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

12 Citations (Scopus)
6 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

Fingerprint

Ecology
Climate
Ecosystem
Economics

Keywords

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

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

Predicting tipping points in mutualistic networks through dimension reduction. / Jiang, Junjie; Huang, Zi-Gang; Seager, Thomas P; Lin, Wei; Grebogi, Celso; Hastings, Alan; Lai, Ying-Cheng.

In: PNAS, Vol. 115, No. 4, 01.2018, p. 639-647.

Research output: Contribution to journalArticle

Jiang, J, Huang, Z-G, Seager, TP, Lin, W, Grebogi, C, Hastings, A & Lai, Y-C 2018, 'Predicting tipping points in mutualistic networks through dimension reduction' PNAS, vol. 115, no. 4, pp. 639-647. https://doi.org/10.1073/pnas.1714958115
Jiang, Junjie ; Huang, Zi-Gang ; Seager, Thomas P ; Lin, Wei ; Grebogi, Celso ; Hastings, Alan ; Lai, Ying-Cheng. / Predicting tipping points in mutualistic networks through dimension reduction. In: PNAS. 2018 ; Vol. 115, No. 4. pp. 639-647.
@article{7c88f85be4234e9f8a61ebb2a31f5f44,
title = "Predicting tipping points in mutualistic networks through dimension reduction",
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.",
keywords = "Journal Article, tipping points, mutualistic networks, dimension reduction, complex systems, nonlinear dynamics",
author = "Junjie Jiang and Zi-Gang Huang and Seager, {Thomas P} and Wei Lin and Celso Grebogi and Alan Hastings and Ying-Cheng Lai",
note = "This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1714958115/-/DCSupplemental.",
year = "2018",
month = "1",
doi = "10.1073/pnas.1714958115",
language = "English",
volume = "115",
pages = "639--647",
journal = "PNAS",
issn = "0027-8424",
publisher = "NATL ACAD SCIENCES",
number = "4",

}

TY - JOUR

T1 - Predicting tipping points in mutualistic networks through dimension reduction

AU - Jiang, Junjie

AU - Huang, Zi-Gang

AU - Seager, Thomas P

AU - Lin, Wei

AU - Grebogi, Celso

AU - Hastings, Alan

AU - Lai, Ying-Cheng

N1 - This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1714958115/-/DCSupplemental.

PY - 2018/1

Y1 - 2018/1

N2 - 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.

AB - 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.

KW - Journal Article

KW - tipping points

KW - mutualistic networks

KW - dimension reduction

KW - complex systems

KW - nonlinear dynamics

U2 - 10.1073/pnas.1714958115

DO - 10.1073/pnas.1714958115

M3 - Article

VL - 115

SP - 639

EP - 647

JO - PNAS

JF - PNAS

SN - 0027-8424

IS - 4

ER -