A universal model for mobility and migration patterns

Subjects

Abstract

Introduced in its contemporary form in 1946 (ref. 1), but with roots that go back to the eighteenth century2, the gravity law1,3,4 is the prevailing framework with which to predict population movement3,5,6, cargo shipping volume7 and inter-city phone calls8,9, as well as bilateral trade flows between nations10. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of the phenomena affected by mobility and transport processes11,12,13,14,15,16,17,18,19,20,21,22,23.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: The radiation model.
Figure 2: Comparing the predictions of the radiation model and the gravity law.
Figure 3: Beyond commuting.
Figure 4: Unveiling the hidden self-similarity in human mobility.

References

  1. 1

    Zipf, G. K. The P1P2/D hypothesis: on the intercity movement of persons. Am. Sociol. Rev. 11, 677–686 (1946)

    Article  Google Scholar 

  2. 2

    Monge, G. Mémoire sur la Théorie des Déblais et de Remblais. Histoire de l’Académie Royale des Sciences de Paris, avec les Mémoires de Mathématique et de Physique pour la même année 666–704 (De l’Imprimerie Royale, 1781)

    Google Scholar 

  3. 3

    Barthélemy, M. Spatial networks. Phys. Rep. 499, 1–101 (2010)

    ADS  MathSciNet  Article  Google Scholar 

  4. 4

    Erlander, S. & Stewart, N. F. The Gravity Model in Transportation Analysis: Theory and Extensions (VSP, 1990)

    Google Scholar 

  5. 5

    Jung, W. S., Wang, F. & Stanley, H. E. Gravity model in the Korean highway. EPL 81, 48005 (2008)

    ADS  Article  Google Scholar 

  6. 6

    Thiemann, C., Theis, F., Grady, D., Brune, R. & Brockmann, D. The structure of borders in a small world. PLoS ONE 5, e15422 (2010)

    ADS  Article  Google Scholar 

  7. 7

    Kaluza, P., Kölzsch, A., Gastner, M. T. & Blasius, B. The complex network of global cargo ship movements. J. R. Soc. Interf. 7 1093–1103 (2010)

    Article  Google Scholar 

  8. 8

    Krings, G., Calabrese, F., Ratti, C. & Blondel, V. D. Urban gravity: a model for inter-city telecommunication flows. J. Stat. Mech. 2009, L07003 (2009)

    Article  Google Scholar 

  9. 9

    Expert, P., Evans, T. S., Blondel, V. D. & Lambiotte, R. Uncovering space-independent communities in spatial networks. Proc. Natl Acad. Sci. USA 108, 7663–7668 (2011)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Pöyhönen, P. A tentative model for the volume of trade between countries. Weltwirtschaftliches Arch. 90, 93–100 (1963)

    Google Scholar 

  11. 11

    Balcan, D. et al. Multiscale mobility networks and the spatial spreading of infectious diseases. Proc. Natl Acad. Sci. USA 106, 21484–21489 (2009)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Helbing, D. Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73, 1067–1141 (2001)

    ADS  MathSciNet  Article  Google Scholar 

  13. 13

    Colizza, V., Barrat, A., Barthélemy, M. & Vespignani, A. The role of the airline transportation network in the prediction and predictability of global epidemics. Proc. Natl Acad. Sci. USA 103, 2015–2020 (2006)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Viboud, C. et al. Synchrony, waves, and spatial hierarchies in the spread of influenza. Science 312, 447–451 (2006)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Ferguson, N. M. et al. Strategies for mitigating an influenza pandemic. Nature 442, 448–452 (2006)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Xu, X. J., Zhang, X. & Mendes, J. F. F. Impacts of preference and geography on epidemic spreading. Phys. Rev. E 76, 056109 (2007)

    ADS  Article  Google Scholar 

  17. 17

    Lind, P. G., Da Silva, L. R., Andrade, J. S., Jr & Herrmann, H. J. Spreading gossip in social networks. Phys. Rev. E 76, 036117 (2007)

    ADS  Article  Google Scholar 

  18. 18

    Roth, C., Kang, S. M., Batty, M. & Barthélemy, M. Structure of urban movements: polycentric activity and entangled hierarchical flows. PLoS ONE 6, e15923 (2011)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Makse, H. A., Havlin, S. & Stanley, H. E. Modelling urban growth patterns. Nature 377, 608–612 (1995)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Bettencourt, L. M. A., Lobo, J., Helbing, D., Kühnert, C. & West, G. B. Growth, innovation, scaling, and the pace of life in cities. Proc. Natl Acad. Sci. USA 104, 7301–7306 (2007)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Batty, M. The size, scale, and shape of cities. Science 319, 769–771 (2008)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Garlaschelli, D., Di Matteo, T., Aste, T., Caldarelli, G. & Loffredo, M. I. Interplay between topology and dynamics in the World Trade Web. The Eur. Phys. J. B 57, 159–164 (2007)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  23. 23

    Eubank, S. et al. Modelling disease outbreaks in realistic urban social networks. Nature 429, 180–184 (2004)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Krueckeberg, D. A. & Silvers, A. L. Urban Planning Analysis: Methods and Models (Wiley, 1974)

    Google Scholar 

  25. 25

    Wilson, A. G. The use of entropy maximising models in the theory of trip distribution, mode split and route split. J. Transp. Econ. Policy 108–126 (1969)

  26. 26

    Stouffer, S. A. Intervening opportunities: a theory relating mobility and distance. Am. Sociol. Rev. 5, 845–867 (1940)

    Article  Google Scholar 

  27. 27

    Block, H. D. & Marschak, J. Random Orderings and Stochastic Theories of Responses (Cowles Foundation, 1960)

    Google Scholar 

  28. 28

    Rogerson, P. A. Parameter estimation in the intervening opportunities model. Geogr. Anal. 18, 357–360 (1986)

    Article  Google Scholar 

  29. 29

    González, M. C., Hidalgo, C. A. & Barabási, A. L. Understanding individual human mobility patterns. Nature 453, 779–782 (2008)

    ADS  Article  Google Scholar 

  30. 30

    Onnela, J. P. et al. Structure and tie strengths in mobile communication networks. Proc. Natl Acad. Sci. USA 104, 7332–7336 (2007)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank J. P. Bagrow, A. Fava, F. Giannotti, Y.-R. Lin, J. Menche, Z. Néda, D. Pedreschi, D. Wang, G. Wilkerson and D. Bauer for many discussions, and N. Ferguson for prompting us to look into the gravity law. A.M. and F.S. acknowledge the Cariparo foundation for financial support. This work was supported by the Network Science Collaborative Technology Alliance sponsored by the US Army Research Laboratory under Agreement Number W911NF-09-2-0053; the Office of Naval Research under Agreement Number N000141010968; the Defense Threat Reduction Agency awards WMD BRBAA07-J-2-0035 and BRBAA08-Per4-C-2-0033; and the James S. McDonnell Foundation 21st Century Initiative in Studying Complex Systems.

Author information

Affiliations

Authors

Contributions

All authors designed and did the research. F.S. analysed the empirical data and performed the numerical calculations. A.M. and F.S. developed the analytical calculations. A.-L.B. was the lead writer of the manuscript.

Corresponding authors

Correspondence to Amos Maritan or Albert-László Barabási.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data 1-9 (see Contents for more details), additional references and Supplementary Figures 1-8 with legends. (PDF 4564 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Simini, F., González, M., Maritan, A. et al. A universal model for mobility and migration patterns. Nature 484, 96–100 (2012). https://doi.org/10.1038/nature10856

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing