Spatial Selection and the Multiscale Dynamics of Urban Change (2511.06165v1)

Abstract: Growth is a multi-layered phenomenon in human societies, composed of socioeconomic and demographic change at many different scales. Yet, standard macroeconomic indicators average over most of these processes, blurring the spatial and hierarchical heterogeneity driving people's choices and experiences. To address this gap, we introduce here a framework based on the Price equation to decompose aggregate growth exactly into endogenous and selection effects across nested spatial scales. We illustrate this approach with population and income data from the Chicago metropolitan area (2014-2019) and show that both growth rates and spatial selection effects are most intense at local levels, fat-tailed and spatially correlated. We also find that selection, defined as the covariance between prevailing income and relative population change, is concentrated in few spatial units and exhibits scaling behavior when grouped by county. Despite the intensity of local sorting, selection effects largely cancel in the aggregate, implying that fast heterogeneous micro-dynamics can yield deceptively stable macro-trends. By treating local spatial units (neighborhoods) as evolving subpopulations under selection, we demonstrate how methods from complex systems provide new tools to classify residential selection processes, such as abandonment and gentrification, in an urban sociological framework. This approach is general and applies to any other nested economic systems such as networks of production, occupations, or innovation enabling a new mechanistic understanding of compositional change and growth across scales of organization.