A biocontrol agent as a commensal in a plant-pest interaction

Abstract

In this work, the dynamics of a differential equation system which models pest control in a plant by means of a biocontrol agent is analyzed. It is assumed that the plant-biocontrol agent relationship is commensalism, the biocontrol agent–pest relationship is that of predator–prey, and the pest is a specialist. The impact of a biocontrol agent on the pest is measured. In particular, conditions for pest eradication and for species coexistence are shown. Some of the results show, somewhat paradoxically, that it is the low initial levels of the biocontrol agent and not the high levels that lead to a greater recovery of the plant population. Indeed, for a certain parameter region the system present simultaneously two positive equilibrium points; numerical analysis shows that the one with the highest population level of the plant is the ω−limit of those trajectories starting at points with smaller population level of the biocontrol agent than those tending to the other stable equilibrium point.