The feasibility and stability of large complex biological networks: A random matrix approach

Stone, L 2018, 'The feasibility and stability of large complex biological networks: A random matrix approach', Scientific Reports, vol. 8, no. 1, pp. 1-12.


Document type: Journal Article
Collection: Journal Articles

Title The feasibility and stability of large complex biological networks: A random matrix approach
Author(s) Stone, L
Year 2018
Journal name Scientific Reports
Volume number 8
Issue number 1
Start page 1
End page 12
Total pages 12
Publisher Nature
Abstract In the 70's, Robert May demonstrated that complexity creates instability in generic models of ecological networks having random interaction matrices A. Similar random matrix models have since been applied in many disciplines. Central to assessing stability is the "circular law" since it describes the eigenvalue distribution for an important class of random matrices A. However, despite widespread adoption, the "circular law" does not apply for ecological systems in which density-dependence operates (i.e., where a species growth is determined by its density). Instead one needs to study the far more complicated eigenvalue distribution of the community matrix S = DA, where D is a diagonal matrix of population equilibrium values. Here we obtain this eigenvalue distribution. We show that if the random matrix A is locally stable, the community matrix S = DA will also be locally stable, providing the system is feasible (i.e., all species have positive equilibria D > 0). This helps explain why, unusually, nearly all feasible systems studied here are locally stable. Large complex systems may thus be even more fragile than May predicted, given the difficulty of assembling a feasible system. It was also found that the degree of stability, or resilience of a system, depended on the minimum equilibrium population.
Subject Applied Mathematics not elsewhere classified
Engineering Systems Design
Keyword(s) mutualistic networks
ecosystems
competition
perturbations
architecture
communities
DOI - identifier 10.1038/s41598-018-26486-2
Copyright notice © The Author(s) 2018 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License
ISSN 2045-2322
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