Simulating urban population density with a gravity-based model

Theoretical justifications for the negative exponential urban density function were first proposed by urban economists, although some of their foundations have been criticized. From the geographer's perspective, the gravity-based model reported in this research uses a well-known concept (the “potential”) to offer an alternative explanation. Using numerical analysis techniques, the model simulates various urban density patterns. By varying the model's parameters (the distance friction coefficient β and the city size), the numerical simulations do confirm two important empirical findings: the flattening of density gradients over time owing to transportation improvements, and flatter gradients in larger cities. The observed relationship between the β value and the urban density gradient, as established by this research, opens an avenue for empirical testing.