Competitive exclusion and coexistence in a Leslie–Gower competition model with Allee effects

Abstract

The classical competitive exclusion principle states that two populations competing for a limited resource cannot coexist, one of the populations will drive the other to extinction. We prove in this work that when one population is subject to Allee effects, then for certain parameter regimes both competing populations may either coexist or one population may drive the other to extinction depending on initial conditions.

Keywords:

• Allee effects
• monotone map
• global stable manifold

AMS Subject Classifications::

• 92D25
• 39A11

Acknowledgements

The author thanks one of the referees for providing many comments and suggestions for improving the original manuscript.