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.
At a glance
- The P1P2/D hypothesis: on the intercity movement of persons. Am. Sociol. Rev. 11, 677–686 (1946)
- 666–704 (De l’Imprimerie Royale, 1781) 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
- Spatial networks. Phys. Rep. 499, 1–101 (2010)
- 1990) & The Gravity Model in Transportation Analysis: Theory and Extensions (VSP,
- Gravity model in the Korean highway. EPL 81, 48005 (2008) , &
- The structure of borders in a small world. PLoS ONE 5, e15422 (2010) , , , &
- The complex network of global cargo ship movements. J. R. Soc. Interf. 7 1093–1103 (2010) , , &
- Urban gravity: a model for inter-city telecommunication flows. J. Stat. Mech. 2009, L07003 (2009) , , &
- Uncovering space-independent communities in spatial networks. Proc. Natl Acad. Sci. USA 108, 7663–7668 (2011) , , &
- A tentative model for the volume of trade between countries. Weltwirtschaftliches Arch. 90, 93–100 (1963)
- Multiscale mobility networks and the spatial spreading of infectious diseases. Proc. Natl Acad. Sci. USA 106, 21484–21489 (2009) et al.
- Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73, 1067–1141 (2001)
- The role of the airline transportation network in the prediction and predictability of global epidemics. Proc. Natl Acad. Sci. USA 103, 2015–2020 (2006) , , &
- Synchrony, waves, and spatial hierarchies in the spread of influenza. Science 312, 447–451 (2006) et al.
- Strategies for mitigating an influenza pandemic. Nature 442, 448–452 (2006) et al.
- Impacts of preference and geography on epidemic spreading. Phys. Rev. E 76, 056109 (2007) , &
- Spreading gossip in social networks. Phys. Rev. E 76, 036117 (2007) , , &
- Structure of urban movements: polycentric activity and entangled hierarchical flows. PLoS ONE 6, e15923 (2011) , , &
- Modelling urban growth patterns. Nature 377, 608–612 (1995) , &
- Growth, innovation, scaling, and the pace of life in cities. Proc. Natl Acad. Sci. USA 104, 7301–7306 (2007) , , , &
- The size, scale, and shape of cities. Science 319, 769–771 (2008)
- Interplay between topology and dynamics in the World Trade Web. The Eur. Phys. J. B 57, 159–164 (2007) , , , &
- Modelling disease outbreaks in realistic urban social networks. Nature 429, 180–184 (2004) et al.
- 1974) & Urban Planning Analysis: Methods and Models (Wiley,
- The use of entropy maximising models in the theory of trip distribution, mode split and route split. J. Transp. Econ. Policy 108–126 (1969)
- Intervening opportunities: a theory relating mobility and distance. Am. Sociol. Rev. 5, 845–867 (1940)
- 1960) & Random Orderings and Stochastic Theories of Responses (Cowles Foundation,
- Parameter estimation in the intervening opportunities model. Geogr. Anal. 18, 357–360 (1986)
- Understanding individual human mobility patterns. Nature 453, 779–782 (2008) , &
- Structure and tie strengths in mobile communication networks. Proc. Natl Acad. Sci. USA 104, 7332–7336 (2007) et al.
- Supplementary Information (4.4M)
This file contains Supplementary Text and Data 1-9 (see Contents for more details), additional references and Supplementary Figures 1-8 with legends.