Sublethal toxic effects in a simple aquatic food chain

In this paper, we study the sublethal effect of toxicants on the functioning (biomass production, nutrient recycling) and structure (species composition and complexity) of a simple aquatic ecosystem in a well-mixed environment (chemostat reactor). The modelled ecosystem consists of a nutrient consumed by a prey (e.g. bacteria, algae) which, in turn, is consumed by a predator (e.g. ciliates, daphnia) population. The dynamic behaviour of this ecosystem is described by a set of ordinary differential equations (ODE)s: one for the nutrient and one for each population. The system is stressed by a toxicant dissolved in the in-flowing water. The transport of the toxicant is modeled using a mass balance formulation leading to an ODE. Bioaccumulation in the prey and predator populations is via uptake from the water, in case of the predator also via consumption of contaminated prey. Mathematically, this process is described by a one-compartment model for the kinetics of the toxicant: uptake (from water and food) and elimination. The toxicant affects individuals which make up populations. In the model the physiological parameters depend on the internal concentration of the toxicant in individuals. Examples of physiological parameters are cost for growth and maintenance, and assimilation efficiency. In this paper, we use bifurcation theory to analyse the long-term dynamics of the models. In this way, the parameter space is divided into regions with qualitatively different asymptotic dynamic behaviour of the system. As logical choice for bifurcation parameters are the input rate of the nutrient and toxicant. The dynamic behaviour of the stressed ecosystem can be much more complicated than that of the unstressed system. For instance, the nutrient-prey-toxicant system can show bi-stability and oscillatory dynamics. Due to the toxic effects a total collapse (both prey and predator population go extinct) of the nutrient-prey-predator-toxicant system can occur after invasion of a predator.