Birth, Annexation, and Squeezing of Cities in a Prefecture: Can the Ranking of Competitive Areas of Municipalities Obey the Authentic Power Law? - Hayata, Kazuya (Frontiers in Physics, 2022)
As the first step for revealing potential rules inherent in cities that are closely squeezed in a sectioned domain, municipalities in the entire prefecture in Japan are considered and their distributions of the areas are analyzed in details according to a rank-size procedure. Computed results suggest that among the population, area, and population density, the last becomes the most important factor in finding the rank-size rule. Indeed, of the 47 Japanese prefectures the Metropolis of Tokyo and Fukuoka Prefecture exhibit the most typical rank-size rules, where the former possesses the exceptionally high population density as well as urbanized rate. The underlying mechanism of the rule can be supported by a toy model with a tournament game using a sequence of random numbers, where teams (municipalities) are highly competitive in gaining the final wins (broadest territory). A stability analysis implying perturbations due to global warming allows one to confirm unexpected robustness of the rank-size relation. Finally, the authenticity of the log-log relation in the rank-area data of Tokyo Metropolis is tested statistically.