Ada Altieri (Labo MSC, U. Paris Cité)
Evidence of glassy phases and aging dynamics in large interacting ecosystems
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 marginal stability condition is often the consequence of the complex underlying interaction network, which can induce large-scale collective dynamics, and therefore critical behavior.
I will address some crucial questions, which are grabbing attention in the last few years in theoretical ecology, by focusing on the generalised Lotka-Volterra model with many randomly interacting species and finite demographic noise. Using techniques rooted in spin glasses and random matrix theory, I will unveil a very rich structure in the organisation of the equilibria and relate slow relaxation of the correlation functions to aging dynamics and glassy-like behavior . I will then discuss possible extensions to non-logistic growth functions in the species abundance dynamics [2-3], which turn out to be of great interest to capture positive feedback mechanisms, notably in the case of weak and strong Allee effects .
 A. Altieri, F. Roy, C. Cammarota, G. Biroli, Phys. Rev. Lett. 126, 258301 (2021);
 A. Altieri, G. Biroli, SciPost Physics 12, 013 (2022);
 I. Hatton, O. Mazzarisi, A. Altieri & M. Smerlak, submitted (2022).