On the relation between transversal and longitudinal scaling in cities

Area of Science:

• Urban dynamics and scaling laws
• Complexity science and network analysis
• Socio-economic systems modeling

Background:

• Transversal scaling describes relationships between city size and urban metrics across cities.
• Longitudinal scaling examines how individual cities evolve over time.
• Empirical data limitations have previously hindered comparative analysis of these scaling types.

Purpose of the Study:

• To investigate whether longitudinal scaling mirrors transversal scaling in urban systems.
• To analyze the temporal evolution of urban metrics (GDP, water network length) in Brazilian cities.
• To develop a mathematical framework connecting micro-level dynamics to macro-level behavior.

Main Methods:

• Analysis of longitudinal scaling exponents for GDP and water network length in over 5500 Brazilian cities.
• Decomposition of data to isolate external factors and focus on high-growth cities.
• Development and application of a mathematical framework for micro-macro connections.

Main Results:

• Longitudinal scaling exponents are city-specific but distributed around an average.
• This average exponent approaches the transversal scaling exponent for high-growth cities after data decomposition.
• The mathematical framework shows good agreement between theoretical predictions and empirical data.

Conclusions:

• Longitudinal urban dynamics are not a simple micro-scaling version of transversal dynamics.
• Scaling behavior varies with city size, urban variables, growth rate, and external factors like policy.
• The study provides a nuanced understanding of urban scaling and opens avenues for research on contextual influences.