  Complex ecosystems generally consist of a large number of different species
utilizing a large number of different resources. Several of their features
cannot be captured by models comprising just a few species and resources.
Recently, Tikhonov and Monasson have shown that a high-dimensional version of
MacArthur's resource competition model exhibits a phase transition from a
'vulnerable' to a 'shielded' phase in which the species collectively protect
themselves against an inhomogeneous resource influx from the outside. Here we
point out that this transition is more general and may be traced back to the
existence of non-negative solutions to large systems of random linear
equations. Employing Farkas' Lemma we map this problem to the properties of a
fractional volume in high dimensions which we determine using methods from the
statistical mechanics of disordered systems.
