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SUMMARY:Evidence of glassy phases in large interacting ecosystems with dem
 ographic noise - Ada Altieri (Laboratoire Matière et Systèmes Complexes\
 , Paris)
DTSTART:20201201T130000Z
DTEND:20201201T140000Z
UID:TALK153571@talks.cam.ac.uk
CONTACT:Camille Scalliet
DESCRIPTION:Zoom link: https://maths-cam-ac-uk.zoom.us/j/94018037756\n\nMa
 ny complex systems in Nature\, from metabolic networks to ecosystems\, app
 ear to be poised at the edge of stability\, hence displaying enormous resp
 onses to external perturbations. This feature\, also known in physics as m
 arginal stability\, is often the consequence of the complexity of the unde
 rlying interaction network\, which can induce large-scale collective dynam
 ics and therefore critical behaviour. \n\nIn this seminar\, I will present
  the problem of ecological complexity by focussing on a reference model in
  theoretical ecology\, the high-dimensional Lotka-Volterra model with rand
 om symmetric interactions and finite demographic noise [1]. By using techn
 iques rooted in mean-field spin-glass theory\, I will show how to obtain a
  complete characterisation of the phase diagrams. Notably\, I will relate 
 emerging collective behaviours and slow relaxation dynamics to the emergen
 ce of different disordered phases akin to those taking place in glassy sys
 tems  [2\,3]. I will describe in particular:  i) a multiple equilibria pha
 se\, which can be proven to be associated with an exponential number of st
 able equilibria in the system size\; ii) a marginally stable amorphous pha
 se (denoted as Gardner phase) as characterised by a hierarchical structure
  of these equilibria [1]. Finally\, I will discuss the extension of our re
 sults: i) to the case of weakly asymmetric interactions\; ii) by consideri
 ng a higher-order potential in the dynamics of the species abundances [4]\
 , which turns out to be beneficial to model cooperative effects in ecologi
 cal and biological communities. \n\n\n[1] A. Altieri\, F. Roy\, C. Cammaro
 ta\, G. Biroli\, Properties of equilibria and glassy phases of the random 
 Lotka-Volterra model with demographic noise\, arXiv:2009.10565  (2020).\n\
 n[2] P. Charbonneau\, J. Kurchan\, G. Parisi\, P. Urbani\, Fractal free en
 ergy landscapes in structural glasses\, Nature Communications 5\, 3725 (20
 14).\n\n[3] A. Altieri\, Jamming and Glass Transitions: In Mean-Field Theo
 ry and Beyond\, Springer Nature (2019).\n\n[4] A. Altieri\, G. Biroli\, Th
 e effect of species cooperation in large interacting ecosystems\, in prepa
 ration.
LOCATION:via zoom\, meeting ID 940-1803-7756
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