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City Growth Is Weirdly Predictable

Researchers unearth a simple pattern of population growth and decline in four major cities in the U.S. and Europe.

By Nathan Collins


Traffic at night in Paris, France. (Photo: Richard Schneider/Flickr)

It would be tempting to think that a city’s population grows steadily upward over time. That is, after all, exactly what the world’s population has basically done for tens of thousands of years. But reality is not so simple: According to a new study, the number of people living in a given city or neighborhood tends to grow to a maximum, shrink back down, then grow again. And the reason could be quite simple: the conversion of residential units into new commercial spaces.

“Although urban development and the distribution of residential activity in urban areas are long-standing problems tackled by economists and geographers, a quantitative understanding of the different processes characterizing this phenomenon is still lacking,” Giulia Carra and Marc Barthelemy write. In particular, they argue, researchers lack testable models of urban growth, in large part because existing models have too many moving parts.

In search of something simpler they could test, Carra and Barthelemy looked to recent land-use data, such as New York City’s Property Land Use Tax Lot Output database, which includes information on the location, size, and age of of nearly all buildings in the five boroughs. The researchers gathered similar data for Chicago, London, and Paris, along with population data going back to the early 19th century and, for Paris, to the late 10th century.

There appears to be a universal pattern of urban growth.

In each city, population density grew at an ever-increasing rate until roughly the second half of the 19th century, after which it peaked, fell slightly, and resumed climbing. That pattern holds up in individual neighborhoods, bureaus, and arrondissements as well, although the details—when the peak happens, what the maximum density is, and so forth—vary. Building construction follows a similar trajectory. At first, it grows rapidly along with the population, then slows dramatically after the population peaks, and picks up again once the population starts to climb back up.

Based on those observations, Carra and Barthelemy propose a simple model of urban growth: At any given time, builders are either constructing new buildings on an empty plot, adding additional residential floors to an existing building, or converting residences to commercial use. (There’s also a chance they’re doing nothing at all.) If builders convert residences faster than they build new ones, the model predicts the first two phases—initial growth and subsequent decline—the team observed in its data. (The last phase, during which population density grows again, appears to kick off all at once citywide, suggesting a coordinated planning effort the team doesn’t attempt to model.)

Model in hand, the researchers turned back to the data and found that each neighborhood in all four cities follows exactly the same pattern of growth—the one predicted by the model—once one adjusts for just two parameters: the average building’s footprint and the typical number of people who live on each floor. In other words, there appears to be a universal pattern of urban growth, at least across the four cities Carra and Barthelemy consider.

“Beside showing that a minimal modeling for describing urbanization is possible despite the large variety of cities, we believe that this approach could constitute the basis for more elaborated models,” Carra and Barthelemy write. “These models could then be thoroughly tested against data, could describe the impact of various parameters and also help to understand some features of the possible future evolution of cities.”