Estimating the Risk of Exceeding Thresholds in Environmental Systems Elena M. Bennett & Stephen R. Carpenter & Jeffrey A. Cardille Received: 3 September 2007 / Accepted: 23 December 2007 / Published online: 15 January 2008 # Springer Science + Business Media B.V. 2007 Abstract Environmental regulations often rely on limits or thresholds to indicate an acceptable pollutant load. Estimates of the Risk of Exceeding such Thresh- olds (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 signifi- cantly 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 man- agement situations where thresholds are important including eutrophication, desertification, fisheries, and many types of pollution control. Keywords Threshold . Environmental pollutant . Risk of exceeding thresholds . Multiple models . Bootstrap aggregating 1 Introduction Efforts to control many water, air, soil, and other pollutants often rely on regulatory limits or thresholds to indicate the magnitude of acceptable pollutant loads (National Research Council 2001; Olsen et al. 1999). For example, health advisories for consumption of fish are based on critical tissue concentrations, Total Maximum Daily Loads arise from assessments of the maximum pollutant load that can be received by a water body and still meet water quality standards Water Air Soil Pollut (2008) 191:131–138 DOI 10.1007/s11270-007-9612-9 E. M. Bennett (*) : S. R. Carpenter Center for Limnology, University of Wisconsin, 680 N. Park St., Madison, WI 53706, USA e-mail: elena.bennett@mcgill.ca J. A. Cardille Department of Zoology, University of Wisconsin, 430 Lincoln Drive, Birge Hall, Madison, WI 53706, USA Present address: E. M. Bennett Department of Natural Resource Sciences and McGill School of Environment, McGill University, 21,111 Lakeshore Rd., Ste. Anne de Bellevue, Quebec H9X 3V9, Canada Present address: J. A. Cardille Département de Géographie, Université de Montréal, C.P. 6128 succursale centre-villeMontréal, Quebec H3C 3J7, Canada