Modelling and analysis of a modified May-Holling-Tanner predator-prey model with Allee effect in the prey and an alternative food source for the predator

TL;DR

This paper modifies the May-Holling-Tanner predator-prey model by incorporating Allee effects and alternative food sources, revealing new dynamics, equilibrium points, and stability conditions through analytical and numerical methods.

Contribution

It introduces a modified predator-prey model with Allee effects and alternative food sources, analyzing its complex dynamics and stability properties.

Findings

New equilibrium points appear in the modified model.

The model can predict species extinction or coexistence.

Numerical simulations show stabilization and oscillation behaviors.

Abstract

In the present study, we have modified the traditional May-Holling-Tanner predator-prey model used to represent the interaction between least weasel and field-vole population by adding an Allee effect (strong and weak) on the field-vole population and alternative food source for the weasel population. It is shown that the dynamic is different from the original May-Holling-Tanner predator-prey interaction since new equilibrium points have appeared in the first quadrant. Moreover, the modified model allows the extinction of both species when the Allee effect (strong and weak) on the prey is included, while the inclusion of the alternative food source for the predator shows that the system can support the coexistence of the populations, extinction of the prey and coexistence and oscillation of the populations at the same time. Furthermore, we use numerical simulations to illustrate the impact that changing the predation rate and the predator intrinsic growth rate have on the basin of attraction of the stable equilibrium point or stable limit cycle in the first quadrant. These simulations show the stabilisation of predator and prey populations and/or the oscillation of these two species over time.