Research Article: Evolution of urban scaling: Evidence from Brazil

Date Published: October 4, 2018

Publisher: Public Library of Science

Author(s): Joao Meirelles, Camilo Rodrigues Neto, Fernando Fagundes Ferreira, Fabiano Lemes Ribeiro, Claudia Rebeca Binder, Celine Rozenblat.


During the last years, the new science of cities has been established as a fertile quantitative approach to systematically understand the urban phenomena. One of its main pillars is the proposition that urban systems display universal scaling behavior regarding socioeconomic, infrastructural and individual basic services variables. This paper discusses the extension of the universality proposition by testing it against a broad range of urban metrics in a developing country urban system. We present an exploration of the scaling exponents for over 60 variables for the Brazilian urban system. Estimating those exponents is challenging from the technical point of view because the Brazilian municipalities’ definition follows local political criteria and does not regard characteristics of the landscape, density, and basic utilities. As Brazilian municipalities can deviate significantly from urban settlements, urban-like municipalities were selected based on a systematic density cut-off procedure and the scaling exponents were estimated for this new subset of municipalities. To validate our findings we compared the results for overlaying variables with other studies based on alternative methods. It was found that the analyzed socioeconomic variables follow a superlinear scaling relationship with the population size, and most of the infrastructure and individual basic services variables follow expected sublinear and linear scaling, respectively. However, some infrastructural and individual basic services variables deviated from their expected regimes, challenging the universality hypothesis of urban scaling. We propose that these deviations are a product of top-down decisions/policies. Our analysis spreads over a time-range of 10 years, what is not enough to draw conclusive observations, nevertheless we found hints that the scaling exponent of these variables are evolving towards the expected scaling regime, indicating that the deviations might be temporally constrained and that the urban systems might eventually reach the expected scaling regime.

Partial Text

Today, more than half of the world population lives in cities [1] and this share is likely to increase in the next years. Thus, it has become more and more important to understand how urban systems evolve with increasing population and what the social, economic, and ecological implications of these developments are. During the last decades, urban data had become increasingly accessible in a structured and machine-readable way. These newly available datasets, combined with approaches from complexity sciences are setting the ground for a new science of cities [2, 3]. In this recent scientific approach to urban studies, a paradigm has arisen, which focuses not on the particularities of cities, but on their common patterns. More specifically, it considers that the form and the function of urban systems are caused by universal laws that emerge from elementary local level interactions [2–5]. Based on this framework, recent findings have suggested similarities between cities from very different cultural, historical, geographical, and economic background, however mostly in the developed world and for a limited set of variables [6–9]. As the possibility of formalizing a universal law of urban growth, in terms of its socio-economic and ecological impacts, might have a large implication for urban planning, it is key to understand whether this universality plays out for cities in countries with different development stages (i.e. BRICS countries, developing countries) and if the findings hold true for other variables.

In this section, the results obtained from the analysis of the Brazilian municipalities dataset are presented. Given the large number of variables, only a representative sample is presented in the plots. Plots with the complete set of variables are presented in the Supporting Information S1 and S2 Figs, S2 Table.

This research aimed at understanding whether the proposed urban scaling laws are universal, under which conditions deviations can be observed and whether these deviations are ephemeral if we test them against a broad number of variables in a economically developing urban system.

This paper tested the universality hypothesis of urban scaling against a broad range or variables for a urban system in a developing country. Our findings confirm that the the scaling-law holds true for the socio-economic variables. However, we found that some infrastructural and basic individual services variables (related to sewage and health services) did not scale as proposed in literature. This observation imposes some limits to the universality hypothesis, which postulates that dense human settlements would generate the same scaling patterns regardless of the specific characteristics of the urban system. We hypothesize that the differences observed relate to country specific investment policies and economic conditions. Thus, if an infrastructural variable is dependent on top-down decisions and/or is not universally accessible across the urban systems, it can deviate from the expected sublinear scaling. In our subset of Brazilian municipalities this is the case for infrastructural variables as length of sewage collection network and health facilities, where superlinear/linear exponents were found. We also found exploratory evidences that the deviations are ephemeral and variables describing such infrastructures tend to evolve, over time, towards their expected values. These findings should be validated and new empirical evidence should be raised for other developing countries, other variables and more comprehensive functional cities definitions. Our findings show the importance of including developing countries to make the universality hypothesis truly universal.




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