On the Meaning of Urban Scaling

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.