Global dynamics of parasitism-competition systems with one host and multiple parasites

Abstract

This paper studies a new parasitism-competition model with one host and multiple parasites, where a plant is the host and nectar robbers are the parasites that compete for nectar of the plant but do not kill and eat the host itself. Based on the plant-nectar-robber interaction, a parasitism model is derived, which is different from previous parasitism models. Then the two-species model is extended to an n-dimensional system characterizing one plant and multiple robbers. Using dynamical system theory, qualitative behavior of the two-species model is exhibited by excluding existence of periodic solution, and global dynamics of the n-species system in the positive octant are completely shown. The dynamics demonstrate necessary and sufficient conditions for the principle of competitive exclusion to hold. It is shown that when the principle of competitive exclusion holds, at least one of the robbers is driven into extinction by other parasites while the others coexist with the plant at a steady state; When the principle of competitive exclusion does not hold, nectar robbers either coexist at a steady state or both go to extinction. The result also demonstrates a mechanism by which abiotic factors lead to persistence of nectar robbing.

Keywords: Coexistence; Competition; Liapunov stability; Parasitism; Principle of competitive exclusion.