Stoichiometry and environmental change drive dynamical complexity and unpredictable switches in an intraguild predation model.

We incorporate stoichiometry (the balance of key elements) into an intraguild predation (IGP) model. Theoretical and numerical results show that our system exhibits complex dynamics, including chaos and multiple types of both bifurcations and bistability. Types of bifurcation present include saddle-node, Hopf, and transcritical bifurcations, and types of bistability present include node-node, node-cycle, and cycle-cycle bistability; cycle-cycle bistability has never been observed in IGP ordinary differential equation models. Stoichiometry can stabilize or destabilize the system via the disappearance or appearance of chaos. The species represented in the model can coexist for moderate levels of light intensity and nutrient availability. When the amount of light or nutrients present is extremely high or low, coexistence of the species becomes impossible, potentially harming biodiversity. Interestingly, stoichiometry can facilitate the re-emergence of severely endangered species as light intensity increases. In a temporally changing environment, the system can jump between different unstable states following changes in light intensity, with the trajectory followed depending strongly on initial conditions.