Cross-City Scaling Laws Mislead About How Individual Cities Grow

Scaling laws have long been one of the most influential tools for comparing cities. By plotting aggregate urban quantities—infrastructure length, socioeconomic output, environmental impacts—against population size across many cities at once, researchers obtain a scaling exponent that seems to say what happens when a city grows. A new study by Ulysse Marquis and Marc Barthelemy, published in Nature Cities, argues that this interpretation is generally misleading, and that the mismatch has real consequences for urban theory, planning and policy.

The core of the argument is statistical. A scaling relationship fitted across many cities at a single point in time does not, in general, describe the trajectory of any individual city. Instead, it reflects a pattern across cities with different histories, constraints, institutions and growth paths. Each city follows its own temporal dynamics, shaped by local conditions, while the cross-sectional exponent aggregates all of those differences into a single number. Confusing the two, the authors show, can lead observers to conclude that an urban quantity increases more slowly or more rapidly than population—even when individual cities follow much simpler dynamics.

The paper illustrates the problem with the relationship between urban area and population. When many cities are compared at one moment, the fitted scaling can suggest a particular growth rule for how land consumption changes as cities expand. But that transversal, or cross-sectional, pattern does not track how any given city actually develops over time. The statistical contributions of cities with different sizes, densities and histories combine to produce an exponent that can diverge substantially from the behaviour of individual urban trajectories, as the authors demonstrate for the area–population relation.

Similar caution applies to the quantities most often cited in urban scaling debates, including wages and other measures of socioeconomic activity. The study’s figures separate the cross-sectional scaling of area and population from the statistical contributions behind the transversal exponent, and from the transversal scaling of wages, showing how a single fitted exponent can emerge from a mixture of city-specific factors rather than from a shared growth mechanism.

The practical implication is direct. Cross-sectional scaling laws describe statistical relationships across cities, not the temporal dynamics of individual cities, and the authors conclude that they should therefore not be used to infer growth mechanisms or to guide policy for any particular city. A planner who reads a superlinear or sublinear exponent from a cross-city comparison as a prediction for one city’s future may be importing a statistical artefact into a decision that demands city-specific evidence. The finding does not dismiss scaling laws as a descriptive tool for comparing urban systems; it draws a sharp line between what such laws can legitimately say—how cities differ from one another at a given time—and what they cannot: how any single city will grow.

Subject of Research: Cross-sectional urban scaling laws versus the growth dynamics of individual cities

Article Title: Urban scaling and the dynamics of individual cities

Article References: Marquis, U., & Barthelemy, M. (2026). Urban scaling and the dynamics of individual cities. Nature Cities. https://doi.org/10.1038/s44284-026-00533-w

Image Credits: AI Generated

DOI: 10.1038/s44284-026-00533-w

Keywords: urban scaling, cities, population growth, urban area, scaling exponents, cross-sectional analysis, urban theory, urban planning, socioeconomic activity, Nature Cities, Urban, scaling