Mathematical modelling — a management tool for aquatic ecosystems?

Abstract

Mathematical modelling may serve as a rational and powerful tool in the management of complex ecosystems. However, ecosystem models are drastic simplifications of the real world. As a rule they are based on a rather incomplete and scattered knowledge of the system in question. Furthermore, ecological systems and in particular marine systems are characterised by a high degree of complexity, spatial and functional heterogeneity, nonlinearity, complex behavioural features such as adptation and self-organisation, and a considerable stochastic element. Nevertheless, if management is to be based on predictions from mathematical models — and it has to be based on some kind of “model” in at least a broad sense — we need an estimate of prediction accuracy in terms of the management variables and constraints. One possible approach to model uncertainty is a probabilistic interpretation of model predictions, generated by use of Monte-Carlo techniques. Fuzzy data sets and ranges are used. The resulting model response allows the derivation of measures for model credibility. Probability distributions can be computed for certain system states under (un)certain input conditions, representing the effects of insufficient data and structural uncertainty on model-based predictions. Such analysis indicates that prediction uncertainty increases, not only with the uncertainty in the data, but also with increasing “distance” from the empirical conditions, and with time. Present ecoystem models can be a tool for qualitative discrimination between different management alternatives, rather than a credible means for detailed quantitative predictions of system response to a wide range of input conditions.