Invading species can stabilize simple trophic systems

Bifurcation analysis is presented for the dynamics of a nutrient–two-prey–predator bi-trophic food web in a chemostat. A simple model where food is converted into energy with a fixed efficiency is used. The available energy is used for maintenance and the rest for growth. The Holling type II functional response is used to model the ingestion rate of the prey consuming the nutrient as well as the predator consuming the two-prey species. The invasion of a competitor of the prey into a nutrient–prey–predator bi-trophic food chain is evaluated using bifurcation diagrams. We will show that an invading competitor prey can stabilize an oscillatory nutrient–prey–predator system. It is well known that in the absence of the predator generally one prey can invade and establish itself while the other is eliminated: this is called competitive exclusion. We will show that the presence of a predator can allow coexistence of two competing prey populations. This illustrates a top-down effect, where one species (predator) affects the interaction of two other species (competing prey). Bifurcation analysis results are here applied to community assembly theory; regions of invasibility where obtained using available computer packages based on the bifurcation theory with the implementation of continuation techniques. Regions with multiple interior attractors can be distinguished systematically. We discuss the applicability of the proposed technique for large-scale food webs.