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The k-core as a predictor of structural collapse in mutualistic ecosystems
Flaviano Morone1, Gino Del Ferraro1, Hernán A Makse1
1Levich Institute and Physics Department, City College of New York, New York, NY, USA.
Nature Physics
|December 5, 2025
Summary
Collapse in dynamical systems, from ecosystems to finance, is unpredictable. Monitoring the network
Area of Science:
- Ecology and complex systems science.
- Network theory and mathematical biology.
Background:
- Dynamical systems, including ecosystems, societies, and financial markets, frequently collapse into irrecoverable states.
- The causes of these collapses are poorly understood, particularly the role of network structure.
Purpose of the Study:
- To quantitatively determine the influence of network structural features on the stability and collapse of mutualistic ecosystems.
- To identify a predictable indicator for catastrophic events in complex systems.
Main Methods:
- Derivation of stability conditions for mutualistic ecosystems based on interaction strengths and network topology.
- Identification of the k-core as a critical topological invariant.
Main Results:
- Ecosystem stability is constrained by interaction strengths and the network's k-core.
- Extinction of species within the maximum k-core, due to weak interactions, predicts system collapse.
- The k-core serves as a key variable for monitoring collapse phenomena.
Conclusions:
- The k-core of a network is a crucial factor in predicting system collapse.
- Monitoring the k-core can provide an early warning system for catastrophic events across diverse fields.
- This framework offers a method to anticipate instability in ecological, financial, and other complex networks.
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