Over years, months and days, city dwellers around the world move similarly: Through a massive, multi-institutional project involving millions of people and billions of data points, an international team of researchers have formulated an equation that is capable of tracking large-scale population mobility in cities from different cultures across the planet. 

The findings, outlined in a Nature paper published Wednesday, show that people travel shorter distances relatively frequently and longer distances less often, suggesting that, in general, residents tend to travel rationally, making longer trips only when necessary. Through partnerships with telecommunication companies and government agencies, the researchers gathered phone records from the greater Boston area as well as Portugal, Senegal, the Ivory Coast and Singapore. Gathered between 2006 and 2013, the data comprised over 3 billion time-stamped locations from more than 8 million anonymized users. The team hailed from the Massachusetts Institute of Technology, the Santa Fe Institute and ETH Zürich, among other institutions.

"We started looking at one of the data sets we are more familiar with, which is the Boston one. And then, as we found this law, of course, the next question was: Is this only in Boston or [does it] occur in other places?" Paolo Santi, a principal research scientist at MIT's Senseable City Lab and a research supervisor for the project, asked in an interview with The Academic Times. "And we started reapplying the same ideas to the several data sets we had access to."

The researchers found that their model remained consistent across each of the locations they examined: People living in a densely packed modern metropolis such as Singapore traveled in roughly the same manner as those in a walkable European city such as Braga, Portugal or a car-centric American hub such as Boston.

The researchers' equation, which closely aligns with the well-established inverse square law in mathematics and science, can be visualized as a light source shining on objects at various distances. The light will shine onto nearby objects with greater intensity over a smaller range than faraway objects, which will receive less concentrated light over a greater area. In population dynamics, the light source can be thought of as a person who frequently visits a small pocket of nearby locations and infrequently travels to a wider range of long-distance locations. 

The paper seems to confirm some aspects of the central place theory, a way of examining the construction of settlements and cities based partly on the goods and services available in different areas. The theory holds that people will seek common, everyday necessities such as groceries at nearby locations but will be willing to make longer trips for more specialized services that are unavailable near their home. Those less-frequented places — a car dealership, for instance, which someone may only need to visit every few years, at most — will also be more likely to attract a geographically diverse customer base, as each visitor will have a higher likelihood of coming from a different area of the city or another town altogether. 

The team contended with several limitations, most having to do with the incomplete results yielded by relatively simplistic cellphone data. For instance, because the phone records were anonymized, researchers could not identify demographic information such as income, race and education level. That information would help scientists understand whether people are more likely to enter ethnically and socioeconomically diverse neighborhoods or whether they instead tend to stay in locations occupied by people demographically similar to themselves. Such data would also help urban planners identify the conditions that help some cities proactively foster more diverse environments in which people of different backgrounds frequently interact.

Economists such as the Nobel Prize-winning Richard Thaler have pointed out that, while weighing life choices, humans may make irrational decisions based on environmental and cognitive biases. That doesn't seem to be the case in large-scale population dynamics: "Although game theory shows that collective human [behavior] is often non-rational and far from the socially desired outcome, this result suggests that, when it comes to travel effort, humans are able to achieve optimal group-level [behavior]," the authors wrote.

The new study suggests that the models urban planners use to assess population dynamics may have a relatively high degree of accuracy. This could have wide-ranging implications for governments, investors and architects, who may want to predict, for instance, the number of potential visitors to a newly constructed shopping mall. 

Humans "are able to understand what is the most convenient location to go to for getting a certain type of service," Santi said. "And this is good news for urban planners and for all of the retail industry." 

The model could also help epidemiologists better estimate how diseases will spread throughout communities, as the researchers' law can be combined with existing epidemic models. During lockdowns throughout the coronavirus pandemic, some governments have enacted travel restrictions that limit access to certain regions. But with the aid of the team's findings, such regulations could also consider the frequency at which people visit particular areas of the city, Santi explained. 

The findings gave the researchers confidence that thoughtful design principles do indeed have an impact on the livability of urban spaces — and that residents, in turn, may naturally make decisions that act in accordance with designers' predictions. 

"If you plan the space well, people can use it well," said Santi. 

The paper "The universal visitation law of human mobility," published May 26 in Nature, was authored by Markus Schläpfer, Massachusetts Institute of Technology, Santa Fe Institute and ETH Zürich; Lei Dong, Massachusetts Institute of Technology and Peking University; Paolo Santi, Massachusetts Institute of Technology, Istituto di Informatica e Telematica del CNR; Michael Szell, Massachusetts Institute of Technology, IT University of Copenhagen and the Institute for Scientific Interchange; Hadrien Salat, ETH Zürich and Orange Labs; Kevin O'Keeffe, Samuel Anklesaria, Mohammad Vazifeh and Carlo Ratti, Massachusetts Institute of Technology; and Geoffrey B. West, Santa Fe Institute.