Appears in collection : 2022 - T1 - WS3 - Mathematical models in ecology and evolution

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 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.