The spectral dimension of human mobility

Abstract: Human mobility patterns are surprisingly structured. In spite of many hard to model factors, such as climate, culture, and socioeconomic opportunities, aggregate migration rates obey a universal, parameter-free, radiation' model. Recent work has further shown that the detailed spectral decomposition of these flows -- defined as the number of individuals that visit a given location with frequency $f$ from a distance $r$ away -- also obeys simple rules, namely, scaling as a universal inverse square law in the combination, $rf$. However, this surprising regularity, derived on general grounds, has not been explained through microscopic mechanisms of individual behavior. Here we confirm this by analyzing large-scale cell phone datasets from three distinct regions and show that a direct consequence of this scaling law is that the averagetravel energy' spent by visitors to a given location is constant across space, a finding reminiscent of the well-known travel budget hypothesis of human movement. The attractivity of different locations, which we define by the total number of visits to that location, also admits non-trivial, spatially-clustered structure. The observed pattern is consistent with the well-known central place theory in urban geography, as well as with the notion of Weber optimality in spatial economy, hinting to a collective human capacity of optimizing recurrent movements. We close by proposing a simple, microscopic human mobility model which simultaneously captures all our empirical findings. Our results have relevance for transportation, urban planning, geography, and other disciplines in which a deeper understanding of aggregate human mobility is key.