Constructing cities, deconstructing scaling laws

TLDR

Cities are modelled by various urban measures, and consistency among these observables is essential for a science of cities; Bettencourt et al propose that many such measures follow universal scaling laws. The study develops a framework that defines cities consistently via commuting patterns and population density thresholds, generating thousands of city‑system realizations for England and Wales. The constructed city‑system realizations serve as a laboratory for scaling analysis of many urban indicators. The analysis reveals that population size alone cannot predict city state, contradicting expected scaling laws; most urban indicators scale linearly with city size regardless of boundary definition, but exponents vary markedly when non‑linear correlations arise.

Abstract

Cities can be characterised 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 realisations 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 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 non-linear correlations are present, the exponent fluctuates considerably.