Truncated lognormal distributions and scaling in the size of naturally defined population clusters.

Abstract

Using population data of high spatial resolution for a region in the south of Europe, we define cities by aggregating individuals to form connected clusters. The resulting cluster-population distributions show a smooth decreasing behavior covering six orders of magnitude. We perform a detailed study of the distributions, using state-of-the-art statistical tools. By means of scaling analysis we rule out the existence of a power-law regime in the low-population range. The logarithmic-coefficient-of-variation test allows us to establish that the power-law tail for high population, characteristic of Zipf's law, has a rather limited range of applicability. Instead, lognormal fits describe the population distributions in a range covering from a few dozen individuals to more than 1×10^{6} (which corresponds to the population of the largest cluster).