The k-core as a predictor of structural collapse in mutualistic ecosystems

Collapses of dynamical systems into irrecoverable states are observed in ecosystems, human societies, financial systems and network infrastructures. Despite their widespread occurrence and impact, these events remain largely unpredictable. In searching for the causes for collapse and instability, th...

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Bibliographic Details
Published in:arXiv.org 2018-10
Main Authors: Morone, Flaviano, Gino Del Ferraro, Makse, Hernán A
Format: Article
Language:English
Subjects:
Catastrophic events
Collapse
Ecosystems
Stability
Online Access:Get full text
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Summary:Collapses of dynamical systems into irrecoverable states are observed in ecosystems, human societies, financial systems and network infrastructures. Despite their widespread occurrence and impact, these events remain largely unpredictable. In searching for the causes for collapse and instability, theoretical investigations have so far been unable to determine quantitatively the influence of the structural features of the network formed by the interacting species. Here, we derive the condition for the stability of a mutualistic ecosystem as a constraint on the strength of the dynamical interactions between species and a topological invariant of the network: the k-core. Our solution predicts that when species located at the maximum k-core of the network go extinct, as a consequence of sufficiently weak interaction strengths, the system will reach the tipping point of its collapse. As a key variable involved in collapse phenomena, monitoring the k-core of the network may prove a powerful method to anticipate catastrophic events in the vast context that stretches from ecological and biological networks to finance.
ISSN:2331-8422
DOI:10.48550/arxiv.1811.00141