Scale-Adjusted Metrics for Predicting the Evolution of Urban Indicators and Quantifying the Performance of Cities

Abstract

More than a half of world population is now living in cities and this number is expected to be two-thirds by 2050. Fostered by the relevancy of a scientific characterization of cities and for the availability of an unprecedented amount of data, academics have recently immersed in this topic and one of the most striking and universal finding was the discovery of robust allometric scaling laws between several urban indicators and the population size. Despite that, most governmental reports and several academic works still ignore these nonlinearities by often analyzing the raw or the per capita value of urban indicators, a practice that actually makes the urban metrics biased towards small or large cities depending on whether we have super or sublinear allometries. By following the ideas of Bettencourt et al. [PLoS ONE 5 (2010) e13541], we account for this bias by evaluating the difference between the actual value of an urban indicator and the value expected by the allometry with the population size. We show that this scale-adjusted metric provides a more appropriate/informative summary of the evolution of urban indicators and reveals patterns that do not appear in the evolution of per capita values of indicators obtained from Brazilian cities. We also show that these scale-adjusted metrics are strongly correlated with their past values by a linear correspondence and that they also display crosscorrelations among themselves. Simple linear models account for 31%–97% of the observed variance in data and correctly reproduce the average of the scale-adjusted metric when grouping the cities in above and below the allometric laws. We further employ these models to forecast future values of urban indicators and, by visualizing the predicted changes, we verify the emergence of spatial clusters characterized by regions of the Brazilian territory where we expect an increase or a decrease in the values of urban indicators.

Rural to Urban Population Density Scaling of Crime and Property Transactions in English and Welsh Parliamentary Constituencies

“…Finally, this study adds evidence to the long-standing challenge to crime rates and per capita comparisons [ 6 , 11 , 15 , 26 ]. It is clear that high or low per capita crime rates are uninterpretable outside of the context of the scaling law to which they belong and, based on the current study, similar considerations are appropriate for the study of property transactions.…”

“…Although scaling behaviour follows similar mathematical forms, urban scaling parameters are not universal with coefficients varying between countries. For example, population scaling of homicide in cities in Colombia, Brazil, Mexico, and the United States vary widely [ 6 , 9 , 11 , 15 ] as well as vary over time for several urban metrics in Brazil [ 26 ].…”

Nursing Research Literature Production in Terms of the Scope of Country and Health Determinants: A Bibliometric Study

“…That might be due to the fact that per capita indicators represent normalized variables, eliminating the population size as a factor in the analysis. The normalization is comparable to scale‐adjusted metrics (Alves, Mendes, Lenzi, & Ribeiro, ), which were better predicators in different urban, environmental, and demographics analyses (Oliveira, Ribeiro, Bastos‐Filho, & Menezes, ; Ribeiro, Hanley, & Lewis, ).…”

Urban scaling in Europe

“…The decomposition of any urban observable into two components, an expected value as a function of city size (scaling relation) and a local deviation ξ , parametrizes the tension between what is general and what is particular, respectively, about each city within an urban system. Because of these properties, the values of ξ i have been used as scale independent urban indicators (SAMIs) to characterize the relative performance of cities within an urban system [ 18 , 33 ] (see the electronic supplementary material). If the dispersion (the variance, ) is larger for a given urban system or a specific quantity, then the scaling relation (average expectation) is less predictive and vice versa.…”