Bifurcations and global dynamics in a toxin-dependent aquatic population model

Abstract

The study of effects of environmental toxins on ecosystems is of great interest from both environmental and conservation points of view. In this paper, we present a global stability and bifurcation analysis of a toxin-dependent aquatic population model. Our analytical and numerical results show that both the environmental toxin level and the depuration capability of the population significantly affect the population persistence. The model exhibits a multifarious array of dynamics. While low levels of external toxin allow population persistence and high levels of toxin lead to an extirpation, intermediate toxin concentrations can produce very rich dynamics, such as transient oscillations, hysteresis, heteroclinic orbits, and a codimension-two bifurcation. In particular, a regime of bistability exists where the population is doomed to extinction or survival, depending on initial state of the system. As a practical implication of our study, the toxic effects of methylmercury on rainbow trout are scrutinized. The theory developed here provides a sound theoretical foundation for understanding the population effects of toxicity.