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      Early warning signals of regime shifts in coupled human–environment systems

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          Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

          Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called ‘early warning signals’, and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.
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            The Importance of Being Discrete (and Spatial)

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              Stability of Grazing Systems: An Application of Predator-Prey Graphs

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                Author and article information

                Journal
                Proceedings of the National Academy of Sciences
                Proc Natl Acad Sci USA
                Proceedings of the National Academy of Sciences
                0027-8424
                1091-6490
                December 20 2016
                December 20 2016
                : 113
                : 51
                : 14560-14567
                Article
                10.1073/pnas.1604978113
                5187665
                27815533
                70d4d1b9-ddf5-48cd-a621-331d118e4b98
                © 2016
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