A Non-Phenomenological Model to Explain Population Growth Behaviors

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.