Biological pest control using cannibalistic predators and with provision of additional food: a theoretical study

Cannibalism is a conspecific lethal interaction, a typical phenomenon in many natural populations, which is used as a "life-boat strategy" to avoid circumstances leading to extinction. It is observed in many experimental studies that the cannibalistic nature of natural enemies deters the outcome of biological pest control programmes. One of the ways to deviate natural enemies from conspecific lethal interactions is to provide them with additional food. In this paper, using the theory of dynamical systems, we analyse the dynamics of a cannibalistic predator-prey system when predators are provided with additional food. A detailed mathematical analysis is carried out to study the permanence, stability and various bifurcations occurring in the system. The system analysis reveals several interesting phenomena. Depending on the choice of quality (characterised by the predator's handling time towards additional food, and prey) and quantity of additional food, the system can exhibit multiple coexisting equilibria, leading to the emergence of a homoclinic loop. Further, it is observed that by varying the quality and quantity of additional food, one can not only limit and control the pest but also eradicate the predators. In the context of biological control programmes, the current theoretical study aids eco-managers in choosing the appropriate additional food that is to be supplied for enhancing the biocontrol efficiency of cannibalistic predators.