of human environments which represent a continuum from the mostrural to heavily urban. We examined monthly police crime reports and propertytransaction values across all 573 Parliamentary Constituencies in England andWales, finding that scaling models based on population density provided a farsuperior framework to traditional population scaling. We found four types ofscaling: i) non-urban scaling in which a single power law explained therelationship between the metrics and population density from the most rural toheavily urban environments, ii) accelerated scaling in which high populationdensity was associated with an increase in the power-law exponent, iii)inhibited scaling where the urban environment resulted in a reduction in thepower-law exponent but remained positive, and iv) collapsed scaling wheretransition to the high density environment resulted in a negative scalingexponent. Urban scaling transitions, when observed, took place universallybetween 10 and 70 people per hectare. This study significantly refines ourunderstanding of urban scaling, making clear that some of what has beenpreviously ascribed to urban environments may simply be the high densityportion of non-urban scaling. It also makes clear that some metrics undergospecific transitions in urban environments and these transitions can includenegative scaling exponents indicative of collapse. This study gives promise offar more sophisticated scale adjusted metrics and indicates that studies ofurban scaling represent a high density subsection of overall scalingrelationships which continue into rural environments.

Rural to urban population density scaling of crime and property transactions in English and Welsh Parliamentary Constituencies