Systematic Relationship Between Areal Extent and Population for Urban Areas in the USA

While the impact of population density on key urban attributes has received considerable research attention, the relationship between areal extent and population size remains less explored and largely undertheorized. In this study, we analyze the systematic relationship between the total area and population of urbanized areas, as defined by the U.S. Census Bureau from 1950 to 2020. The delineated urban areas represent a long-standing effort to demarcate spaces where “urban life” takes place. Utilizing urban scaling theory, we characterize this relationship as a scale-invariant function of city population size, demonstrating that its predicted elasticity has remained consistent, within statistical uncertainty, over seven decades. We also examine the temporal variations in the prefactor of these scaling relationships in the context of technological changes. Our findings reveal that the predicted relationship between area and population size underscores the fact that urban areas are fundamentally social networks embedded within physical and infrastructural spaces.