Early warning signals to anticipate critical transitions in high-dimensional systems

Early warning signals to anticipate critical transitions in high-dimensional systems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Early warning signals to anticipate critical transitions in high-dimensional systems Koushik Garain, Chao-Jui Chang, Jer-Horng Wu, Hsiao-Pei Lu, Arndt Telschow, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7865028/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Predicting critical transitions in complex systems remains a fundamental challenge. Most existing early warning signals (EWSs) target the variable of interest, overlooking the high-dimensional nature of real-world systems, where interdependent nodes create information redundancy and bifurcations often emerge locally within specific nodes. To overcome these limitations, we extend the Dynamical Eigenvalue (DEV) method, a univariate EWS for anticipating the timing and type of critical transition, into a high-dimensional framework. Our approach, Manifold-projected Multivariate DEV (MM-DEV), integrates (1) nonlinear manifold learning via ISOMAP to project high-dimensional data onto a lower-dimensional space, and (2) a multivariate extension of DEV method. MM-DEV accurately detects both the timing and bifurcation types of critical transitions in theoretical models. For empirical validation, we conducted controlled experiments in which critical transitions are induced in an engineered methanogenic ecosystem by systematically increasing salinity stress, ultimately causing biogas production failure. Using daily time-series data of chemical factors and microbial taxa, MM-DEV effectively functions as an EWS for ecosystem collapse. When applied to monthly plankton data from long-term Lake Zurich surveys, MM-DEV anticipates a regime shift in the plankton food web driven by re-oligotrophication. These applications across experimental and natural ecosystems demonstrate MM-DEV's efficacy for high-dimensional real-world systems. Biological sciences/Ecology Earth and environmental sciences/Environmental sciences/Environmental impact Full Text Additional Declarations There is NO Competing Interest. Supplementary Files Supplementary20251013.docx Supplementary Text Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7865028","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":541752059,"identity":"124b06b9-6c1f-438a-8761-4ee7e7170a05","order_by":0,"name":"Koushik Garain","email":"","orcid":"","institution":"Institute of Oceanography, National Taiwan University, Taipei 10617, Taiwan","correspondingAuthor":false,"prefix":"","firstName":"Koushik","middleName":"","lastName":"Garain","suffix":""},{"id":541752060,"identity":"719f3f54-3aae-41db-94ca-77165ad5d7f5","order_by":1,"name":"Chao-Jui 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