Estimating the Risk of Exceeding Thresholds in Environmental Systems

Environmental regulations often rely on limits or thresholds to indicate an acceptable pollutant load. Estimates of the Risk of Exceeding such Thresholds (RET) are often based on a single model deemed to be the best for the particular pollutant or particular case. However, if many models make different predictions but explain the data almost equally well, predictions based on a single model may omit important information contained in other models that fit almost as well as the “best” single model. More accurate assessments of RET may result if multiple models are considered. We compared performance of the single best model relative to that of an ensemble of models estimated by bagging (Bootstrap AGGregatING) using the example of soil P concentrations and the risk of exceeding environmental limits of soil P concentrations in the watershed of Lake Mendota, Wisconsin, USA. Bagging yielded significantly better predictions of the risk of exceeding a threshold level of soil P (99.6% accuracy versus 74% for single-model prediction at a 20 mg kg^?1 threshold). Use of multiple model techniques can improve estimates of RET over a range of realistic thresholds in other management situations where thresholds are important including eutrophication, desertification, fisheries, and many types of pollution control.