The way the process works varies. Almost every system is designed differently. Different marine life is used. Hydroponics and the way hydro systems are put together is an art in and of itself. The goal is to process the nitrates from the fish poop using algae and feed it to the plants through the hydroponic system. Then the fresh water that has been scrubbed by the plants is fed back into the fish tank. If you have never grown in hydro, I would suggest starting small. Hydroponics requires constant monitoring for proper PH levels as well as monitoring the nutrient breakdown in the water. If one feels confident that they have that down, rigging for aquaponics might be the next step in mastering the many cultivation systems of the world.
Hydroponics, as well an aquaponics works best with smaller plants. We find plants that live longer than 12 weeks tend to develop nutrient deficiencies that are harder to manage in hydro. Also, hybrid strains tend to grow more robustly in these systems. The concept is more plants in a given surface area that have shorter life cycles works best.
To see one of these systems in action is amazing. In western Michigan, we saw two of these systems running. Horizon in Grand Rapids has a beautiful running system that has been running for almost a year and feeds a variety of indoor plants on display. Jumping on the Aquaponics bandwagon, Cultivation Station in Wyoming has just completed their Aquaponics display that is done on a much bigger scale and will be impressive once the starter plants take. If one is interested in starting one of these systems, a trip to western Michigan is a good start. I would also recommend picking up Aquaponic Gardening, by Sylvia Bernstein.
