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Home page > Seminars > Séminaires théorie > Theory Club Tuesday, May 31st, 2022 (on Zoom). Tobias Galla on "Non-Gaussian random matrices predict the stability of feasible Lotka-Volterra communities"..

Theory Club Tuesday, May 31st, 2022 (on Zoom). Tobias Galla on "Non-Gaussian random matrices predict the stability of feasible Lotka-Volterra communities".

Unless otherwise stated, seminars and defences take place at 11:30 in room 454A of Condorcet building.

Speaker: Tobias Galla (IFISC Palma de Mallorca & University of Manchester)

Title: Non-Gaussian random matrices predict the stability of feasible Lotka-Volterra communities

Abstract: 50 years ago Robert May sparked the “diversity-stability debate” in ecology. Assuming that the so-called community matrix has random entries May’s analyses indicated that an increased number of species promotes instability. A decade-long debate has ensued, including a number of recent high-profile papers extending May’s work to matrices with more structure. Much of the work in this area relies on random matrix theory, i.e., techniques for the calculation of the eigenvalue spectrum of ensembles of random matrices. One major criticism of May’s approach is that it does not address the question how the ecological community arises from dynamics and whether the equilibrium is `feasible’ or not. 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. This ensemble of interactions turns out to be non-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 characterize the stability of feasible equilibria. Feasibility is encoded in the non-Gaussian statistics of the community matrices arising from the survivors in Lotka-Volterra systems, even if the interactions of the initial pool of species are Gaussian.

Contact : Équipe séminaires / Seminar team - Published on / Publié le 5 June 2022

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