A minimal model of eutrophication in freshwater ecosystems

A very simple model of eutrophication is presented. It includes several quite aggregated parameters and can be studied by analytical methods. Nevertheless, its dynamic behaviour reflects well real reservoir evolution as observed under the impact of increasing biogenic pollution. Such models, simple in construction but sensitive to the main trends of an ecosystem, are termed ‘minimal’. The state variables in the model are the concentrations of: (1) phytoplankton; (2) biogenic elements (nutrients); (3) detritus; and (4) dissolved oxygen. Transformations among the substances are described by a system of four ordinary differential equations. Steady-state dynamics are studied (the so-called quasi-stationary process). The qualitative analysis undertaken shows that the total amount of substances in a reservoir (phytoplankton + detritus + nutrients) is a very important ecosystem control parameter. In fact, it is this parameter that determines the rate and the degree of eutrophication. It also turns out that the relations between some observed characteristics of the ecosystem may define beforehand the future behaviour of the reservoir.