  The consensus that complexity begets stability in ecosystems was challenged
in the seventies, a result recently extended to ecologically-inspired networks.
The approaches assume the existence of a feasible equilibrium, i.e. with
positive abundances. However, this key assumption has not been tested. We
provide analytical results complemented by simulations which show that
equilibrium feasibility vanishes in species rich systems. This result leaves us
in the uncomfortable situation in which the existence of a feasible equilibrium
assumed in local stability criteria is far from granted. We extend our analyses
by changing interaction structure and intensity, and find that feasibility and
stability is warranted irrespective of species richness with weak interactions.
Interestingly, we find that the dynamical behaviour of ecologically inspired
architectures is very different and richer than that of unstructured systems.
Our results suggest that a general understanding of ecosystem dynamics requires
focusing on the interplay between interaction strength and network
architecture.
