Modeling the co-evolution of cities and networks

Abstract

The complexity of interactions between networks and territories has been widely acknowledged empirically, in particular through the existence of circular causal relations in their co-development, that can be understood as a co-evolution. This contribution aims at investigating models that endogenize this co-evolution, in the particular case of cities and transportation networks. We introduce a family of models of co-evolution for systems of cities at the macroscopic scale. Interactions between cities are the main driver of population growth rates, capturing a network effect at the first order (direct interactions). Network growth follows a demand-induced thresholded growth scheme, that can occur at the global level or locally. The exploration of the model on synthetic systems of cities shows the ability of the model to capture co-evolutive patterns. We apply the model on the French system of cities, with population data spanning 1831-1999 and a dynamical railway network (1850-2000). The model is calibrated on successive time-windows, assuming local temporal stationarity. We extract therein indirect knowledge on underlying processes and find that the prediction for city populations are in some cases improved in comparison to a static model.