Predicting tipping points in mutualistic networks through dimension reduction

Junjie Jiang, Zi-Gang Huang, Thomas P Seager, Wei Lin, Celso Grebogi, Alan Hastings, Ying-Cheng Lai

Research output: Contribution to journalArticle

29 Citations (Scopus)
8 Downloads (Pure)

Abstract

Complex networked systems ranging from ecosystems and the climate to economic, social, and infrastructure systems can exhibit a tipping point (a "point of no return") at which a total collapse of the system occurs. To understand the dynamical mechanism of a tipping point and to predict its occurrence as a system parameter varies are of uttermost importance, tasks that are hindered by the often extremely high dimensionality of the underlying system. Using complex mutualistic networks in ecology as a prototype class of systems, we carry out a dimension reduction process to arrive at an effective 2D system with the two dynamical variables corresponding to the average pollinator and plant abundances. We show, using 59 empirical mutualistic networks extracted from real data, that our 2D model can accurately predict the occurrence of a tipping point, even in the presence of stochastic disturbances. We also find that, because of the lack of sufficient randomness in the structure of the real networks, weighted averaging is necessary in the dimension reduction process. Our reduced model can serve as a paradigm for understanding and predicting the tipping point dynamics in real world mutualistic networks for safeguarding pollinators, and the general principle can be extended to a broad range of disciplines to address the issues of resilience and sustainability.

Original languageEnglish
Pages (from-to)639-647
Number of pages9
JournalPNAS
Volume115
Issue number4
Early online date8 Jan 2018
DOIs
Publication statusPublished - Jan 2018

Keywords

  • Journal Article
  • tipping points
  • mutualistic networks
  • dimension reduction
  • complex systems
  • nonlinear dynamics

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  • Cite this

    Jiang, J., Huang, Z-G., Seager, T. P., Lin, W., Grebogi, C., Hastings, A., & Lai, Y-C. (2018). Predicting tipping points in mutualistic networks through dimension reduction. PNAS, 115(4), 639-647. https://doi.org/10.1073/pnas.1714958115