Population Density In A Central-Place System

type="main"> The existing empirical literature about polycentric population density has focused on the urban scale, and the alternative models proposed in that context have been justified using heuristic arguments. This paper describes how polycentric density distributions can, in general, be endowed with a theoretical framework which differs from the existing literature with respect to the treatment of centers: instead of assuming that they represent places of work, it assumes they are places that provide goods and services to households. This imposes a hierarchical structure on the model, which allows replacing the set of distances to all centers (typically used in the existing literature as the same explanans irrespectively of location) with a smaller set of distances that corresponds to the number of levels in the hierarchy and varies with location. The central-place framework used also provides a direct link between a polycentric model and the Clark formula, in the sense that the latter can emerge through a smoothing procedure of the former. Finally, in the context of central places, the scope of related empirical investigations can be extended naturally from the urban to the regional scale. This is the scale of a simple test presented here, which has been specifically included to support the corresponding theoretical arguments about the structure of a polycentric density gradient. The paper concludes with some expected problems and advantages of applying these ideas to the urban scale.