A model of urban scaling laws based on distance-dependent interactions
Authored by Fabiano L Ribeiro, Joao Meirelles, Fernando F Ferreira, Camilo Rodrigues Neto
Date Published: 2017
DOI: 10.1098/rsos.160926
Sponsors:
Brazilian Ministry of Education (CAPES)
Brazilian National Council for Scientific and Technological Development (CNPq)
Platforms:
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Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
Model code not found
Abstract
Socio-economic related properties of a city grow faster than a linear
relationship with the population, in a log-log plot, the so-called
superlinear scaling. Conversely, the larger a city, the more efficient
it is in the use of its infrastructure, leading to a sublinear scaling
on these variables. In this work, we addressed a simple explanation for
those scaling laws in cities based on the interaction range between the
citizens and on the fractal properties of the cities. To this purpose,
we introduced a measure of social potential which captured the influence
of social interaction on the economic performance and the benefits of
amenities in the case of infrastructure offered by the city. We assumed
that the population density depends on the fractal dimension and on the
distance-dependent interactions between individuals. The model suggests
that when the city interacts as a whole, and not just as a set of
isolated parts, there is improvement of the socio-economic indicators.
Moreover, the bigger the interaction range between citizens and
amenities, the bigger the improvement of the socio-economic indicators
and the lower the infrastructure costs of the city. We addressed how
public policies could take advantage of these properties to improve
cities development, minimizing negative effects. Furthermore, the model
predicts that the sum of the scaling exponents of social-economic and
infrastructure variables are 2, as observed in the literature.
Simulations with an agent-based model are confronted with the
theoretical approach and they are compatible with the empirical
evidences.
Tags
power laws
Complex systems
networks
scaling laws
Population-growth
Cities
Zipfs law
Agglomeration effects
Urban
indicators
Public policies