CRM and CNRS researchers introduce a novel concept, Late Warning Signals (LWS), for aiding post-tipping point ecosystem recovery, enhancing resilience in biodiversity management. LWS may offer crucial insights for timely intervention in ecosystem dynamics, potentially revolutionizing conservation strategies.
Scientists are perennially aware that it is best not to trust theory until it is confirmed by evidence. It is equally true . . . that it is best not to put too much faith in facts until they have been confirmed by theory.
Robert MacArthur (Geographical Ecology, 1972)
Conservation Biology is at the forefront of efforts to understand and protect Earth’s ecosystems and biodiversity from threats that erode biotic interactions and lead to extinctions. With the goal of developing research and providing tools for preserving biodiversity and promoting sustainable ecological management, researchers Josep Sardanyés and Filip Ivančić, from the Centre de Recerca Matemàtica (CRM), along with Blai Vidiella, who was affiliated with the Institute of Evolutionary Biology (IBE) at the time of the research and is now with the Station d’Écologie Théorique et Expérimentale (CNRS), have delved into the complexities of ecological dynamics to introduce a novel concept—late warning signals (LWS)—in their recent publication in the journal Biological Conservation. Their article is part of a special Issue about Non-equilibrium perspectives in biological conservation (edited by Sonia Kefi, Pierre Gaüzère, and Daniel Oro).Central to this exploration is the recognition of regime shifts—sudden, often irreversible alterations in the structure and function of ecosystems—that can be triggered by tipping points. These tipping points represent critical thresholds in the system’s behaviour, beyond which small changes can lead to large and often unforeseen consequences.
Ecosystems, despite their resilience and adaptability, are susceptible to abrupt regime shifts driven by tipping points, especially under the scenario of global change; even efforts to reduce or eliminate stressors that trigger these tipping points may not guarantee a return to their previous states. This highlights the importance of understanding not only the factors that lead to regime shifts but also the dynamics that govern the system’s recovery or potential collapse. To effectively mitigate the impacts of tipping points, conservation policies must incorporate monitoring mechanisms to track the indicators of ecosystems’ resilience, allowing for timely intervention and adaptive management strategies.
The research team’s investigation focuses on unravelling the complexities of ecological regime shifts triggered by tipping points in real ecosystems by means of theoretical and computational research. By studying these phenomena, they aim to bridge the gap between theoretical ecology and conservation practice, translating abstract concepts into tangible strategies for ecosystem management and restoration. Furthermore, the team examines how the properties of tipping points, such as hysteresis and resilience, influence ecosystems’ conservation, management, and restoration efforts.
“In our contribution, we discuss the critical transitions (CTs) that ecosystems undergo, emphasizing the need to identify warning signals indicating the approach of tipping points (so-called early warning signals), and especially those signals emerging after a tipping point has occurred” explains lead author Josep Sardanyés (CRM). “These signals are crucial for detecting the potential collapse or recovery of ecosystems.”
Introducing Late Warning Signals: new strategies for ecosystem recovery
One key innovation introduced in the study is the concept of late warning signals (LWS). Unlike early warning signals (EWS) that indicate an approaching tipping point, LWS provide evidence that a tipping point has already been surpassed, but the system remains in a transient state, offering a window of opportunity for recovery efforts.
“We provide evidence of late warning signals as a means to identify when a system has crossed a tipping point, yet the systems typically remain in a long transient state opening the possibility to take actions to avoid the collapse. This concept opens new avenues for conservation strategies aimed at restoring ecosystems even after critical transitions have occurred,” adds co-lead author Blai Vidiella (CNRS).
The paper discusses various mechanisms causing transients, including examples such as coral reef degradation, kelp forests overgrazing, and overexploitation of ocean fish stocks. These real-world instances highlight the challenges ecosystems face and the importance of timely intervention to prevent irreversible damage.
Furthermore, the study emphasizes the importance of incorporating nonlinear dynamics and non-equilibrium phenomena into management and conservation strategies. Ecosystems are complex adaptive systems and their responses to e.g., perturbations, are often highly nonlinear. By understanding the nature of critical transitions through mathematical and computational models, researchers can aid in developing effective conservation policies.
“In our pursuit to prevent ecosystem collapse and promote resilience, it is essential to consider the dynamic nature of ecosystems and the potential for late warning signals,” concludes Sardanyés. “By integrating these concepts into conservation practice, we can enhance our ability to safeguard Earth’s biodiversity for future generations.” The research by Sardanyés, Ivančić and Vidiella presents a significant contribution to conservation biology, offering valuable insights into ecosystem dynamics by integrating theoretical ecology with empirical evidence. Understanding these mechanisms is crucial for effective conservation as it allows policymakers and practitioners to anticipate and respond to ecosystem changes, fostering resilience and promoting sustainable management practices.
References: Sardanyés, J., Ivančić, F. and Vidiella, B. (2024), “Identifying regime shifts, transients and late warning signals for proactive ecosystem management”, Biological Conservation, Vol. 290, p. 110433, doi: 10.1016/j.biocon.2023.110433.
|
|
CRM CommPau Varela & Mariona Fucho
|
Dídac Gil Rams defends his doctoral thesis on the splitting of separatrices in generalized standard maps
Supervised by Inmaculada Baldomá and Pau Martín, the thesis proves the existence of chaotic dynamics in a broad family of area-preserving maps and combines classical analysis with computer-assisted proof. The defence took place on 3 July 2026 at the FME (UPC).Dídac...
How to Protect Bacteriophages Without Trapping Them? Mathematics to Improve an Alternative to Antibiotics
Bacteriophages — viruses capable of infecting and destroying bacteria — are considered one of the most promising alternatives to tackle the growing problem of antibiotic resistance. However, for these treatments to work, phages must overcome several obstacles before...
The CRM hosts nine international students for the 10th Barcelona International Youth Science Challenge
Nine secondary school students from six countries spent eight days at the CRM in July, working through four minicourses on fluid dynamics, perturbation methods, iteration and chaos, and randomness from Markov chains to machine learning, plus a session on how...
The Mathematics Behind the Three CRM Lectures at ICM 2026
Three CRM-affiliated researchers, Xavier Tolsa (plenary speaker), Xavier Cabré and Joaquim Ortega-Cerdà, lectured at the ICM 2026 in Philadelphia. Cabré surveyed the regularity of stable solutions to reaction-diffusion equations, including his optimal dimension-9...
Crossing Dimensional Frontiers: a breakthrough in the shape of stable solutions to semilinear elliptic equations
More than twenty years of efforts were required to solve a central problem in the theory of partial differential equations. A body of work developed over decades —and recognized with the Frontiers of Science Award (2023)— culminates in the resolution of an open...
Anna Florio, third CRM Chair of Excellence: billiards, friction, and the value of staying
The dynamicist Anna Florio (CEREMADE, Université Paris Dauphine-PSL) spends the summer at the CRM as the centre's third María de Maeztu Chair of Excellence. She is working with Immaculada Baldomà and Tere Martínez-Seara on billiards in the analytic setting, and on 22...
Hong Wang wins the Fields Medal, a year after her Kakeya lecture at the CRM
Hong Wang (NYU Courant and IHES) has received the Fields Medal at the International Congress of Mathematicians in Philadelphia, alongside Yu Deng (University of Chicago), John Pardon (Stony Brook University) and Jacob Tsimerman (University of Toronto). In June 2025,...
A Conference on Nonlinear PDEs on the Occasion of Xavier Cabré’s Anniversary
One anniversary, eight speakers, July and PDES (People, Discussions, Emotions and Summer) in BarcelonaThe conference Nonlinear PDEs was held at the Institut d'Estudis Catalans (IEC) on 6 and 7 July 2026. While PDEs usually stand for Partial Differential Equations, the...
Jezabel Curbelo receives the 2026 ECCOMAS Jacques-Louis Lions Award
Jezabel Curbelo, full professor at the Universitat Politècnica de Catalunya and affiliated researcher at the Centre de Recerca Matemàtica, has been awarded the ECCOMAS Jacques-Louis Lions Young Investigator Award 2026, in the field of computational mathematics. The...
An asteroid now carries the name of Àngel Jorba
An asteroid has been named (20137) Àngeljorba in honour of Àngel Jorba (1963-2025), UB professor and CRM affiliated researcher. Approved by the IAU, the name recognises his career in dynamical systems and celestial mechanics, from the orbital theory behind ESA's SOHO...
BIMR 2026: a first taste of research for future mathematicians
For four weeks in July 2026, the Centre de Recerca Matemàtica hosted the Barcelona Introduction to Mathematical Research (BIMR), a BGSMath summer programme built to give undergraduate and master's students a first, genuine experience of mathematical research and a...
Cambridge University Press publishes Single and Multiple Number Series, co-authored by Sergey Tikhonov (ICREA, CRM)
Sergey Tikhonov (ICREA, CRM) is one of four authors of the volume, published in the Encyclopedia of Mathematics and Its Applications series, which develops the theory of number series in one and several dimensions.Cambridge University Press has...












