On the Meaning of Urban Scaling

TL;DR

This paper critically examines urban scaling laws, revealing that their exponents do not accurately describe individual city growth but instead reflect broader statistical patterns across many cities.

Contribution

It challenges the common interpretation of scaling exponents, showing they do not represent individual city trajectories but are influenced by diverse city histories and constraints.

Findings

Scaling exponents reflect statistical patterns, not individual city growth.

Cross-sectional laws reveal system-level regularities, not growth mechanisms.

Apparent sublinear or superlinear scaling can occur without complex dynamics.

Abstract

Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are influential because their exponent is often interpreted as describing what happens when a city grows, with implications for urban theory, planning, and policy. Here, we show that this interpretation is generally misleading. An exponent measured by comparing many cities at one date does not, in general, describe the trajectory of any individual city. Instead, it reflects a statistical pattern produced by cities with different histories, constraints, institutions, and growth paths. Apparent sublinear or superlinear scaling can therefore arise even when individual cities follow simpler dynamics, as we show for the area--population relation. Cross-sectional scaling laws can reveal system-level regularities, but should not be used alone to infer growth mechanisms or guide policy for a given city.