Resilience to tipping points in ecosystems

Spatial pattern formation has been proposed as an early warning signal for dangerous tipping points and imminent critical transitions in complex systems, including ecosystems. Rietkerk et al. review how ecosystems and Earth system components can actually evade catastrophic tipping through various pathways of spatial pattern formation. With mathematical and real-world examples, they argue that evading tipping and enhancing resilience could be relevant for many ecosystems and Earth system components that until now were known as tipping prone. Many of these complex systems may be more resilient than currently thought because of overlooked spatial dynamics and multiple stable states, and may thus not undergo critical or catastrophic transitions with global change. —AMS

Structured Abstract


In the Anthropocene, there is a need to better understand the catastrophic effects that climate and land-use change may have on ecosystems, Earth system components, and the whole Earth system. The concept of critical transitions, or tipping from one state to another, contributes to this understanding. Tipping occurs in a system when it is forced outside the basin of attraction of the original equilibrium, resulting in a critical transition to an alternative, often less-desirable, stable state. In this context, the search for early warning signals for such imminent critical transitions has become a focus of research. In particular, spatial self-organization in ecosystems, such as the spontaneous formation of regular vegetation patterns—so-called Turing patterns—has been suggested as a prominent early warning signal.


However, recent findings indicate that such spatial self-organization should not necessarily be interpreted as an early warning signal for critical transitions. Instead, spatial self-organization can cause ecosystems to evade tipping points and can thereby be a signal of resilience. These findings are based on recent mathematical analyses of spatial models and on observations of real ecosystems. Both have revealed multistability, meaning that many different spatial patterns can co-occur under the same environmental conditions, and each of these patterns can stay stable for a wide range of conditions. This enables complex system states to persist beyond tipping points through spatial self-organization. Moreover, if a complex system with tipping properties experiences a perturbation, subsequent change of the system does not necessarily lead to tipping of the complete system. Instead, the change can stay localized because the system allows for alternative states to coexist in space—thus referred to as coexistence states. These spatial patterns can also persist beyond tipping points with worsening conditions through this alternative pathway. We refer to both Turing patterns and coexistence states as spatial pattern formation. Evasion of tipping through these various pathways of spatial pattern formation may be relevant for many ecosystems and Earth system components that were hitherto interpreted as prone to tipping, including for Earth as a whole.


To further study how complex systems evade tipping through spatial pattern formation, savanna ecosystems can be considered as a concrete archetypal example because of the alternative states and spatial patterns observed for them. Moreover, universal conditions for evading tipping points in both ecosystems and Earth system components can be derived by mathematical analyses. Scenarios can be revealed by which Turing patterns with small amplitudes can grow and form large-scale localized interacting structures, thereby aiding complex systems to evade tipping. The effects that global change has on the spatial boundaries between coexistence states should be studied, and the impacts of restrictions of spatial domain and localized and nonlocal homogenizing effects by humans should be revealed. This approach will advance our understanding and predictions of critical transitions in nature and reveal how these may be avoided or reversed.
Evasion of tipping points.
We illustrate the response of complex systems to changes in external conditions (i.e., a bifurcation diagram). Homogeneous dark gray squares depict high density of the system state variable, and homogeneous light gray squares illustrate low density. (A) Classic view. (B) Multistability of Turing patterns. Recent model analysis has revealed multistability of Turing patterns in Busse balloons, supported by satellite observations of real ecosystems. A Busse balloon is the region in parameter space in mathematical models where multistability of patterned equilibria occurs. (C) Multistability of coexistence states. Evading tipping can also be the result of multistability of coexistence states. These spatial patterns originate in the bistability region before the tipping point; the evolving spatial patterns can also persist beyond the tipping point with worsening external conditions, thereby constituting an alternative pathway to evade tipping points.


The concept of tipping points and critical transitions helps inform our understanding of the catastrophic effects that global change may have on ecosystems, Earth system components, and the whole Earth system. The search for early warning indicators is ongoing, and spatial self-organization has been interpreted as one such signal. Here, we review how spatial self-organization can aid complex systems to evade tipping points and can therefore be a signal of resilience instead. Evading tipping points through various pathways of spatial pattern formation may be relevant for many ecosystems and Earth system components that hitherto have been identified as tipping prone, including for the entire Earth system. We propose a systematic analysis that may reveal the broad range of conditions under which tipping is evaded and resilience emerges.

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M. te Beest and A. Staal critically reviewed earlier versions of this manuscript. M. Eppinga, J. Rademacher, E. Siero, K. Siteur, and S. van der Stelt contributed to research that led to new insights leading to this paper. We thank T. Markus for designing figures. Funding: The research leading to this paper was funded by the Netherlands Organization of Scientific Research, NWO Complexity and NWO Mathematics of Planet Earth programs. This project is TiPES contribution no. 83. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement 820970. Author contributions: All authors contributed to the conceptualization and research ideas. M.R., A.D., and R.B. wrote the original draft, and all authors contributed to reviewing and editing the paper. M.R., R.B., S.B., J.v.d.K., and M.B. prepared visual materials. Competing interests: The authors declare no competing interests.



Copernicus Institute of Sustainable Development, Utrecht University, 3508 TC, Utrecht, Netherlands.
Department of Physics, Institute for Marine and Atmospheric Research Utrecht, Utrecht University, 3508 TA, Utrecht, Netherlands.
Copernicus Institute of Sustainable Development, Utrecht University, 3508 TC, Utrecht, Netherlands.
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.
Indian Statistical Institute, Agricultural and Ecological Research Unit, Kolkata 700108, India.
Department of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research, 4400 AC, Yerseke, Netherlands.
Groningen Institute for Evolutionary Life Sciences, Conservation Ecology Group, University of Groningen, 9700 CC, Groningen, Netherlands.
Copernicus Institute of Sustainable Development, Utrecht University, 3508 TC, Utrecht, Netherlands.
National Research Council of Italy, Institute of Atmospheric Sciences and Climate (CNR-ISAC), 10133 Torino, Italy.
Mathematical Institute, Leiden University, 2300 RA, Leiden, Netherlands.

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*Corresponding author. Email: [email protected]

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