Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data

The rapid increase of population and settlement structures in the Global South during recent decades motivates the development of suitable models to describe their formation and evolution. Such settlement formation has been previously suggested to be dynamically driven by simple pattern-forming mechanisms. Here, we explore the use of a data-driven white-box approach, called SINDy, to discover differential equation models directly from available spatiotemporal demographic data for three representative regions of the Global South. We show that the current resolution and observation time of the available data is insufficient to uncover relevant pattern-forming mechanisms in settlement development. Using synthetic data generated with a generic pattern-forming model, the Allen-Cahn equation, we characterize what the requirements are on spatial and temporal resolution, as well as observation time, to successfully identify possible model system equations. Overall, the study provides a theoretical framework for the analysis of large-scale geographical/ecological systems, and it motivates further improvements in optimization approaches and data collection.