A non-phenomenological model of competition and cooperation to explain population growth behaviors

Abstract

This paper is an extension of a previous work which proposes a non-phenomenological model of population growth that is based on the interactions among the individuals of a population. In addition to what had already been studied—that the individuals interact competitively—in the present work it is also considered that the individuals interact cooperatively. As a consequence of this new consideration, a richer dynamics is observed. For instance, besides getting the population models already reached from the original version of the model (as the Malthus, Verhulst, Gompertz, Richards, Bertalanffy and power-law growth models), the new formulation also reaches the von Foerster growth model and also a regime of divergence of the population at a finite time. An agent-based model is also presented in order to give support to the analytical results. Moreover, this new approach of the model explains the Allee effect as an emergent behavior of the cooperative and competitive interactions among the individuals. The Allee effect is the characteristic of some populations of increasing the population growth rate in a small-sized population. 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. Another interesting macroscopic emergent behavior from the model proposed 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 from 1000 AD to nowadays.