My interest outcomes from a revisor question, appointingthe continuous water flow as a false replicates system when applying probiotic supplemented diet.
I would agree that a trial such as this would require independent systems where the water would not mix. when the diet is added to the system some of the probiotic would mix in the water. therefore if your systems were not independent, there could be a mixing of your treatments. As for continuous flow, i do not how this would invalidate the replicates. This would only me the case if your continuous water flow was within a closed recirculating system. if it was continuous flow in a flow through system where the water was used only once and discarded don't see how it effects your replicates.
Researchers most frequently carry out experiments with probiotics in order to see if supplementation of feeds with probiotics increase growth of fish, or result in better feed conversion.
Since growth highly depends on water quality, one should think over how he makes bigger error: using different waters for the control and treatment, what itself may cause different growth, or uses the same RAS and has the risk that a minimal portion of the probiotics will come over from the treated tanks into the control tanks.
You are most lucky if having a trough flow system, where all tanks have the same water and their outflow does not come back.
If you work in RAS systems, I would suggest to use only one (the same) for the control and treatment tanks. I believe it makes smaller error than putting your fish in two independent RAS.
If searching for other parameters than growth, e.g. immune parameters, best is to use trough flow (with the necessary number of replications.