2025/12/27 by Mattia Tarabolo, Tarabolo, Mattia, Luca Dall’Asta +3
Environmental Science · Social Sciences · Physics and Astronomy · #Ecosystem dynamics and resilience #Evolutionary Game Theory and Cooperation #Opinion Dynamics and Social Influence
paper · doi:10.48550/arxiv.2512.22563
Classical approaches to ecological stability rely on fully connected interaction models, yet real ecosystems are sparse and structured--a feature that qualitatively reshapes their collective dynamics. Here, we establish a thermodynamically exact stability phase diagram for generalized Lotka-Volterra dynamics on sparse random graphs, resolving how finite connectivity and interaction heterogeneity jointly govern ecosystem resilience. Using a small-coupling expansion of the dynamic cavity method, we derive an effective single-site stochastic process that is solvable via population dynamics. Our approach uncovers a topological phase transition--driven purely by the finite connectivity structure of the network--that leads to multi-stability. This instability is fundamentally distinct from the disorder-driven transitions induced by quenched randomness of the couplings. Our framework overcomes the considerable computational cost of direct simulations, offering a scalable and versatile analysis of stability, biodiversity, and alternative stable states in realistic, large-scale ecological ecosystems.