Population-mobility coevolution drives spatial heterogeneity of cities

Abstract

The spatial heterogeneity of cities -- the uneven distribution of population and activities -- is fundamental to urban dynamics and related to critical issues such as infrastructure overload, housing affordability, and social inequality. Despite sharing similar scaling laws of population and mobility, cities exhibit vastly different spatial patterns. This paradox call for a mechanistic explanation for the emergence of spatial heterogeneity, while existing qualitative or descriptive studies fail to capture the underlying mechanisms. Here, we propose a coupled dynamical model that describe the intra-city population-mobility coevolution, explaining spatial heterogeneity as an emergent outcome of mutual feedback between the fast-changing mobility and the slow-adapting population. Our model is validated on over 388 million records from eight diverse global cities, successfully reproduces both the statistical laws and realistic spatial patterns. We find out realistic heterogeneity emerges as a distinct stable state, intermediate between disordered homogeneity and unsustainable super-hub dominance. Moreover, we theoretically and empirically show that populated areas are predominantly shaped by coevolution strength, while the increasing distance decay leads cities through a three-phase transition of homogeneity-heterogeneity-homogeneity. Besides, functional attractiveness between areas consistently enhances the ordered heterogeneous structure. Simulations of real-world planning scenarios -- including crisis-induced lockdown, planned zone expansions, and dispersal from congested centers -- indicate that integrated population-mobility policies are more cost-effective than single interventions. Our model can provides mechanistic, high-resolution insights to rigorously inform policy design.