Researchers put human mobility into new formula

For most people, everyday mobility is something concrete and easy to understand. On a daily basis, we typically move around in our local area, occasionally go to another city, and only more sporadically travel further away.

With location data from mobile phones, it is has become easier to map these movements accurately, and such data has been used to develop completely new mathematical models for human movement patterns within the field of statistical physics.

However, as revolutionary these models have been, they have also created deep scientific contradictions.

While social scientists, like the rest of us, divide the world into geographical spaces such as cities and countries, the physicists’ models have not been able to detect that we move within or between such places with typical scales. In fact, they have only found that our movements follow a so-called power law, in which the chance of being in a particular place decreases exponentially with distance. They are scale free.

It contradicts our everyday experience and it is actually misleading, according to researchers associated with DTU and the University of Copenhagen. In an article published in Nature, one of the world's leading journals, they now challenge the prevailing mathematical models.

"The power laws that physicists have found in mobility research are the 'state-of-the-art' in physics and are very robust. Nevertheless, common sense also tells us that there are indeed geographical scales. We have, for example, maps of continents, countries and cities, so the claim that scales do not exist seems a bit crazy. It is a paradox,” says Sune Lehmann, professor at DTU and Copenhagen Center for Social Science Data (SODAS) at the University of Copenhagen.

Against this backdrop, a strong motivator behind the team’s work has been two questions: How can there be paper after paper in high impact journals, which all find that human mobility is scale free? And why have we not been able to find scales in mobile data?

The answer to the latter puzzle is simple: You can indeed find scales – if you look closely enough.

New model finds natural scales

In close collaboration with the co-authors of the article, assistant professor Laura Alessandretti and postdoc Ulf Aslak, Lehmann has developed a new mathematical model that derives geographical sizes of mobile tracking data that match normal notions of neighborhoods, cities and countries.

Thus, the three researchers in the Nature article build a bridge between the mathematical models of natural science and the geographical concepts used in social sciences, and this is, according to Sune Lehmann, the great breakthrough.

“The model brings two academic worlds together: the approach from traditional areas such as geography and transportation research and the newer approaches driven by big data. These two literatures had different results that no one could explain. We can do that now, and it is a new insight that we hope can drive science forward in both fields.”

The mathematics in the model are somehow technical. Simply stated, the model can, based on movement data, identify when we are within certain areas of a typical size by, e.g. by including a time perspective into the calculations. At the same time, the model is able to describe how we move from one area to another. That could be between two neighborhoods in the same city or to a neighborhood in another city – or other types of movements.

The researchers call the areas 'containers', but by combining individual movement patterns, they can be translated into common geographical places. By adding mobile data from more than 700,000 individuals in Denmark and around the world, the model precisely identifies sizes of neighborhoods, cities, regions and countries (see figure).

Figure: Example of one person's movement patterns (in large format)

A model of great practical significance

The key problem with the previous models, according to Lehmann, is that they have mixed movements within an area along with movements across geographical places. With the right mathematical lens, one rediscovers the natural scales.

The question then is whether this has any greater significance other than bridging a theoretical discussion between physicists and geographers.

Yes, the researchers argue. The new model does not only describe people's movement patterns more accurately by including the typical sizes of areas people are located and how long they stay there. It can also generate new knowledge about how we move from place to place.

“Better models of mobility can always be used. In traffic planning, the transport sector and in the fight against epidemics, to mention a few examples. We can measure and understand movements in such fields better with more accurate models,” says Lehmann.

In the article, the three researchers test their own model by examining mobility differences in different population groups and geographical areas. Among other things, they find that women in 21 of the 53 countries surveyed on a daily basis switch between more geographical levels compared with men. This is a new finding.

Other results confirm well-establish knowledge. For example, that women tend to move within smaller areas, and that the local areas of people living in the countryside are larger compared to those of urban individuals.

Read more at Nature: 
The Scales of Human Mobility (article) 
Hierarchies defined through human mobility (editorial story)

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