In this talk, I will address some timely questions in theoretical ecology — from configurational landscape analysis to the long-standing diversity/stability debate up to the emergence of spatial patterns — by discussing the Generalized Random Lotka-Volterra model in the presence of demographic fluctuations and finite migration [1, 2]. 

Leveraging on disordered systems’ techniques, I will unveil a rich — eventually hierarchical  — organization of the equilibria and relate the slowing down of dynamical correlation functions to glassy-like features. Such a framework works surprisingly well also for integrating and interpreting datasets of patients suffering from Crohn's disease [3], for which a statistically rigorous description is still missing. 

Finally, I will discuss possible extensions to non-logistic growth functions [4] allowing us, on the one hand, to capture positive feedback mechanisms, and, on the other hand, to pinpoint novel phases as a smoking-gun signature of criticality.

References:

[1] A. Altieri, F. Roy, C. Cammarota, G. Biroli, Phys. Rev. Lett. 126, 258301 (2021);    

[2] G. Garcia Lorenzana, A. Altieri, Phys. Rev. E 105 (2022);

[3] J. Pasqualini, A. Altieri* & S. Suweis*, to be submitted to PRX Life (2023).

[4] A. Altieri, G. Biroli, SciPost Physics 12, 013 (2022).