A Non-Phenomenological Model to Explain Population Growth Behaviors

TL;DR

This paper introduces a non-phenomenological population growth model based on individual interactions, unifying various known models and explaining phenomena like the Allee effect through interaction dynamics, with empirical validation on human population data.

Contribution

It presents a novel interaction-based model that generalizes existing population growth models and explains ecological behaviors without phenomenological assumptions.

Findings

The model reproduces known growth models as special cases.

It explains the Allee effect through individual interactions.

It fits well with human population data since 1000 A.D.

Abstract

This paper proposes a non-phenomenological model of population growth that is based on the interactions between the individuals that compose the system. It is assumed that the individuals interact cooperatively and competitively. As a consequence of this interaction, it is shown that some well-known phenomenological population growth models (such as the Malthus, Verhulst, Gompertz, Richards, Von Foerster, and power-law growth models) are special cases of the model presented herein. Moreover, other ecological behaviors can be seen as the emergent behavior of such interactions. For instance, the Allee effect, which is the characteristic of some populations to increase the population growth rate at a small population size, is observed. Whereas the models presented in the literature explain the Allee effect with phenomenological ideas, the model presented here explains this effect by the interactions between the individuals. The model is tested with empirical data to justify its formulation. Other interesting macroscopic emergent behavior from the model proposed here is the observation of a regime of population divergence at a finite time. It is interesting that this characteristic is observed in humanity's global population growth. It is shown that in a regime of cooperation, the model fits very well to the human population growth data since 1000 A.D.