Evidence of glassy phases in large randomly interacting ecosystems

By Ada Altieri (U. Paris Cité)
Abstract: 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 perturba-tions. This feature, also known in physics as marginal stability, is often the consequence of the complex underlying interaction network, which can induce large-scale collective dynamics, and therefore critical behaviors.
In this talk, I will focus on a benchmark in theoretical ecology, the disordered Lotka-Volterra model, with random interactions and finite demographic noise. Through advanced disordered system techniques, I will unveil a very rich structure in the organization of the equilibria and relate critical features and slow relaxation dynamics to the appearance of disordered glassy-like phases. Finally, I will discuss the generalization of these results to strongly competitive interactions as well as to non-logistic growth functions in the dynamics of the species abundances, which turn out to be of great interest for modeling intra-specific mutualistic effects.
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