On Qualitative Equilibria in Lotka-Volterra Models

The aim of this paper is to provoke the discussion on general conditions for the existence of what is called here "qualitatively positive equilibria" in Lotka-Volterra predator-prey models. "Qualitatively positive equilibria" are understood as those which are positive depending only on the qualitative structure of the ecological model, i.e., depending only on the signed digraph associated with the community matrix. Preliminary results are derived based on a theorem stemming from qualitative mathematical economics. It is believed that these results and further research may contribute for a better understanding of the qualitative dynamical behaviour of such ecological models.