Exploring and simulating the regularities in intra-urban population density structure

Sizes in a system of cities follow the so-called rank–size distribution or the more general Zipf's law. Previous research demonstrates that the rank–size relationship can be explained and simulated by a rather simple spatial choice model, describing individual residential behavior across cities. In studying population density within each of the 20 largest metropolitan areas in the United States, we discovered another type of regularity: population density at the tract level and the logarithm of the rank by tract density within a city exhibit a linear relationship. We call this rank–density regularity. In this article, we explore whether the simple spatial choice model originally developed to simulate city size distribution at the inter-urban scale can be used at the intra-urban scale to explain the rank–density pattern and the formation of urban density structure. We found that after adjusting the simple model for the city-edge constraint, the model can simulate the rank–density relationship reasonably well. In order to depict the spatial structure of population density more realistically, the model must include sub-centers, which increase the complexity of the model. Overall, the spatial choice model can reproduce the rank–density structure quite well. We believe the model captures the dominant forces in the formation of the population density distribution at the intra-urban scale.