Estimates in deterministic fate modelling of environmental chemicals

Ecological modelling is frequently confronted with the problem of unavailable parameters, or input data of poor quality. This makes the interpretation of the results difficult, and predictions questionable, unless the quality of the parameters is taken into account. In this paper, we propose a mathematical approach to address the problem of large parameter variability in deterministic models, and especially in linear compartmental models. The method is based on a classical comparison theorem for differential equations, and yields upper and lower estimates for solutions when upper and lower estimates for the model input functions are given. Such estimates may be checked against experimental data, and thus play a crucial role in verification or falsification of model predictions. Applications are presented with regard to fate modelling of environmental chemicals in a pond sediment.