Most of the cities that exist today originally grew from an important marketplace or town square. Over time, they developed multiple centers where people could go to work, shop and play—in fact, no major world city has just a single center anymore. So, what governs the transition of a city from monocentric to polycentric? Economists have suggested polycentrism is driven by business agglomeration—the idea that companies are more successful when they are clustered. But physicist Marc Barthelemy of the Institute for Theoretical Physics in France says that is only part of the story.

In a new paper in Physical Review Letters, Barthelemy and his colleague, Remi Louf, have constructed a mathematical model to explain how cities and their surrounding suburbs evolve to be polycentric. Their findings suggest that population size and automobile traffic congestion play large roles in driving the creation of alternative hot spots, even in small- to medium-size cities. “It’s an interplay between how attractive the place is, and how much time it takes to go there,” he says. At first everyone goes to the city center, but as the city becomes increasingly crowded it becomes more difficult to get there. Eventually subcenters spring up toward the city’s outskirts, providing more convenient locations for residents to work and shop. Cities with accommodating transportation networks remain centralized longer, but once population density passes a certain threshold, cities inevitably become polycentric, Barthelemy says.

It’s a simple model—for instance, it does not account for zoning restrictions or for the fact that some cities, such as London, emerged as polycentric entities hundreds of years ago when several smaller villages consolidated—but it is still a useful model for exploring polycentricity, says Michael Batty, an urban planner at University College London, who wasn’t involved in the study. “Although it is a major simplification of the real world, it has enough elements to make it work, and the dynamics they produce are interesting and plausible.”

David Levinson, a transportation engineer at the University of Minnesota, says it is not altogether surprising to find a relationship between population size and the number of urban subcenters. A group of economists made that assumption a few decades ago. Barthelemy counters that the economic models were “fuzzy” and untested. “After 20 pages of calculation, they don’t have a prediction and they don’t test their model,” Barthelemy says. “We can test our results against data.”

To test the prediction that the number of subcenters scales with population, the researchers used employment data across 9,000 U.S. cities and towns. “If you know where people are working, you can see these activity centers,” Barthelemy says. The data showed that as a city’s population increases, so does the number of subcenters. But the two do not scale linearly—if a population grows to 10 times its original size, the number of centers is multiplied by five, on average. Barthelemy says he expects the pattern to hold across cities in other countries of the world as well.

Having a clearer understanding of the evolution of metropolitan polycentricity could prove useful, Levinson says, especially considering that two thirds of the world’s population is expected to be urban by the year 2050. “There’s a lot of urbanization left to happen,” Levinson says. “If planners imagine a city to take a particular form, but that’s not the way the city wants to behave, we’ll be making unwise investments.”

The authors are still fine-tuning their model. Future versions will likely include other modes of transportation, such as public transportation, which would be expected to slow the appearance of new centers of activity.

Barthelemy says the model could also come in handy for estimating traffic delays, gas consumption and carbon dioxide emissions, so that urban planners and policy makers can better understand how those different factors evolve as a city grows. “I think that this this opens up the path to some really quantitative insights about cities,” he says. “We can take simple mechanisms, simple ingredients, and in the end predict how important properties are scaling with population.”