Dynamics of complex communities with random, structured interactions

Microbial communities harbour (tens of) thousands of species, whose dynamics is shaped by their interactions. Random generalized Lotka-Volterra equations are used to explore how the collective behaviour of species abundances depends on statistical properties of such interactions. In real systems, however, interactions are not as featureless. In this talk, I will introduce interaction matrices that are the superposition of a random and a structured component, reflecting the knowledge of ecological functions. A macroscopic description generalizes the results obtained by Dynamical Mean Field Theory for fully disordered communities. Moreover, it allows us to understand how oscillations, induced by nonlinear relations between groups of species, can be suppressed by unknown sources of heterogeneity. Community stability is lost through two distinct routes: a collective phase transition, and a synchronous bifurcation of the macroscopic degrees of freedom. 



Presential in the seminar room, Zoom:

https://us06web.zoom.us/j/82363030254?pwd=HsgNaoSlMuyPkiHcPztLzrmb7Oty2I.1