Scaling of urban amenities: generative statistics and implications for urban planning

Cities have been extensively studied as complex adaptive systems over the last 50 years. Recently, several empirical studies and emerging theory provided support for the fact that many different urban indicators follow general consistent statistical patterns across countries, cultures and times. In particular, total personal income, measures of innovation, crime rates, characteristics of the built environment and other indicators have been shown to exhibit non-linear power-law scaling with the population size of functional cities. Here, we show how to apply this type of analysis inside cities to establish universal patterns in the quantity and distribution of urban amenities such as restaurants, parks, and universities. Using a unique data set containing millions of amenities in the 50 largest US metropolitan areas, we establish general non-linear scaling patterns between each city’s population and many different amenities types, the small-area statistics of their spatial abundance, and the characteristics of their mean distance to each other. We use these size-specific statistical findings to produce generative models for the expected amenity abundances of any US city. We then compute the deviations observed in given cities from this statistical many-amenity model to build a characteristic signature for each urban area. Finally, we show how urban planning can be guided by these systemic quantitative expectations in the context of new city design or the identification of local deficits in service provision in existing cities.