Marginal stability of the generalized random Lotka-Volterra model: logistic growth case and beyond

The incredible biodiversity that characterises natural ecosystems has attracted ecologists for a long time and, more recently, has started gathering interest also among theoretical physicists. From a statistical physics perspective, measuring all interactions in a diversity-rich ecosystem is extremely demanding and requires advanced inference techniques. Moreover, a well-established theory allowing us to capture different facets and explain data-driven outcomes is still missing, compounded by a series of general unresolved questions. 

In this talk, I will address some of these questions by discussing the generalised Lotka-Volterra model with many randomly interacting species and finite demographic noise. Using techniques rooted in spin-glass and random matrix theory, I will unveil a very rich structure in the organisation of the equilibria and relate slow the relaxation of the correlation functions to aging dynamics and glassy-like phases [1].

I will then discuss possible extensions to non-logistic growth in the dynamics of the species’ abundances [2-3]. Such developments turn out to be of great interest to capture positive feedback mechanisms, notably in the case of weak and strong Allee effects [2]. In the latter, I will pinpoint a phase transition belonging to a different universality class as well as a pseudo-gap in the distribution of the local curvatures of the effective potentials as a smoking-gun signature of marginal phases.

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

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

[3] I. Hatton, O. Mazzarisi, A. Altieri & M. Smerlak, submitted to Nature (2022).

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