Anticipating regime shifts by mixing early warning signals from different nodes

Real systems showing regime shifts, such as ecosystems, are often composed of many interacting dynamical elements on a network. Various early warning signals have been proposed to anticipate regime shifts from observed data, but it remains unclear how to combine early warning signals from different nodes for improved performance. Using theory of stochastic differential equations, the authors propose a method to optimize the node set from which to construct an early warning signal. The method accounts for both the signal magnitude and its uncertainty in determining predictive performance, shows that a large magnitude or small uncertainty at one node does not necessarily imply high performance, and clarifies that combining signals from different nodes is often but not always beneficial. The method performs particularly well when nodes are subject to different amounts of dynamical noise and stress.