  In this letter we study a reference model in theoretical ecology, the
disordered Lotka-Volterra model for ecological communities, in the presence of
finite demographic noise. Our theoretical analysis, which takes advantage of a
mapping to an equilibrium disordered system, proves that for sufficiently
heterogeneous interactions and low demographic noise the system displays a
multiple equilibria phase, which we fully characterize. In particular, we show
that in this phase the number of stable equilibria is exponential in the number
of species. Upon further decreasing the demographic noise, we unveil a
"Gardner" transition to a marginally stable phase, similar to that observed in
jamming of amorphous materials. We confirm and complement our analytical
results by numerical simulations. Furthermore, we extend their relevance by
showing that they hold for others interacting random dynamical systems, such as
the Random Replicant Model. Finally, we discuss their extension to the case of
asymmetric couplings.
