In a new paper, published in Nature Human Behaviour, scientists from DTU (the Technical University of Denmark) examine how geography shapes human mobility and propose a way to separate physical constraints from behavioural patterns; a result that may improve urban planning, transportation design as well as epidemiology models.
Using 36 years of detailed residential relocation data from Denmark, which covers 39 million moves, between more than three million addresses, the researchers show that when you account for the influence of geography, the likelihood of moving decreases consistently with distance. This means, roughly speaking, that if you double the distance, the likelihood of people moving there is half. In cities, however, distance matters less.
The reader would be right in thinking this result seems obvious. But from a scientific perspective, the data describing these several million moves was anything but simple.
"Looking at how people have moved, it was initially hard to understand. It didn't follow any clear pattern," says Sune Lehmann, corresponding author and Professor at DTU.
"For example, we saw a lot of moves at around 180 kilometres, while other distances were not observed nearly as often. But if you think about where you can actually move, there are certain places that people flock to, while others are completely inaccessible. When we look at a map, it may look like we can go anywhere, but we are actually only using a very small part of the country."
Do people move at random?
The researchers realized that 180 kilometres is roughly the distance between Copenhagen and Denmark's second largest city, Aarhus, so of course many people are moving between them. And on the opposite end of the spectrum, moving to places such as the middle of lakes, highways, or beyond the coastlines is impossible. So, they approached the very particular way that Danes move as a reflection of geography instead.
To make sense of the data and see if there is a pattern behind it, the team includes a concept from physics called the pair distribution function. It usually describes how particles are spaced, but here, it measures the distances between every possible pair of addresses in Denmark.
This approach creates a map of what the researchers call pairwise geographic distribution, or possible moves. The researchers then compare actual moves to the number of possible moves at each distance, thereby removing the effect of geography. What remains is a reflection of choices rather than the layout of land and cities.
"When you normalise by what's physically possible, the pattern becomes very clear," says Louis Boucherie, first author and a Postdoc at DTU Compute.
"What we have done, which no one has done before, is to consider that people are moving within a structure. People don't just go anywhere; they move to specific locations. So, when you want to interpret people's choices at different distances, you should first count how many real options exist at those distances. And then, when all constraints are removed, it reveals a consistent pattern."
After this adjustment, the data follows a power-law—a mathematical relationship where, as one quantity increases, the other decreases accordingly. This relationship is found across five orders of magnitude, from 10 meters to hundreds of kilometres. So, as distances increase, the likelihood of people moving there steadily decreases.
"We perceive our everyday life as complex and indescribable, but if we approach it in a different way, then what seems complicated is, in reality, pretty simple. You cannot make one natural law for human behaviour, but nevertheless, there are all kinds of laws governing how we behave," says Sune Lehmann.
We move in predictable ways
In the study, the scientists also looked specifically at more than 1,400 Danish towns. And here, the pattern is more nuanced: moves inside a city are less dependent on distance than moves between cities.
Denmark's size at just below 45,000 square kilometres ensures, however, that distances are never that long, usually way below 400 kilometres. And Copenhagen, at 1.6 million, is the only city with a population above 300,000.
So, to make sure this wasn't just a Danish anomaly, the researchers used the same approach to parts of the world where similar data was available. They find the same patterns in movements between cities in France (roughly 13 times the size of Denmark) and movements inside Houston (2.3 million), Singapore (6 million), and San Francisco (830,000).
Future work will apply the method to commuting patterns and explore differences across demographic groups. Louis Boucherie suggest that this baseline could help improve urban planning, transportation design, and even epidemiology models:
"While we have looked at everyone in this study, an obvious next step would be to see what happens when we divide people into demographic groups. It would be interesting to compare the mobility of people based on gender, financial circumstances or trade, and it might prove helpful for policy makers to ensure that their citizens have equal opportunities."
