ArticleScientific reports2019
Eigenvalues of the covariance matrix as early warning signals for critical transitions in ecological systems.
Article in Scientific reports, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 24 papers.
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Who cites it
24 citing papers in PubMed.
- Early Warning Signals in Ecological Time-Series.Entropy (Basel, Switzerland) · 2026Review
- Detecting and forecasting tipping points from sample variance alone.PNAS nexus · 2026Article
- Interpretable early warnings using machine learning in an online game-experiment.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Identifying COVID-19 peaks using early warning signals.PLoS computational biology · 2025Article
- Introduction to correlation networks: Interdisciplinary approaches beyond thresholding.Physics reports · 2025Article
- Quantifying the intra- and inter-species community interactions in microbiomes by dynamic covariance mapping.Nature communications · 2025Article
- Assessing and comparing early warning signal performance in spatially-structured systems.PloS one · 2025Article
- Anticipating regime shifts by mixing early warning signals from different nodes.Nature communications · 2024Article
- Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis.Frontiers in network physiology · 2024Article
- Early warning signals have limited applicability to empirical lake data.Nature communications · 2023Article
- Attractor landscapes: a unifying conceptual model for understanding behaviour change across scales of observation.Health psychology review · 2023Article
- Anticipating the occurrence and type of critical transitions.Science advances · 2023Article
- The single-sample network module biomarkers (sNMB) method reveals the pre-deterioration stage of disease progression.Journal of molecular cell biology · 2022Article
- Community structure determines the predictability of population collapse.The Journal of animal ecology · 2022Article
- Data-driven prediction in dynamical systems: recent developments.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2022Article
- Practical guide to using Kendall'sRoyal Society open science · 2022Article
- Anticipating the direction of symptom progression using critical slowing down: a proof-of-concept study.BMC psychiatry · 2022Article
- Rethinking the design of resilience and adaptation indicators supporting coastal communities.Journal of environmental planning and management · 2022Article
- Structure-based identification of sensor species for anticipating critical transitions.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- scGET: Predicting Cell Fate Transition During Early Embryonic Development by Single-cell Graph Entropy.Genomics, proteomics & bioinformatics · 2021Article
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4 authors.
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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.
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