A Toy Model Mechanism for Greater-Than-Exponential Human Population Growth

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The term, exponential, has long been associated with the growth of organismal populations from microbial populations to the populations of complex multicellular eukaryotes. It can be shown, however, that human population growth occurs at greater-than-exponential rates. Von Foerster et al. (1960) but followed more elegantly by Korotayev et al. (2006a), have proposed models to more accurately represent this characteristic mode of human population growth. In this paper an underlying mechanism is proposed which generates this greater-than-exponential growth. The mechanism is represented by a toy model of two differential equations of interacting populations, the interactions of which enhance the reproductive abilities of the other population. The end result of this enhancement due to positive human interaction, a quintessential characteristic of our species, is a pattern of growth motivated by a greater-than-exponential rate of growth. It should be noted that the model being proposed is one of many potential models and not the sole, the only, possible model.

Keywords: population, exponential, greater-than-exponential growth (GTEG), hyperbolic.

Antony Harper, a researcher in the general area of applied mathematics to human his-torical processes, also understood as quantitative history and more appropriately, using Peter Turchin's term, as cliodynamics more