An official website of the United States government
The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of defining city boundaries and a lack of historical data to study city dynamics over time and space. To address this issue, we analyze scaling between city infrastructure and population across 857 metropolitan areas in the conterminous United States over an unprecedented 115 years (1900–2015) using dasymetrically refined historical population estimates, historical urban road network models, and multi-temporal settlement data to define dynamic city boundaries. We demonstrate that urban scaling exponents closely match theoretical models over a century. Despite some close quantitative agreement with theory, the empirical scaling relations unexpectedly vary across regions. Our analysis of scaling coefficients, meanwhile, reveals that contemporary cities use more developed land and kilometers of road than cities of similar population in 1900, which has serious implications for urban development and impacts on the local environment. Overall, our results provide a new way to study urban systems based on novel, geohistorical data.
more »
« less
This content will become publicly available on December 1, 2026
The spatiotemporal scaling laws of urban population dynamics
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.
more »
« less
- PAR ID:
- 10614665
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 16
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community—income inequality. We propose a new method to study the scaling of income distributions by analysing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyse the shapes of income distributions. First, we find that mean, variance, skewness and kurtosis of income distributions all increase with city size. Second, the Kullback–Leibler divergence between a city’s income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.more » « less
-
Urban heat mitigation is a pressing concern for cities. Intense urban heat poses a threat to human health and urban sustainability. Tree planting is one of the most widely employed nature-based heat mitigation methods worldwide. Therefore, city policy makers require knowledge of how much temperature will be reduced by increasing urban tree canopy (UTC). Cooling efficiency (CE), which was been proposed to quantify the magnitude of temperature reduction associated with a 1% increase in UTC, has been primarily investigated at smaller scales previously. However, such small-scale results cannot be used to develop policy at the whole-city scale. This study developed a method that reveals the scaling relations of CE so as to predict its effects at the city scale. CE was found to follow the form of a power law as spatial scale increased from the small analytical units through intermediate size units up to the extent of a whole city. The power law form appeared consistently across cities with different climate backgrounds during summer daylight hours. Furthermore, the power law form was robust within cities under different summer weather conditions. The power-law scaling approach can thus be used to predict CE at the whole-city scale, providing a useful tool for managers to set UTC goals to mitigate extreme urban heat.more » « less
-
Oliveira, Marcos (Ed.)Impulsivity has been proposed as a key driver of obesity. However, evidence linking impulsivity and obesity has relied on the study of individual factors, with limited account for the urban attributes of obesogenic environments. Here, we investigate the relationship between obesity and impulsivity through urban scaling and causal discovery. For 915 cities in the United States of America, we study the prevalence of obesity in adults, attention deficit hyperactivity disorder (ADHD) in children, and relevant urban features. We observe sublinear scaling of obesity and ADHD with population size, these disorders being less prevalent in larger cities. By applying a causal discovery tool to the deviations of cities from the urban scaling laws, we identify an influence of ADHD on obesity, moderated by lifestyle. The strength of these associations is confirmed by individual-level data on a cohort of 19,333 children, wherein we observe that ADHD modulates obesity both directly and indirectly.more » « less
-
Abstract Implicit biases - differential attitudes towards members of distinct groups - are pervasive in human societies and create inequities across many aspects of life. Recent research has revealed that implicit biases are generally driven by social contexts, but not whether they are systematically influenced by the ways that humans self-organize in cities. We leverage complex system modeling in the framework of urban scaling theory to predict differences in these biases between cities. Our model links spatial scales from city-wide infrastructure to individual psychology to predict that cities that are more populous, more diverse, and less segregated are less biased. We find empirical support for these predictions in U.S. cities with Implicit Association Test data spanning a decade from 2.7 million individuals and U.S. Census demographic data. Additionally, we find that changes in cities’ social environments precede changes in implicit biases at short time-scales, but this relationship is bi-directional at longer time-scales. We conclude that the social organization of cities may influence the strength of these biases.more » « less
