Modeling Income Distribution with the Gause-Witt Population Ecology System

Abstract: This paper presents an empirical application of the Gause-Witt model of population ecology and ecosystems to the income distribution competitive dynamics of social classes in economic systems. The Gause-Witt mathematical system of coupled nonlinear first-order ordinary differential equations employed to model population of species sharing the same ecological niche and competing for the same resources was applied to the income data of Brazil. Previous studies using Brazilian income data from 1981 to 2009 showed that the complementary cumulative distribution functions built from yearly datasets have two distinct segments: the lower income region comprising of about 99% of the population can be represented by the Gompertz curve, whereas the richest 1% is described by the Pareto power-law. The results of applying the Gause-Witt system to Brazilian income data in order to describe the distributive competition dynamics of these two population shares indicate that the 99% and 1% income classes are mostly in the dynamic state of stable coexistence.