The power of Allee effects: inducing multistability and oscillations in a stoichiometric producer-herbivore system.

Abstract

Understanding producer-herbivore dynamics is fundamental for maintaining ecosystem stability and biodiversity. This study proposes a novel stoichiometric producer-herbivore model that incorporates positive density dependence induced by demographic factors. We conduct a rigorous mathematical analysis of the proposed model, covering well-posedness, nullcline analysis, and system stability. This analysis is expanded through numerical bifurcation analysis to explore the effects of critical biological parameters, including light intensity, on producer-herbivore interactions. Our findings reveal that variations in the severity of the Allee effect significantly influence these interactions, driving multistability and periodic oscillations. Severe Allee effects lead to complex dynamics, including four forms of bistability and three forms of tristability. Severe Allee effects can also lead to the extinction of both producer and herbivore populations due to positive density dependence. Intermediate levels of parameters such as light intensity, producer growth rate, herbivore loss rate, saturation levels of the Allee effect, total phosphorus, and sufficiently high production efficiency can lead to system instability and oscillations. Conversely, in scenarios with low-severity Allee effects, the system shows relatively simpler dynamics, with three types of bistability. Low producer growth rate and herbivore loss rate, moderate saturation levels of the Allee effect, light intensity, and sufficiently high herbivore production efficiency and total phosphorus levels can induce periodic oscillations. These findings emphasize the importance of managing Allee effect severity in conservation efforts to sustain biodiversity and prevent undesirable state transitions.