Abstract
Cities can be characterized and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al. have proposed that many of these urban measures can be predicted through universal scaling laws. We develop a framework to consistently define cities, using commuting to work and population density thresholds, and construct thousands of realizations of systems of cities with different boundaries for England and Wales. These serve as a laboratory for the scaling analysis of a large set of urban indicators. The analysis shows that population size alone does not provide us enough information to describe or predict the state of a city as previously proposed, indicating that the expected scaling laws are not corroborated. We found that most urban indicators scale linearly with city size, regardless of the definition of the urban boundaries. However, when nonlinear correlations are present, the exponent fluctuates considerably.
Highlights
Cities are the outcome of intricate social and economic dynamics, shaped by geographical, cultural and political constraints
It is conjectured that the nature of the urban observable will unequivocally define one of the three universal categories to which the scaling exponent b belongs: (i) b, 1, a sublinear regime given by economies of scale associated with infrastructure and services, e.g. road surface area; (ii) b % 1, a linear regime associated with individual human needs, e.g. housing and household electrical consumption and (iii) b . 1, a superlinear regime associated with outcomes from social interactions, e.g. number of patents and income [18]
We investigate the extent to which in England and Wales (E&W)1, urban indicators can be estimated on the basis of size alone according to equation (1.1), regardless of constraints, such as intercity interactions, globalization or historical dependencies
Summary
Cities are the outcome of intricate social and economic dynamics, shaped by geographical, cultural and political constraints. Instead of limiting the analysis to a single predefined definition of cities such as LUZ, we define a simple procedure that produces a system of cities by aggregating small statistical units We chose this approach for the following reasons: (i) the LUZ selection of cities is very small as only 21 cities in E&W are considered, whereas important cities such as Oxford and Reading are missing, leading to a small sample space; (ii) the procedure can be reproduced in other countries and it allows for a consistent comparison with other urban systems, and more importantly, (iii) this methodology provides a set of different realizations of the urbanized space, serving as a laboratory to explore the sensitivity of the urban indicators to a comprehensive set of different city and metropolitan area demarcations in E&W, leading to a more rigorous framework to test urban hypotheses.
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