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MIT study: people globally follow a “visitation law”; inverse relationship between distance and frequency of visits

A new paper by an MIT team and colleagues in Singapore, China, Italy and Denmark, drawing on global data, finds that people visit places more frequently when they have to travel shorter distances to get there. By examining cellphone data on four continents, the researchers were able to arrive at a distinctive new finding in the urban studies literature. Their paper is published in Nature.

Human mobility impacts many aspects of a city, from its spatial structure to its response to an epidemic. It is also ultimately key to social interactions, innovation and productivity. However, our quantitative understanding of the aggregate movements of individuals remains incomplete. Existing models—such as the gravity law or the radiation model—concentrate on the purely spatial dependence of mobility flows and do not capture the varying frequencies of recurrent visits to the same locations.

Here we reveal a simple and robust scaling law that captures the temporal and spatial spectrum of population movement on the basis of large-scale mobility data from diverse cities around the globe. According to this law, the number of visitors to any location decreases as the inverse square of the product of their visiting frequency and travel distance. We further show that the spatio-temporal flows to different locations give rise to prominent spatial clusters with an area distribution that follows Zipf’s law.

—Schläpfer et al.

To conduct the study, the researchers used anonymized cellphone data from large communications providers to track the movement of people in the metro areas of Abidjan, Ivory Coast; Boston; Braga, Lisbon, and Porto, Portugal; Dakar, Senegal; and Singapore.

Cellphone data are ideal for this kind of study because they establish both the residence area of people and the destinations they travel to. In some cases, the researchers defined areas visited by using grid spaces as small as 500 square meters. Overall, the researchers charted more than 8 billion location-indicating pieces of data generated by more than 4 million people, charting movement for a period of months in each location.

In each case, from city to city, the same inverse law of visitation held up, with the charted data following a similar pattern: The frequency of visits declined over longer distances, and higher-density areas were filled with people who had, on aggregate, taken shorter trips. To the extent that there was some variation from this pattern, the largest deviations involved sites with atypical functions, such as ports and theme parks.

The paper itself both measures the data and presents a model of movement, in which people seek out the closest locations that offer particular kinds of activity. Both of those buttress central place theory, an idea developed in the 1930s by German scholar Walter Christaller, which seeks to describe the location of cities and towns in terms of the functions they offer to people in a region.

The scholars note that the similarity in movement observed in very different urban areas helps reinforce the overall finding.

This generalized behavior is not just something you observe in Boston. From a scientific viewpoint, we are adding evidence about a generalized pattern of behavior.

—Paolo Santi, a research scientist at the Senseable City Lab at MIT and co-author

The researchers also hope the finding, and the methods behind it, can be usefully applied to urban planning. Santi suggests this type of study can help predict how substantial changes in the physical layout of a city will affect movement within it. The method also makes it possible to examine how changes in urban geography affect human movement over time.

The visitation law could have many practical applications—from the design of new infrastructure to urban planning. For instance, it could help implement the concept of the Fifteen-Minute City, which aims to reorganize physical space around walkable neighborhoods and which has become very popular during the COVID-19 pandemic. Our law suggests that we can indeed capture a large fraction of all urban trips within a fifteen-minute radius, while leaving the rest—perhaps 10 percent—further away.

—Carlo Ratti, a co-author of the paper and director of the Senseable City Lab

Support for the research was provided by the National Science Foundation, the AT&T Foundation, the Singapore-MIT Alliance for Research and Technology (SMART), the MIT Center for Complex Engineering Systems, Audi Volkswagen, BBVA, Ericsson, Ferrovial, GE, the MIT Senseable City Lab Consortium, the John Templeton Foundation, the Eugene and Clare Thaw Charitable Trust, the US Army Research Office Minerva program, the Singapore National Research Foundation, and the National Natural Science Foundation of China.


  • Schläpfer, M., Dong, L., O’Keeffe, K. et al. (2021) “The universal visitation law of human mobility.” Nature 593, 522–527 doi: 10.1038/s41586-021-03480-9



This also shows the problem with EVs, that of battery size. If most of your trips are short, you should require a smaller (lighter, cheaper) battery. However, the requirement to undertake the odd long run pushes people to purchase larger batteries that they really need.
Also, it is hard to find a threshold - there is no obvious "just enough" point - it tends to be whatever the manufacturers are providing (and is about 50 kWh now, as far as I can see).
I can see several solutions:
a: Small/medium (12-25 kWh) batteries and range extenders
b: PHEVs (6-12 kWh)
c: Car swapping (formal or informal) for either large battery EVs or ICE cars
d: Flooding the main roads with high speed charging stations.
e: Hydrogen (vast amount of infrastructure needed)
f: Public transport
g: Allow people to keep their ICE cars in parallel with EVs and have a merged insurance / road tax system (and high carbon taxes)
h: Covalent car ownership, where a group of N (N>1) people own M Vehicles (M>=N) of different types.


Actually 300 mile range is adequate. In the past, I have made 3 transcontinental trips (2200 miles in 4 days) with vehicles that had that range. You need to stop after 200 miles or 3 hours, even pets need to stretch their legs or require a bio break.
The 400+ ranges that are available in many vehicles have only happened in the last 20 years thanks to improvements in fuel economy.
From Wired:
"According to Carnegie Mellon University electric vehicle researchers Shashank Sripad and Venkat Viswanathan, who track the relative efficiencies of various electric powertrains and have been analyzing the Lucid Air over the past several weeks, the new car scores 218 watt-hours per mile in overall efficiency—factoring in the car’s stated range, weight, drag, frontal area, and rolling resistance . . .".
That would translate to a 65.4 kWh battery or about the size of a Chevy Bolt battery.
If an advanced LiFePo battery was used cost and weight would be similar a 18 kWh PHEV battery currently used by Honda and Toyota.

Bernard Harper

This study is missing two important metrics: time of typical journeys and method e.g. cycling. Most of my daily journeys last only 10 minutes by car. Cycling (if it were safe and practical for me) would be life-changing because so many places without car parking are only 10-15 minutes away. So duration and method matter, as do safety, comfort and weather.

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