Coexistence in the design of a series of two chemostats

We revisit the design problem of series of two chemostats, when more than one species are present for a single resource. We give precise conditions under which coexistence of two species is possible for such configurations. Furthermore, we show that for a broad class of growth functions, the optimal design cannot sustain coexistence of more than one species (either a new species is rejected or it invades the whole system).