Abstract
The identification of disturbance thresholds is important for many aspects of aquatic resource management, including the establishment of regulatory criteria and the identification of stream reference conditions. A number of quantitative or model-based approaches can be used to identify disturbance thresholds, including nonparametric deviance reduction (NDR), piecewise regression (PR), Bayesian changepoint (BCP), quantile piecewise constant (QPC), and quantile piecewise linear (QPL) approaches. These methods differ in their assumptions regarding the nature of the disturbance-response variable relationship, which can make selecting among the approaches difficult for those unfamiliar with the methods. We first provide an overview of each of the aforementioned approaches for identifying disturbance thresholds, including the types of data for which the approaches are intended. We then compare threshold estimates from each of these approaches to evaluate their robustness using both simulated and empirical datasets. We found that most of the approaches were accurate in estimating thresholds for datasets with drastic changes in responses variable at the disturbance threshold. Conversely, only the PR and QPL approaches performed well for datasets with conditional mean or upper boundary changes in response variables at the disturbance threshold. The most robust threshold identification approach appeared to be the QPL approach; this method provided relatively accurate threshold estimates for most of the evaluated datasets. Because accuracy of disturbance threshold estimates can be affected by a number of factors, we recommend that several steps be followed when attempting to identify disturbance thresholds. These steps include plotting and visually inspecting the disturbance-response data, hypothesizing what mechanisms likely generate the observed pattern in the disturbance-response data, and plotting the estimated threshold in relation to the disturbance-response data to ensure the appropriateness of the threshold estimate.
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Acknowledgments
The authors thank Wei-Yin Loh for assistance in using GUIDE and for reviewing our descriptions of the QPC and QPL approaches. Dale Robertson, Dave Graczyke, and seasonal workers of USGS collected the nutrient data and Paul Kanehl and seasonal workers of Wisconsin DNR collected the fish data for the Wisconsin dataset. Arthur Cooper captured the land-use data for the Michigan streams. The authors thank three anonymous reviewers for commenting on early versions of the manuscript. This project was partly supported by Federal Aid in Sport Fishery Restoration Program, Project F-80-R, through the Fisheries Division of the Michigan Department of Natural Resources. This is manuscript 20YY-NN of the Quantitative Fisheries Center at Michigan State University.
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Brenden, T.O., Wang, L. & Su, Z. Quantitative Identification of Disturbance Thresholds in Support of Aquatic Resource Management. Environmental Management 42, 821–832 (2008). https://doi.org/10.1007/s00267-008-9150-2
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DOI: https://doi.org/10.1007/s00267-008-9150-2