Eigenvalues of the covariance matrix as early warning signals for critical transitions in ecological systems

[Datseris]

Indicator summary

paper abstract:

Many ecological systems are subject critical transitions, which are abrupt changes to contrasting states
triggered by small changes in some key component of the system. Temporal early warning signals such
as the variance of a time series, and spatial early warning signals such as the spatial correlation in a
snapshot of the system’s state, have been proposed to forecast critical transitions. However, temporal
early warning signals do not take the spatial pattern into account, and past spatial indicators only
examine one snapshot at a time. In this study, we propose the use of eigenvalues of the covariance
matrix of multiple time series as early warning signals. We first show theoretically why these indicators
may increase as the system moves closer to the critical transition. Then, we apply the method to
simulated data from several spatial ecological models to demonstrate the method’s applicability.
This method has the advantage that it takes into account only the fluctuations of the system about
its equilibrium, thus eliminating the effects of any change in equilibrium values. The eigenvector
associated with the largest eigenvalue of the covariance matrix is helpful for identifying the regions that
are most vulnerable to the critical transition.

Reference

Scientific Reports | (2019) 9:2572 | https://doi.org/10.1038/s41598-019-38961-5

Shiyang Chen1, Eamon B. O’Dea2,3, John M. Drake2,3 & Bogdan I. Epureanu1