  The interaction of all mobile species with their environment hinges on their
movement patterns: the places they visit and how frequently they go there. In
human society, where the prevalent form of cohabitation is in cities, the
highly dynamic and diverse movement of people is fundamental to almost every
aspect of socio-economic life, including social interactions or disease
spreading, and ultimately is key to the evolution of urban infrastructure,
productivity, innovation and technology. However, despite the crucial role of
the spatio-temporal structure of movement in cities, the laws that govern the
variation of population flows to specific locations have remained elusive. Here
we show that behind the apparent complexity of movement a surprisingly simple
universal scaling relation drives the flow of individuals to any specific
location based on both frequency of visitation and distance travelled. We
derive a first principles argument stating that the number of visiting
individuals should decrease as an inverse square of the product of visitation
frequency and travel distance; or, equivalently, as a power law with exponent
$\approx \! -$2. Using large-scale data analyses, we demonstrate that
population flows obey this theoretical prediction in virtually all tested areas
across the globe, ranging from Europe and America to Asia and Africa,
regardless of the detailed geographies, cultures or levels of development. The
revealed regularity offers unprecedented possibilities for the modelling of
mobility fluxes at high spatial and temporal resolution, and it places an
important constraint on any theory of movement, spatial organisation and social
interaction in cities.
