11:40-12:00 Thursday, 8 May 2025
Abstract
I will present a study on the equilibrium phases of the generalized Lotka-Volterra model with a sparse species interaction network characterized by symmetric and normally distributed interactions. While real ecosystems are inherently non-equilibrium systems, understanding their long-term behaviour often involves analyzing effective equilibrium states. In this spirit, we study the stationary distribution reached by the stochastic dynamics of the system, which we exploit to compute species abundance marginals using cavity equations. Our findings reveal a rich and non-trivial phenomenology, significantly deviating from the predictions of fully connected models. Consistently with real ecosystems data, we observe strong deviations from Gaussianity in species abundance distributions even within a single equilibrium phase, at high levels of interaction disorder. Furthermore, at zero interaction disorder, we identify a topological multiple equilibria phase driven by the interplay between network sparsity and high competition. These results offer new insights into the complex dynamics of ecosystems, emphasizing the importance of incorporating sparse interactions into ecological models to better capture real-world phenomena.