Abstract
Driven by access to large volumes of movement data, the study of human mobility has grown rapidly over the past few decades. The field has shown that human mobility is scale-free, proposed models to generate scale-free moving distance distributions and explained how the scale-free distribution arises. It has not, however, explicitly addressed how mobility is structured by geographical constraints, such as how mobility relates to the outlines of landmasses, lakes and rivers and the placement of buildings, roadways and cities. On the basis of millions of moves, we show how separating the effect of geography from mobility choices reveals a power law spanning five orders of magnitude. To do so, we incorporate geography via the pair distribution function, which encapsulates the structure of locations on which mobility occurs. By showing how the spatial distribution of human settlements shapes human mobility, our approach bridges the gap between distance- and opportunity-based models of human mobility.
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Data availability
The data for Denmark used in this study are not publicly available due to Danish Data Protection regulations. However, access to the data is possible for research purposes. The data can be obtained via Statistics Denmark for Researchers in accordance with Statistics Denmark’s Research Scheme: https://www.dst.dk/en/TilSalg/Forskningsservice/. The location data for France are publicly available at https://adresse.data.gouv.fr/donnees-nationales and https://www.data.gouv.fr. The residential mobility data were obtained from https://www.insee.fr/fr/statistiques. The Foursquare data are publicly available at https://sites.google.com/site/yangdingqi/home/foursquare-dataset. Source data are provided with this paper.
Code availability
The geography model and estimation code are available via GitHub at https://github.com/benmaier/ljhouses. The code for the figures, data and statistical analysis is available via GitHub at https://github.com/LCB0B/role-of-geo. The code is also available via Zenodo at https://doi.org/10.5281/zenodo.14329837 (ref. 68).
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Acknowledgements
We thank J. Dzubiella and Y. Ahn for helpful comments in the early development of this study, as well as L. Alessandretti and S. De Sojo for providing insightful comments on the manuscript. The work was supported in part by the Villum Foundation Grant Nation-Scale Social Networks (grant no. 00034288) (S.L.) and the Danish Council for Independent Research (grant no. 0136-00315B) (S.L.). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.
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L.B., B.F.M. and S.L. designed the study and the model. L.B. and B.F.M. performed the analyses and implemented the model. L.B., B.F.M. and S.L. analysed the results and wrote the paper.
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Extended data
Extended Data Fig. 1 Pair distribution of buildings and addresses in France.
Pair distribution of buildings and addresses in France shows three scales: (I) Immediate neighborhood-scale with linear onset and oscillating modulation, (II) city-scale with power-law growth (α = 0.67, for addresses), and (III) country-scale with slower growth and rapid decay (see Supplementary Section 1.6).
Extended Data Fig. 2 Demographic characteristics of the Danish Residential Mobility dataset.
The gender imbalance is the first panel due to the 1.07 male/female ratio rate at birth55. Indeed, we study the total population, not the currently alive population, that is balanced for gender due higher death rate for men. Therefore, although there is an imbalance in gender, the dataset is not biased. The second panel shows the birth year of every individual in the dataset, it closely follows the birth rate of Denmark, and the differences are due to migrations56.
Extended Data Fig. 3 Age Distribution.
Distribution of Age at the time of moving in the Danish residential mobility data (see Methods: Data).
Extended Data Fig. 4
Comparison between our framework, the gravity model and the radiation model for cities.
Extended Data Fig. 5
A continuous gravity law.
(a) This framework can be represented as a continuous gravity law, if we take a toy model of two distant cities, (b) the pair distribution at the distance d between the two cities collapses into a Dirac distribution, with the height equal to the product of cities population, N1N2. (c) The toy intrinsic distance cost of the simulation model. For a comparison with a continuous radiation model, see Supplementary Section 3.1.2.
Supplementary information
Source data
Source Data Fig. 2
Distribution values for fitting the power laws.
Source Data Fig. 4
Distribution values for fitting the piecewise power laws.
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Boucherie, L., Maier, B.F. & Lehmann, S. Decoupling geographical constraints from human mobility. Nat Hum Behav (2025). https://doi.org/10.1038/s41562-025-02282-7
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DOI: https://doi.org/10.1038/s41562-025-02282-7
