Emergent dense suburbs in a schelling metapopulation model: A simulation approach

The Schelling model describes the formation of spatially segregated clusters starting from individual preferences based on tolerance. To adapt this framework to an urban scenario, characterized by several individuals sharing very close physical spaces, we propose a metapopulation version of the Schelling model defined on the top of a regular lattice whose cells can be interpreted as a bunch of buildings or a district containing several agents. We assume the model to contain two kinds of agents relocating themselves if their individual utility is smaller than a tolerance threshold. While the results for large values of the tolerances respect the common sense, namely coexistence is the rule, for small values of the latter we obtain two non-trivial results: first we observe complete segregation inside the cells, second the population redistributes highly heterogeneously among the available places, despite the initial uniform distribution. The system thus converges toward a complex heterogeneous configuration after a long quasi-stationary transient period, during which the population remains in a well mixed phase. We identify three possible global spatial regimes according to the tolerance value: microscopic clusters with local coexistence of both kinds of agents, macroscopic clusters with local coexistence (hereafter called soft segregation) and macroscopic clusters with local segregation but homogeneous densities (hereafter called hard segregation).