Evolution of urban scaling: Evidence from Brazil

Abstract

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.

On the relation between transversal and longitudinal scaling in cities

“…Those cases behave differently from the pattern uncovered by our approach. This result (10) was also obtained by Bettencourt et al [47] using a slightly different approach. The result (10) also suggests that if F ext > 0 and b i > 1, which means that both the intercept parameter (global growth) and the population are growing in time, then β i will always be greater than the global exponent β T .…”

“…A recent work [10] has shown that over 60 variables for the Brazilian urban system are well described by a power-law equation of the form:…”

“…A crucial finding concerns the scaling properties of urban systems. Empirical evidence has shown that an urban variable, Y, scales with the population size N of a city, obeying a power law of the kind Y / N β , where β is the scaling exponent quantifying how the urban metric reacts to the population increase [6][7][8][9][10][11][12]. On the one hand, the data revealed that socioeconomic urban variables such as the number of patents, wages, and GDP present a superlinear behavior in relation to the population size (β > 1).…”

“…According to this proposition, in the long term, the general performance of a particular city would be largely independent of individual political choices. However, the universality proposition has been challenged, either by counter-evidence [10,28,[35][36][37], or by methodological arguments [38][39][40][41][42]. Thus, the universality proposition is still an open question both from the methodological and the theoretical point of views.…”

The statistical physics of cities

“…Determining under which conditions scaling is correct is then a challenge for studies in this directions. Additionally, it has been recently suggested [85] that scaling exponents could experience time dependence and could converge to 'equilibrium' values, but more data are needed to test this assumption.…”