Perturbation analysis of the rank-size rule for municipalities squeezed in a prefecture: Effects of the archipelagoes, rapidly increasing rural depopulation, ethnic minority issues, and future sea-level rise due to global warming

Abstract

Perturbation analysis of the rank-size rule is made for municipalities that are squeezed in a prefecture. Specifically, attention is focused on Japanese prefectures, for which effects of the archipelagoes, municipal consolidations, and coastal inundations due to the future sea-level rise are examined. In each prefecture, typically tens of municipalities are closely packed with a unique configuration that has been arranged according to a self-organized process. With a mind to sustainable development goals, analysis is made from three points of view. First, comparisons between the results of the mainland and those of the entire prefecture with territorial islands suggest that historical interactions over a long period become a key factor to enhance the statistical rule. Next, to cope with rapidly increasing rural depopulation, simulations are made on the basis of three consolidatory schemes. Of prefectures with extremely depopulated areas, particular emphasis is laid on Fukushima Prefecture, the east coast of which was damaged by the nuclear disaster on 11 March 2011. Lastly, analysis is made implying perturbations due to global warming. Among three parameters that characterize the rank-size relation, stabilities are confirmed for the scaling exponent.