Allometric Scaling of Countries

TL;DR

This paper investigates how various properties of countries scale with size, revealing super-linear and sub-linear relationships with economic and geographic measures, and highlighting differences from urban systems.

Contribution

It systematically analyzes allometric scaling laws in countries, contrasting them with urban systems, and uncovers distinct scaling behaviors for economic, geographic, and demographic properties.

Findings

Economic and trade properties scale super-linearly with GDP.

Geographic and transportation properties scale sub-linearly with area.

Differences in population scaling between countries and cities are identified.

Abstract

As huge complex systems consisting of geographic regions, natural resources, people and economic entities, countries follow the allometric scaling law which is ubiquitous in ecological, urban systems. We systematically investigated the allometric scaling relationships between a large number of macroscopic properties and geographic (area), demographic (population) and economic (GDP, gross domestic production) sizes of countries respectively. We found that most of the economic, trade, energy consumption, communication related properties have significant super-linear (the exponent is larger than 1) or nearly linear allometric scaling relations with GDP. Meanwhile, the geographic (arable area, natural resources, etc.), demographic(labor force, military age population, etc.) and transportation-related properties (road length, airports) have significant and sub-linear (the exponent is smaller than 1) allometric scaling relations with area. Several differences of power law relations with respect to population between countries and cities were pointed out. Firstly, population increases sub-linearly with area in countries. Secondly, GDP increases linearly in countries but not super-linearly as in cities. Finally, electricity or oil consumptions per capita increases with population faster than cities.