Modeling distances between humans using Taylor’s law and geometric probability

Abstract

ABSTRACT Taylor’s law states that the variance of the distribution of distance between two randomly chosen individuals is a power function of the mean distance. It applies to the distances between two randomly chosen points in various geometric shapes, subject to a few conditions. In Réunion Island and metropolitan France, at some spatial scales, the empirical frequency distributions of inter-individual distances are predicted accurately by the theoretical frequency distributions of inter-point distances in models of geometric probability under a uniform distribution of points. When these models fail to predict the empirical frequency distributions of inter-individual distances, they provide baselines against which to highlight the spatial distribution of population concentrations.