  In this work, some phenomenological models, those that are based only on the
population information (macroscopic level), are deduced in an intuitive way.
These models, as for instance Verhulst, Gompertz and Bertalanffy models, are
posted in such a manner that all the parameters involved have physical
interpretation. A model based on the interaction (distance dependent) between
the individuals (microscopic level) is also presented. This microscopic model
reachs the phenomenological models presented as particular cases. In this
approach, the Verhulst model represents the situation in which all the
individuals interact in the same way, regardless of the distance between them.
That means Verhulst model is a kind of mean field model. The other
phenomenological models are reaching from the microscopic model according to
two quantities: i) the relation between the way that the interaction decays
with the distance; and ii) the dimension of the spatial structure formed by the
population. This microscopic model allows understanding population growth by
first principles, because it predicts that some phenomenological models can be
seen as a consequence of the same individual level kind of interaction. In this
sense, the microscopic model that will be discussed here paves the way to
finding universal patterns that are common to all types of growth, even in
systems of very different nature.
