A Cellular-Automaton Model for Population-Density and Urban-Extent Dynamics at the Regional Level: The Case of Ukrainian Provinces

The efficient modeling of population-density and urban-extent dynamics is a precondition for monitoring urban sprawl and managing the accompanying conflicts. Currently, one of the most promising approaches in this field is cellular automata—spatial models allowing one to anticipate the behavior of unit areas (e.g., evolution or degradation) in response to the influence of their neighborhood. In the present study, the possibility of modeling the population-density and urban-extent dynamics via a cellular automaton with density-specific parameters is tested. Using an adaptive genetic algorithm, three key model parameters (the evolution and degradation thresholds of a cell and its impact upon the neighbors) are optimized to ensure minimal deviation of the model predictions from actual population dynamics data for 24 Ukrainian provinces during three subsequent time windows from 2010–2019. The performance of the obtained optimized models is assessed in terms of the ability to (1) predict population-density classes and (2) discriminate between urban and rural areas. Generally, the obtained optimized models show high performance for both population-density and urban-extent dynamics (with the average Cohen’s Kappa reaching ~0.81 and ~0.91, respectively). Rare cases with poor prediction accuracy usually represent politically and economically unstable Eastern Ukrainian provinces involved in the military conflict since 2014. Statistical analysis of the obtained model parameters reveals significant differences (p < 0.001) in all of them among population-density classes, arguing for the plausibility of the selected density-specific model architecture. Upon exclusion of the above-mentioned Eastern Ukrainian provinces, all model coefficients appear rather stable (p > 0.135) through the three analyzed time windows, indicating the robustness of the model. The ability of the model to discriminate between urban and rural areas depends on the population density threshold. The best correspondence between actual and predicted urban areas emerges upon the 3000 persons/km2 population-density threshold. Further improvement of the model seems possible via extending its input beyond the population density data alone, e.g., by accounting for the existing infrastructure and/or natural boundaries—known factors stimulating or inhibiting urban sprawl.