Allometric Scaling of Countries

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.Comment: 23 pages, 3 figure

Capabilities' Substitutability and the "S" Curve of Export Diversity

Product diversity, which is highly important in economic systems, has been highlighted by recent studies on international trade. We found an empirical pattern, designated as the "S-shaped curve", that models the relationship between economic size (logarithmic GDP) and export diversity (the number of varieties of export products) on the detailed international trade data. As the economic size of a country begins to increase, its export diversity initially increases in an exponential manner, but overtime, this diversity growth slows and eventually reaches an upper limit. The interdependence between size and diversity takes the shape of an S-shaped curve that an be fitted by a logistic equation. To explain this phenomenon, we introduce a new parameter called "substitutability" into the list of capabilities or factors of products in the tri-partite network model (i.e., the country-capability-product model) of Hidalgo et al. As we observe, when the substitutability is zero, the model returns to Hidalgo's original model but failed to reproduce the S-shaped curve. However, in a plot of data, the data increasingly resembles an the S-shaped curve as the substitutability expands. Therefore, the diversity ceiling effect can be explained by the substitutability of different capabilities