A Bayesian hierarchical model to predict benthic oxygen demand from organic matter loading in estuaries and coastal zones

Ecological models that have a theoretical basis and yet are mathematically simple enough to be parameterized using available data are likely to be the most useful for environmental management and decision-making. Mechanistic foundations improve confidence in model predictions, while statistical meth ods provide empirical support for parameter selection and allow for estimat es of predictive uncertainty. However, even models that are mechanistically simple can be overparameterized when system-specific data are limited. To overcome this problem, models are often fit to data sets composed of observ ations from multiple systems. The resulting parameter estimates are then us ed to predict changes within a single system, given changes in management v ariables. However, the assumption of common parameter values across all sys tems may not always be valid. This assumption can be relaxed by adopting a hierarchical approach. Under the hierarchical structure, each system has it s own set of parameter values, but some commonality in values is assumed ac ross systems. An underlying population distribution is employed to structur e this commonality among parameters, thereby avoiding the problems of overf itting. The hierarchical approach is, therefore, a practical compromise bet ween entirely site-specific and globally-common parameter estimates. We app lied the hierarchical method to annual data on organic matter loading and b enthic oxygen demand from 34 estuarine and coastal systems. Both global and system-specific parameters were estimated using Bayes Theorem. Compared to the global model, the hierarchical model results in predictions of oxygen demand that more accurately represent site-specific observation but are les s precise than the global model. Lower precision occurs because, by allowin g each system to have its own parameter values, we effectively reduce the a mount of information we have to estimate those parameters. However, if, by permitting model parameters to differ by location, the hierarchical model i s believed to be more realistic than the global model, then the lower preci sion represents a more proper translation of our knowledge into predictions . Appropriate representation of prediction precision can have important imp lications for management intended to reduce oxygen depletion. Depending on the predictive precision resulting from the availability and nature of site -specific data, the hierarchical model may suggest more or less stringent o rganic matter loading rates than a model assuming global parameter commonal ity. The generality of the hierarchical approach makes it suitable for a nu mber of ecological modeling applications in which cross-system data are req uired for empirical parameter estimation, yet only partial commonality can be assumed across sampling units. (C) 2001 Elsevier Science B.V. All rights reserved.