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., 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.Comment: Accepted for publication in PLoS ON
