Allee effect in models of interacting species

TL;DR

This paper examines the integration of the Allee effect with density-dependent carrying capacity in models of interacting species, highlighting potential issues and proposing solutions for more realistic ecological modeling.

Contribution

It demonstrates the importance of careful formulation when combining the Allee effect with density-dependent carrying capacity in predator-prey and competition models.

Findings

Incorrect implementation can lead to meaningless effects

Proper inclusion of cubic terms resolves modeling issues

Highlights the need for careful model formulation in ecology

Abstract

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.