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Abstract Human mobility is becoming increasingly complex in urban environments. However, our fundamental understanding of urban population dynamics, particularly the pulsating fluctuations occurring across different locations and timescales, remains limited. Here, we use mobile device data from large cities and regions worldwide combined with a detrended fractal analysis to uncover a universal spatiotemporal scaling law that governs urban population fluctuations. This law reveals the scale invariance of these fluctuations, spanning from city centers to peripheries over both time and space. Moreover, we show that at any given location, fluctuations obey a time-based scaling law characterized by a spatially decaying exponent, which quantifies their relationship with urban structure. These interconnected discoveries culminate in a robust allometric equation that links population dynamics with urban densities, providing a powerful framework for predicting and managing the complexities of urban human activities. Collectively, this study paves the way for more effective urban planning, transportation strategies, and policies grounded in population dynamics, thereby fostering the development of resilient and sustainable cities. 

Abstract Major disasters such as extreme weather events can magnify and exacerbate pre-existing social disparities, with disadvantaged populations bearing disproportionate costs. Despite the implications for equity and emergency planning, we lack a quantitative understanding of how these social fault lines translate to different behaviours in large-scale emergency contexts. Here we investigate this problem in the context of Hurricane Harvey, using over 30 million anonymized GPS records from over 150,000 opted-in users in the Greater Houston Area to quantify patterns of disaster-inflicted relocation activities before, during, and after the shock. We show that evacuation distance is highly homogenous across individuals from different types of neighbourhoods classified by race and wealth, obeying a truncated power-law distribution. Yet here the similarities end: we find that both race and wealth strongly impact evacuation patterns, with disadvantaged minority populations less likely to evacuate than wealthier white residents. Finally, there are considerable discrepancies in terms of departure and return times by race and wealth, with strong social cohesion among evacuees from advantaged neighbourhoods in their destination choices. These empirical findings bring new insights into mobility and evacuations, providing policy recommendations for residents, decision-makers, and disaster managers alike.