A Bayesian network of eutrophication models for synthesis, prediction, and uncertainty analysis

Abstract

A Bayesian network consists of a graphical structure and a probabilistic description of the relationships among variables in a system. The graphical structure explicitly represents cause-and-effect assumptions that allow a complex causal chain linking actions to outcomes to be factored into an articulated series of conditional relationships. Each of these relationships can then be independently quantified using a submodel suitable for the type and scale of information available. This approach is particularly useful for ecological modelling because predictable patterns may emerge at a variety of scales, necessitating a multiplicity of model forms. As an example, we describe a Bayesian network integrating models of the various processes involved in eutrophication in the Neuse River estuary, North Carolina. These models were developed using a range of methods, including: process-based models statistically fit to long-term monitoring data, Bayesian hierarchical modelling of cross-system data gathered from the literature, multivariate regression modelling of mesocosm experiments, and judgements elicited from scientific experts. The ability of the network to accommodate such a diversity of methods allowed for the prediction of policy-relevant ecosystem attributes not normally included in models of eutrophication. All of the submodels in the network include estimates of predictive uncertainty in the form of probability distributions which are propagated to model endpoints. Predictions expressed as probabilities give stakeholders and decision-makers a realistic appraisal of the chances of achieving desired outcomes under alternative nutrient management strategies. In general, the further down the causal chain a variable was, the greater the predictive uncertainty. This suggests that a compromise is necessary between policy relevance and predictive precision, and that, to select defensible environmental management strategies, public officials must adopt decision-making methods that deal explicitly with scientific uncertainty.