Estimating comparable distances to tipping points across mutualistic systems by scaled recovery rates

Huixin Zhang, Qi Wang, Weidong Zhang, Shlomo Havlin, Jianxi Gao

Research output: Contribution to journalArticlepeer-review


Mutualistic systems can experience abrupt and irreversible regime shifts caused by local or global stressors. Despite decades of efforts to understand ecosystem dynamics and determine whether a tipping point could occur, there are no current approaches to estimate distances (in state/parameter space) to tipping points and compare the distances across various mutualistic systems. Here we develop a general dimension-reduction approach that simultaneously compresses the natural control and state parameters of high-dimensional complex systems and introduces a scaling factor for recovery rates. Our theoretical framework places various systems with entirely different dynamical parameters, network structure and state perturbations on the same scale. More importantly, it compares distances to tipping points across different systems on the basis of data on abundance and topology. By applying the method to 54 real-world mutualistic networks, our analytical results unveil the network characteristics and system parameters that control a system’s resilience. We contribute to the ongoing efforts in developing a general framework for mapping and predicting distance to tipping points of ecological and potentially other systems.

Original languageEnglish
Pages (from-to)1524-1536
Number of pages13
JournalNature Ecology and Evolution
Issue number10
StatePublished - Oct 2022

Bibliographical note

Funding Information:
W.Z. acknowledges support from the National Natural Science Foundation of China (grant nos. 61702200, 61473183, U1509211 and 61627810) and National Key R&D Program of China grant no. 2017YFE0128500. J.G. acknowledges the support of the USA National Science Foundation under Grant No. 2047488, and the Rensselaer-IBM AI Research Collaboration.. Q.W. was partially supported by the US National Science Foundation (grant no. 1761950 and 2125326). We sincerely thank J. Bascompte for early discussion and detailed suggestions that helped improve our paper.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Limited.


Dive into the research topics of 'Estimating comparable distances to tipping points across mutualistic systems by scaled recovery rates'. Together they form a unique fingerprint.

Cite this