Bulletin of the American Physical Society
2023 APS March Meeting
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session PP08: V: Multicellular Phenomena II
9:00 AM–11:00 AM,
Tuesday, March 21, 2023
Room: Virtual Room 8
Sponsoring
Unit:
DBIO
Chair: Dominic Alfonso, National Energy Technology Laboratory
Abstract: PP08.00001 : Non-Gaussian random matrices predict the stability of feasible Lotka-Volterra communities*
9:00 AM–9:36 AM
Presenter:
Tobias Galla
(U Manchester)
Authors:
Tobias Galla
(U Manchester)
Joseph W Baron
(Ecole Normale Superieure, Paris)
Thomas Jun Jewell
(University of Oxford, UK)
Christopher Ryder
(The University of Manchester, UK)
Here, I will first discuss recent work in which we calculate the bulk and outlier eigenvalues of the most general Gaussian ensemble of random matrices, which does not systematically give preference to any species over another. I will then show how May’s approach can be used for feasible communities arising from the survivors in a dynamic Lotka-Volterra model with random interactions. The ensemble of interactions among extant species turns out to be non-Gaussian, even if the original interaction matrix among all species is Gaussian. I will then demonstrate that random-matrix universality does not apply, i.e. a Gaussian calculation fails to predict the leading eigenvalue correctly. I will show how tools from the theory of disordered systems can be used to account for non-Gaussian features of the interactions, and to obtain the spectra of the community matrix of survivors. The stability criteria from these eigenvalue spectra agree with those obtained from the Lotka-Volterra equations. Hence, we have demonstrated how May’s random-matrix approach can be used to characterise the stability of feasible equilibria. Feasibility is encoded in the higher-order non-Gaussian statistics of the community matrices arising from the survivors in Lotka-Volterra systems.
*We acknowledge funding from the Agencia Estatal de Investigación (AEI/MCI, Spain), Fondo Europeo de Desarrollo Regional (FEDER, UE), Project PACSS (RTI2018-093732-B-C21), and the Maria de Maeztu Program for Units of Excellence, MDM-2017-0711 funded by MCIN/AEI/10.13039/501100011033.
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