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

Abstract

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 methods provide empirical support for parameter selection and allow for estimates 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 observations from multiple systems. The resulting parameter estimates are then used to predict changes within a single system, given changes in management variables. However, the assumption of common parameter values across all systems may not always be valid. This assumption can be relaxed by adopting a hierarchical approach. Under the hierarchical structure, each system has its own set of parameter values, but some commonality in values is assumed across systems. An underlying population distribution is employed to structure this commonality among parameters, thereby avoiding the problems of overfitting. The hierarchical approach is, therefore, a practical compromise between entirely site-specific and globally-common parameter estimates. We applied the hierarchical method to annual data on organic matter loading and benthic 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 less precise than the global model. Lower precision occurs because, by allowing each system to have its own parameter values, we effectively reduce the amount of information we have to estimate those parameters. However, if, by permitting model parameters to differ by location, the hierarchical model is believed to be more realistic than the global model, then the lower precision represents a more proper translation of our knowledge into predictions. Appropriate representation of prediction precision can have important implications 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 organic matter loading rates than a model assuming global parameter commonality. The generality of the hierarchical approach makes it suitable for a number of ecological modeling applications in which cross-system data are required for empirical parameter estimation, yet only partial commonality can be assumed across sampling units. (C) 2001 Elsevier Science B.V. All rights reserved