Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Domaines cond-mat.stat-mech
Date Mercredi 18 Novembre 2020
Heure 14:30
Institut LPENS
Nom de l'orateur Altieri
Prenom de l'orateur Ada
Addresse email de l'orateur
Institution de l'orateur Ecole Normale Supérieure (LPENS)
Titre Properties of equilibria and glassy phases in large interacting ecosystems
Résumé An astonishing feature shared by many complex systems in Nature is that they appear to be poised at the edge of stability, hence developing enormous responses to very small perturbations. This unifying concept — known in physics as marginal stability — regulates flow in metabolic networks as well as critical behaviour in marine ecosystems and flocks of birds. In all these cases, the complexity of the interaction network can be responsible for large- scale collective dynamics. In this seminar, I will present the problem of ecological complexity by focusing on a reference model in theoretical ecology, the Lotka-Volterra model with random interactions and finite demographic noise in the species pool. Taking advantage of sophisticated analytical techniques based on the theory of mean-field spin glasses, I will relate the emergence of critical collective behaviours and slow relaxation dynamics in the Lotka-Volterra model to the emergence of different disordered phases akin to ones appearing in glassy systems [1]. I will thus discuss how our framework can provide an innovative approach to unveil a direct mapping between large interacting ecosystems and glasses. Remarkably, at low demographic noise or sufficiently heterogeneous interactions, I will show the appearance of two different phases: i) a multiple equilibria phase, which can be proven to be associated with an exponential number of stable equilibria in the system size; ii) a marginally stable amorphous phase (denoted as Gardner phase) characterized by a hierarchical structure of the equilibria [2]. Finally, I will discuss the extension of these results: i) in the case of weakly asymmetric interactions; ii) in the presence of a higher-order potential in the dynamics of the species abundances, which turns out to be beneficial to model cooperative Allee effects in ecological and biological communities [3]. In both cases, the structure of the equilibria appears to be strongly modified. [1] P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, Fractal free energy landscapes in structural glasses, Nature Communications 5, 3725 (2014). [2] A. Altieri, F. Roy, C. Cammarota, G. Biroli, Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise, arXiv:2009.10565    (2020). [3] A. Altieri, G. Biroli, The effect of species cooperation in large interacting ecosystems, in preparation.
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