Corral, A; Udina, F; Arcaute, E; (2020) Truncated lognormal distributions and scaling in the size of naturally defined population clusters. Physical Review E , 101 (4) , Article 042312. 10.1103/PhysRevE.101.042312.

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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 × 106 (which corresponds to the population of the largest cluster).

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