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

Scientific Reports
Lewi Stone

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, ...Continue Reading

References

May 6, 1976·Nature·M E Gilpin, T J Case
Aug 18, 1972·Nature·R M May
Mar 5, 2004·Physical Review Letters·Marc TimmeTheo Geisel
Aug 25, 2004·Physical Review Letters·Viktor K Jirsa, Mingzhou Ding
Sep 29, 2005·PLoS Biology·Robert J PrillAndre Levchenko
Jan 21, 2011·Nature·Andrew G Haldane, Robert M May
Feb 22, 2012·Nature·Stefano Allesina, Si Tang
Jul 26, 2014·Science·Rudolf P RohrJordi Bascompte
Mar 15, 2015·Physical Review Letters·Johnatan AljadeffTatyana Sharpee
Jul 23, 2015·Nature Communications·Stefano AllesinaAmos Maritan
Nov 7, 2015·Science·Katharine Z CoyteKevin R Foster
Nov 7, 2015·Journal of Theoretical Biology·J-F ArnoldiB Haegeman
Feb 25, 2017·Nature Communications·Jacopo GrilliAmos Maritan

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Citations

May 13, 2020·Journal of the Royal Society, Interface·Susanne PetterssonMartin Nilsson Jacobi
Jul 1, 2020·PLoS Computational Biology·Samuel R Bray, Bo Wang
Feb 26, 2020·Nature Ecology & Evolution·Jimmy J Qian, Erol Akçay
May 29, 2020·Nature Communications·Lewi Stone
Nov 29, 2020·Nature Communications·Joseph W Baron, Tobias Galla
Nov 19, 2020·Ecology Letters·Hsi-Cheng HoSamraat Pawar
Jan 21, 2021·Physical Review. E·Susanne PetterssonMartin Nilsson Jacobi
Feb 25, 2021·Nature Communications·Homayoun HamedmoghadamLewi Stone
Mar 20, 2021·Physical Review. E·S Belga FedeliJ R Ipsen
May 5, 2021·Nature Ecology & Evolution·Thorsten WiegandAndreas Huth
Jun 26, 2021·Physical Review Letters·Pierre A Haas, Raymond E Goldstein
Oct 21, 2021·PloS One·Jie Li, Matteo Convertino

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Software Mentioned

RMT
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