Urban population scaling of resource use, creativity metrics, and human behaviors has been widely studied. These studies have not looked in detail at the full range of human environments which represent a continuum from the most rural to heavily urban. We examined monthly police crime reports and property transaction values across all 573 Parliamentary Constituencies in England and Wales, finding that scaling models based on population density provided a far superior framework to traditional population scaling. We found four types of scaling: i) non-urban scaling in which a single power law explained the relationship between the metrics and population density from the most rural to heavily urban environments, ii) accelerated scaling in which high population density was associated with an increase in the power-law exponent, iii) inhibited scaling where the urban environment resulted in a reduction in the power-law exponent but remained positive, and iv) collapsed scaling where transition to the high density environment resulted in a negative scaling exponent. Urban scaling transitions, when observed, took place universally between 10 and 70 people per hectare. This study significantly refines our understanding of urban scaling, making clear that some of what has been previously ascribed to urban environments may simply be the high density portion of non-urban scaling. It also makes clear that some metrics undergo specific transitions in urban environments and these transitions can include negative scaling exponents indicative of collapse. This study gives promise of far more sophisticated scale adjusted metrics and indicates that studies of urban scaling represent a high density subsection of overall scaling relationships which continue into rural environments.
Scale-adjusted metrics (SAMs) are a significant achievement of the urban scaling hypothesis. SAMs remove the inherent biases of per capita measures computed in the absence of isometric allometries. However, this approach is limited to urban areas, while a large portion of the world’s population still lives outside cities and rural areas dominate land use worldwide. Here, we extend the concept of SAMs to population density scale-adjusted metrics (DSAMs) to reveal relationships among different types of crime and property metrics. Our approach allows all human environments to be considered, avoids problems in the definition of urban areas, and accounts for the heterogeneity of population distributions within urban regions. By combining DSAMs, cross-correlation, and complex network analysis, we find that crime and property types have intricate and hierarchically organized relationships leading to some striking conclusions. Drugs and burglary had uncorrelated DSAMs and, to the extent property transaction values are indicators of affluence, twelve out of fourteen crime metrics showed no evidence of specifically targeting affluence. Burglary and robbery were the most connected in our network analysis and the modular structures suggest an alternative to “zero-tolerance” policies by unveiling the crime and/or property types most likely to affect each other.
Eq 3 and the subsequent inline equation are incorrect. The correct equation and inline equation should be: "where d à is a population density threshold, β L (β H ) is the power-law exponent for low (high) population density, y 0 and y 1 are constants. In particular, we have chosen log
Cyril Dean Darlington’s paternal great-grandfather was Henry Robertson, a merchant of Liverpool, Buenos Aires and Montevideo, and a cousin of W. E. Gladstone, the nineteenth century Liberal Prim e Minister of Great Britain. Henry fathered a son illegitimately by his Welsh nursemaid, Mary Davies of Wrexham , at Salford in 1873; this son was given the name Henry Robertson Darlington, the name Darlington coming from Mary Davies’s later husband, William Darlington, a black smith and iron-founder. Henry Darlington married Alice Dean who gave birth to Cyril’s father, William Henry Robertson Darlington (1866-1943), a schoolm aster and secretary. Cyril has described this change of his paternal name with his characteristic light-hearted and irreverent style— ‘The business end of my Y chromosome therefore comes from Fife and not Durham ’— the county containing the town Darlington. Cyril’s maternal grandfather was a Frankland, son of a Unitarian minister of Whitby, married to a Cowling, an old family of solicitors of York. His mother, Ellen Darlington
née
Frankland (1874-1949) had two sons, Alfred Frankland Dean and Cyril Dean.
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