Hierarchies defined through human mobility

An analysis of worldwide data finds that human mobility has a hierarchical structure. A proposed model that accounts for such hierarchies reproduces differences in mobility behaviour across genders and levels of urbanization.
Elsa Arcaute is at the Centre for Advanced Spatial Analysis, University College London, London W1T 4TJ, UK.

Search for this author in:

Our intuition suggests that humans travel across characteristic spatial scales, such as neighbourhoods, cities and countries. However, analyses of large data sets indicate that human mobility has no intrinsic scales13. Writing in Nature, Alessandretti et al.4 combine worldwide data with modelling to solve this conundrum.

Rural areas, settlements and cities evolve to sustain the lives of their inhabitants. For example, footpaths sometimes transition into roads or even railways to facilitate the different inter-actions between individuals, communities and other social groups. At the individual level, each person travels to connect with others and exchange friendship, knowledge or goods, to be part of rituals and to access urban functions such as education, economic opportunities and leisure.

Each of us is unique, and we might be convinced that our lives are more exciting than are those of our neighbours — but maybe not as exciting as those of musicians, who are regularly out rehearsing, holding gigs in different parts of the city and touring all over the country or even the world. However, if our daily movements left traces, as ants leave pheromone trails, would these have a perceptible pattern? And would this pattern hold if we were living in a different city or country?

These questions can be answered properly only by analysing global mobility patterns. Widespread geographical tracking of the use of smartphones, credit cards and other technologies has allowed academics to tap into these data sets and conclude that human travel cannot be characterized by spatial scales13. Such results have made their way into leading scientific journals. However, they seem to contradict not only our intuition but also what is accepted in the field of geography — that the mobility of individuals depends on context and is constrained by cost.

We plan our trips and perceive the associated space in a hierarchical way. This viewpoint is reflected in the selection of a specific mode of transport according to where we want to go. For example, we might ask which metro line will take us north of the city, whether there are direct trains to a particular city or which airline will take us to a particular country.

The paper by Alessandretti and colleagues provides a solution to this mobility riddle. It presents a model that agrees with our hierarchical perception of space — that individuals have different scales of mobility depending on context. The authors analysed GPS location data for hundreds of thousands of people worldwide at a high temporal and spatial resolution, and they inferred the hierarchical structure of each individual’s mobility. They confirmed that the perceived structure is not an artefact of our brains, nor of the imposition of administrative delimitations, but corresponds to the way we move in space.

Alessandretti et al. used these global traces to identify typical spatial scales, which are referred to as containers in the paper (Fig. 1a). The authors discovered that container size has a probability distribution known as a log-normal distribution (Fig. 1b), corroborating recent results on the distribution of settle-ment sizes5. They found that a log-normal distribution provides a better statistical fit than does a scale-free (power-law) distribution, in opposition to the scale-free mobility behaviour reported in the literature13. The authors reconciled these results by obtaining a power-law distribution from the aggregation of all containers (Fig. 1c).

Figure 1

Figure 1 | A model of human mobility. a, Alessandretti et al.4 present a model that can reproduce key properties of human mobility. In the model, observed spatial scales of human movement — such as the scales of neighbourhoods, cities and countries — are represented by different-sized containers. In this schematic, a person moves between particular locations in small containers, which are inside medium-sized containers, which are inside large containers. b, The authors applied their model to global mobility data. This plot illustrates, for two individual containers, the probability of it having a particular size, on a log–log scale. Such probability distributions are known as log-normal distributions. c, When all the containers are aggregated, rather than being considered individually, the container size instead follows a distribution called a power law. The generation of these two different distributions from the same data set reconciles two different perspectives on human mobility.

A further achievement of the paper relates to the use of the model to produce simulated traces of human mobility, and how these traces reproduce differences in mobility behaviour associated with gender and level of urbanization. Alessandretti et al. found that, although the mobility of women is more complex than is that of men, it is also spatially smaller. Moreover, they confirmed that people living in rural areas have much larger containers than those of individuals in urban areas.

The origin of the observed hierarchical structure has puzzled academics for more than a century. Many theories and models68 have been developed in an attempt to capture patterns resulting from the co-evolution of the physical form9 and the function of cities. However, these attempts have encountered various challenges emerging from the fact that infrastructure changes slowly, whereas land use and demographics change quickly.

Urban systems have been shaped by mobility and the need to satisfy different human interactions modulated by the speed of transportation10. For centuries, we have left traces of mobility through our road networks11, encoding the hierarchical structure of urban systems at multiple scales. An open question is whether Alessandretti and colleagues’ research can be extended to explain why such patterns emerge worldwide and why cities have their particular morphologies. Is the observed organization of urban spaces the result of centuries of mobility? And could the authors’ work help us predict the future of our cities, now that we can tap into the traces of the movements that shape them?

Nature 587, 372-373 (2020)


  1. 1.

    Brockmann, D., Hufnagel, L. & Geisel, T. Nature 439, 462–465 (2006).

  2. 2.

    González, M. C., Hidalgo, C. A. & Barabási, A.-L. Nature 453, 779–782 (2008).

  3. 3.

    Song, C., Koren, T., Wang, P. & Barabási, A.-L. Nature Phys. 6, 818–823 (2010).

  4. 4.

    Alessandretti, L., Aslak, U. & Lehmann, S. Nature 587, 402–407 (2020).

  5. 5.

    Corral, Á., Udina, F. & Arcaute, E. Phys. Rev. E 101, 042312 (2020).

  6. 6.

    Christaller, W. Central Places in Southern Germany (Prentice-Hall, 1966).

  7. 7.

    Alonso, W. Location and Land Use: Toward a General Theory of Land Rent (Harvard Univ. Press, 1964).

  8. 8.

    Wilson, A. G. Entropy in Urban and Regional Modelling (Pion, 1970).

  9. 9.

    Batty, M. & Longley, P. Fractal Cities: A Geometry of Form and Function (Academic, 1994).

  10. 10.

    Pumain, D. Espace Géogr. 26, 119–134 (1997).

  11. 11.

    Arcaute, E. et al. R. Soc. Open Sci. 3, 150691 (2016).

Download references

Nature Briefing

An essential round-up of science news, opinion and analysis, delivered to your inbox every weekday.