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Título: | Breakdown of Random-Matrix Universality in Persistent Lotka-Volterra Communities |
Autor: | Baron, Joseph W. CSIC ORCID; Jewell, Thomas Jun; Ryder, Christopher; Galla, Tobias CSIC ORCID | Palabras clave: | Quantitative Biology - Populations and Evolution Physics - Disordered Systems and Neural Networks Physics - Disordered Systems and Neural Networks |
Fecha de publicación: | 31-mar-2023 | Editor: | American Physical Society | Citación: | Physical Review Letters 130(13): 137401 (2023) | Resumen: | The eigenvalue spectrum of a random matrix often only depends on the first and second moments of its elements, but not on the specific distribution from which they are drawn. The validity of this universality principle is often assumed without proof in applications. In this Letter, we offer a pertinent counterexample in the context of the generalized Lotka-Volterra equations. Using dynamic mean-field theory, we derive the statistics of the interactions between species in an evolved ecological community. We then show that the full statistics of these interactions, beyond those of a Gaussian ensemble, are required to correctly predict the eigenvalue spectrum and therefore stability. Consequently, the universality principle fails in this system. We thus show that the eigenvalue spectra of random matrices can be used to deduce the stability of "feasible" ecological communities, but only if the emergent non-Gaussian statistics of the interactions between species are taken into account. | Descripción: | 27 pages, 7 figures | Versión del editor: | https://doi.org/10.1103/PhysRevLett.130.137401 | URI: | http://hdl.handle.net/10261/340139 | DOI: | 10.1103/PhysRevLett.130.137401 | ISSN: | 0031-9007 | E-ISSN: | 1079-7114 | Referencias: | Baron, Joseph W.; Jewell, Thomas Jun; Ryder, Christopher; Galla, Tobias; 2022; Non-Gaussian random matrices determine the stability of Lotka-Volterra communities [preprint]; arXiv; https://doi.org/10.48550/arXiv.2202.09140 |
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