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

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This work proposes a non-phenomenological model of population growth
that is based on the interactions among the individuals of a
population.
When there is competition between the individuals, the model proposed
reaches the Malthus, Verhulst, Gompertz, Richards, Bertalanffy and
power-law growth models.
And when there is cooperation, the model reaches the von Foerster
growth model and also presents a regime of divergence of the
population at a finite time. This approach 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.

The presentation is based on two recent published papers:
1. RIBEIRO, F. L. ; RIBEIRO, K. N. . A one dimensional model of
population growth. Physica. A (Print), v. 434, p. 201-210, 2015.
2. RIBEIRO, F. L. . A Non-phenomenological Model of Competition and
Cooperation to Explain Population Growth Behaviors. Bulletin of
Mathematical Biology (Print), v. 77, p. 409-433, 2015.

I would like to acknowledge the financial support from FAPEMIG.