  The search for more realistic models for interacting species has produced
many adaptations of the original Lotka-Volterra equations, such as the
inclusion of the Allee effect and the different Holling's types of functional
response. In the present work we show that a correct implementation of both
ideas together requires a careful formulation. We focus our work in the fact
that a density dependent carrying capacity, combined with the Allee effect, can
lead to meaningless effects. We illustrate the difficulties in predator-prey
and two-species competition models, together with our proposed solution of the
careful inclusion of the corresponding cubic terms.
