Early Warning Signals for Critical Transitions: A Generalized Modeling Approach
Steven J. Lade and Thilo Gross
PLoS Comput Biol 8, e1002360, 2012
Critical transitions are sudden, often irreversible, changes that can occur in a large variety of complex systems. Signals that warn of critical transitions are highly desirable, but their construction can be impeded by limited availability of data. We propose a method that can significantly reduce the amount of time series data required for a robust early warning signal by using other information about the system. This information is integrated through the framework of a generalized model. We demonstrate the applicability of the proposed approach through several examples, including a previously published fisheries model.
Figure 1: Early warning signal for a critical transition in a tri-trophic food chain. (a) Time series of \(X_1\) (blue circles, left axis), \(X_2\) (green crosses, left axis) and \(X_3\) (red triangles, left axis) generated by Eq. (2). Only the data subsequently used in the early warning analysis were plotted. Some of the data during the oscillations between \(t = 40\) and \(45\) were outside the scale of this graph, with \(X_3\) exceeding \(30\). The estimates of top-predator mortality used to calculate the early warning signal are also shown (black dots, right axis).