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Résumé |
An astonishing feature shared by many complex systems in Nature is that they
appear to be poised at the edge of stability, hence developing enormous
responses to very small perturbations. This unifying concept — known in physics
as marginal stability — regulates flow in metabolic networks as well as
critical behaviour in marine ecosystems and flocks of birds. In all these
cases, the complexity of the interaction network can be responsible for large-
scale collective dynamics.
In this seminar, I will present the problem of ecological complexity by
focusing on a reference model in theoretical ecology, the Lotka-Volterra model
with random interactions and finite demographic noise in the species pool.
Taking advantage of sophisticated analytical techniques based on the theory of
mean-field spin glasses, I will relate the emergence of critical collective
behaviours and slow relaxation dynamics in the Lotka-Volterra model to the
emergence of different disordered phases akin to ones appearing in glassy
systems [1].
I will thus discuss how our framework can provide an innovative approach to
unveil a direct mapping between large interacting ecosystems and glasses.
Remarkably, at low demographic noise or sufficiently heterogeneous
interactions, I will show the appearance of two different phases: i) a multiple
equilibria phase, which can be proven to be associated with an exponential
number of stable equilibria in the system size; ii) a marginally stable
amorphous phase (denoted as Gardner phase) characterized by a hierarchical
structure of the equilibria [2].
Finally, I will discuss the extension of these results: i) in the case of
weakly asymmetric interactions; ii) in the presence of a higher-order potential
in the dynamics of the species abundances, which turns out to be beneficial to
model cooperative Allee effects in ecological and biological communities [3].
In both cases, the structure of the equilibria appears to be strongly modified.
[1] P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, Fractal free energy
landscapes in structural glasses, Nature Communications 5, 3725 (2014).
[2] A. Altieri, F. Roy, C. Cammarota, G. Biroli, Properties of equilibria and
glassy phases of the random Lotka-Volterra model with demographic noise,
arXiv:2009.10565    (2020).
[3] A. Altieri, G. Biroli, The effect of species cooperation in large
interacting ecosystems, in preparation. |
