On the relation between transversal and longitudinal scaling in cities

• Published in: PloS one 2020-05, Vol.15 (5), p.e0233003
• Main Authors: Ribeiro, Fabiano L, Meirelles, Joao, Netto, Vinicius M, Neto, Camilo Rodrigues, Baronchelli, Andrea
• Format: Article
• Language: English
• Subjects: Biology and Life Sciences; Brazil; Cities; Cities - economics; Cities - statistics & numerical data; Cities and towns; Complex systems; Earth Sciences; Ecology and Environmental Sciences; Economic aspects; Economic research; Empirical analysis; Evolution; Gross domestic product; Gross Domestic Product - statistics & numerical data; Growth rate; Humans; Infrastructure (Economics); Longitudinal Studies; Mathematical analysis; Metropolitan areas; Models, Statistical; Nature; People and places; Population; Population Density; Population Growth; Population number; Profits; Public Policy; Scaling; Scaling laws (Mathematical physics); Social Sciences; Time; Urban areas; Urban Population - statistics & numerical data; Urban Renewal - economics; Urban Renewal - statistics & numerical data; Urbanization; Variables; Water; Water Supply - statistics & numerical data
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0233003

Does the scaling relationship between population sizes of cities with urban metrics like economic output and infrastructure (transversal scaling) mirror the evolution of individual cities in time (longitudinal scaling)? The answer to this question has important policy implications, but the lack of suitable data has so far hindered rigorous empirical tests. In this paper, we advance the debate by looking at the evolution of two urban variables, GDP and water network length, for over 5500 cities in Brazil. We find that longitudinal scaling exponents are city-specific. However, they are distributed around an average value that approaches the transversal scaling exponent provided that the data is decomposed to eliminate external factors, and only for cities with a sufficiently high growth rate. We also introduce a mathematical framework that connects the microscopic level to global behaviour, finding good agreement between theoretical predictions and empirical evidence in all analyzed cases. Our results add complexity to the idea that the longitudinal dynamics is a micro-scaling version of the transversal dynamics of the entire urban system. The longitudinal analysis can reveal differences in scaling behavior related to population size and nature of urban variables. Our approach also makes room for the role of external factors such as public policies and development, and opens up new possibilities in the research of the effects of scaling and contextual factors.