A widespread interaction between generalist and specialist enemies: The role of intraguild predation and Allee effect

Abstract

A natural food web system involves a diverse community of natural enemies and one of the widespread and common phenomena of such systems is intraguild predation (IGP) (i.e., presence of eating and killing among potential competitors). Here, we investigate the dynamics of a food web system with Allee effect and intraguild predation. In the present study, generalist and specialist natural enemies competing for a shared resource (prey) (intraguild predation) have been introduced. The Allee effect has also been incorporated in the shared prey growth rate. We investigate how parameters defining Allee effect and intraguild predation affect the long-term persistence, extinction and co-existence regions of such species. We outline the conditions under which different types of interior and non-interior equilibria exist and are locally stable. Bi-stable dynamics has also been investigated for the proposed model system for a suitable range of parametric values. A threshold condition on the strength of Allee effect has been obtained assuring the absence of IG predator population along with extinction region of shared prey. To understand the dynamics of the system, a comprehensive study of bifurcation analysis has also been provided taking Allee effect and fertility rate of intraguild predator as bifurcation parameters. These two parameters generate various interesting bifurcations like saddle-node bifurcation and Hopf-bifurcation. We have obtained different parametric regions of Allee parameter for the existence of different boundary and interior equilibria. All the analytical results related with local stability of equilibrium points and all possible successive bifurcations have been supported by different numerical examples, one and two parameter bifurcation diagrams, bi-stability diagram and stability regions of all possible equilibrium points. The impacts of Allee effect on co-existence, stability, extinction of species, their persistence, bistability and bifurcations have been explicitly discussed and the whole dynamics has also been successfully compared with the dynamics of food web without Allee effect. It is observed that the introduction of Allee effect and IG predator induce more rich dynamics and compel the system to be more sensitive to initial population densities.