Finite-size scaling of human-population distributions over fixed-size cells and its relation to fractal spatial structure

TL;DR

This study reveals that population distributions over fixed-size cells exhibit a stable shape under scaling, following a gamma distribution, and are linked to the fractal nature of spatial population patterns.

Contribution

It introduces a finite-size scaling law for population distributions, connecting their invariance to fractal spatial structures, supported by empirical data.

Findings

Distribution shape remains constant under scaling

Distribution fits a gamma distribution well

Distribution moments follow power-law relations

Abstract

Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases its variability when the size of the cells is increased. Nevertheless, the shape of the distributions is kept constant, which allows us to introduce a scaling law, analogous to finite-size scaling, with a scaling function reasonably well fitted by a gamma distribution. This means that the distribution of the number of inhabitants per cell is stable or invariant under addition with neighboring cells (plus rescaling), defying the central-limit theorem, due to the obvious dependence of the random variables. The finite-size scaling implies a power-law relations between the moments of the distribution and its scale parameter, which are found to be related with the fractal properties of the spatial pattern formed by the population. The match between theoretical predictions and empirical results is reasonably good.