Interdisciplinary theoretical physics is a difficult business. Frequently physicists who work outside of the traditional realm of physics are ignored or misunderstood by those whose fields they plough — biologists, economists, social scientists, to name but a few. Similarly, all too often their work is labelled as 'nice, but not physics' by conservative peers in the physics community. But the candid model for human mobility that Chaoming Song and colleagues report1 in Nature Physics is unlikely to suffer this fate. Starting from random-walk processes, and taking on board elements from the theory of scale-free networks, they arrive at a conceptually simple model that accounts for a broad range of scaling patterns seen in data that capture human-mobility patterns. Their model, in combination with straightforward back-of-the-envelope scaling arguments, is of distinct statistical-physics flavour, yet highly transparent to behavioural and social scientists, epidemiologists and transportation experts, among many others who rely on a better understanding of human mobility.

Modern mobility is massive and complex2. It has dramatically changed over the past few decades — today we can, in principle, travel to any place on the globe within a day or two. More than three billion passengers travel each year on the global air-transportation network that connects more than 4,000 airports worldwide. Hundreds of millions of commuters travel to work each day on an intricate web of highways and public transportation systems that often operate at their maximum capacity. Our mobility plays a key role in the rapid global spread of emergent infectious diseases — the latest example being the worldwide spread of pandemic influenza H1N1 in 2009 — and in human-mediated bioinvasion, which is a key factor in the global biodiversity crisis (that is, humans aid the relocation of non-endemic species to new habitats where they proliferate and potentially extinguish endemic species). In the light of these phenomena, research that advances our understanding of how we travel is vital.

A promising avenue of research emerged a few years ago when researchers began to analyse large-scale datasets tracing individual human movements. The data are typically generated either directly or indirectly by modern technologies such as mobile phones or precise GPS devices, combined with websites that collect records of individuals' locations. Pervasive data of this type reveals aspects of when and where we go with unprecedented spatiotemporal precision. One of the earliest quantitative discoveries was made by analysing the circulation of banknotes3 (and subsequently confirmed by a more detailed study on mobile phones4). Looking at the statistics of distances travelled (r) and interjourney times of rest (t), it was found that the probabilities of travel distance, p(r), and rest times, p(t), both follow an inverse power-law: p(r) r−(1+α) and p(t) t−(1+β), where α = 0.8 and β = 0.6. This implied that human mobility had anomalous properties both spatially and temporally — it lacks a characteristic scale and is fractal as well as self-similar.

What does this mean for modelling human mobility? For instance, in continuous-time random walks, which are frequently employed to model random processes in physics and biology, the first relation typically yields superdiffusive behaviour (that is, the average squared displacement increases faster than linearly with time), whereas the second relation yields subdiffusion. If human trajectories were indeed random walks, an individual's position would scale with time according to X tα/β. It doesn't require a degree in physics to realize that trajectories of individuals are not purely random. In fact, for random walks as described above, the expected time to revisit a point in space is infinite, which clearly is at odds with most humans' habit of returning home after work.

Song and colleagues1 show to what extent real human-mobility patterns deviate from those expected from simple random-walk predictions. But this is not why their model is important. It is important because they propose a slightly more intricate random-walk model that, unlike the simple continuous-time random walks, can account for many of the empirical scaling relations observed in mobility data. Studying the same dataset on the trajectories of mobile-phone users that was investigated in earlier studies4,5, Song et al. focus on two key quantities: the number of new locations visited as a function of time, S(t), and the visitation rank frequency fk of those locations (which measures how often an individual goes to the kth-most-visited location).

The model1 has two basic dynamic ingredients: exploration and preferential return. More specifically, Song et al. assume that at every step of the process an individual can explore unvisited locations with a probability p ρS−γ, where the pre-factor ρ and the (strictly positive) exponent γ are the two parameters of the model. This means that the more sites there are in a person's individual 'network of places', the less likely it is that he or she will explore new places. With the complementary probability a person returns to previously visited places, choosing between the set of known places according to their rank probability — a person is more likely to return to places already visited many times. Song and colleagues refer to this behaviour as 'preferential return'. The main principle behind preferential return is the same as in 'preferential attachment', a mechanism for the growth of scale-free networks. Preferential return generates a strong heterogeneity in the set of locations that a person visits. Combined with the exploratory component, the mobility model of Song et al.1 accounts for many of the observed scaling laws.

The parameter γ in the model of Song et al.1 turns out to be 0.2. This of course invites the question of why this exponent, which captures our exploratory behaviour so well, has precisely this value. The present model cannot address this question — and doesn't need to. But the simplicity of the key principles of exploration and preferential return are most likely to trigger new investigations in other contexts, as these principles are so common in human decision processes. We can therefore look forward to diverse applications of the model of Song et al.1. For example, one may wonder if the same basic mechanisms determine what restaurants we visit, what recipes we try if we decide to dine at home or what locations we pick for a summer holiday. Once data for these contexts are available we should expect to see similar patterns emerging.