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Evidence of glassy phases in large interacting ecosystems with demographic noise

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Many complex systems in Nature, from metabolic networks to ecosystems, appear to be poised at the edge of stability, hence displaying enormous responses to external perturbations. This feature, also known in physics as marginal stability, is often the consequence of the complexity of the underlying interaction network, which can induce large-scale collective dynamics and therefore critical behaviour.

In this seminar, I will present the problem of ecological complexity by focussing on a reference model in theoretical ecology, the high-dimensional Lotka-Volterra model with random symmetric interactions and finite demographic noise [1]. By using techniques rooted in mean-field spin-glass theory, I will show how to obtain a complete characterisation of the phase diagrams. Notably, I will relate emerging collective behaviours and slow relaxation dynamics to the emergence of different disordered phases akin to those taking place in glassy systems [2,3]. I will describe in particular: 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) as characterised by a hierarchical structure of these equilibria [1]. Finally, I will discuss the extension of our results: i) to the case of weakly asymmetric interactions; ii) by considering a higher-order potential in the dynamics of the species abundances [4], which turns out to be beneficial to model cooperative effects in ecological and biological communities.

[1] 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).

[2] P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, Fractal free energy landscapes in structural glasses, Nature Communications 5, 3725 (2014).

[3] A. Altieri, Jamming and Glass Transitions: In Mean-Field Theory and Beyond, Springer Nature (2019).

[4] A. Altieri, G. Biroli, The effect of species cooperation in large interacting ecosystems, in preparation.

This talk is part of the DAMTP Statistical Physics and Soft Matter Seminar series.

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