  We consider a couple of models for the dynamics of the populations of two
interacting species, inspired by Lotka-Volterra's classical equations. The
novelty of this work is that the interaction terms are non local and the
interaction occurs within a bounded range. These terms include the competitive
intraspecific interaction among individuals and the interspecific terms for
which we consider two cases: Competition and predation. The results show that
not only the non-locality induces spatial structures but also allows for the
survival of the species when due to predation or the competitive exclusion
extinction was expected, and even promotes spatio-temporal patterns not linked
to eventual temporal oscillations in the local case. In this work we also
explore some interesting details about the behavior of the population dynamics
that shows spatial patterns that interfere in a way that leads to non-trivial
results.
