IMHO, following the land-based aquaponics movement is a necessity. By expanding it, in coordination with biogas production, waste-handling and standard hydroponics, we can do more, with less.
The model I am trying to develop, at home-scale, is primarily to handle animal and food waste. A biogas digester will treat the wastes, producing an organic effluent, that is nutritious to plants and effectively free of pathogens. By 'effectively' I mean that, according to the documentation I've seen, the counts are so minuscule as to be undetectable, yet no lab will certify it is 100% free of pathogens. The simplest way around that is an additional treatment by storage (sealed and anaerobic for 30 days at comfortable temps, less at higher temps), or other means (chlorination, irradiation, etc.).
So far, I've described waste handling, and using the effluent in hydroponics. This is a simple process. To get Aquaponics, you have to include fish and re-utilize the fish wastes, as well... Since the hydroponics will only use 'X' amount of the effluent, the balance can be used, in less complicated hydroponics, to raise Duckweed.
Duckweed is a very adaptable waterborne plant. It has oil that can be pressed, for biodiesel, the resulting mass, when dried is high in protein. It is edible and used raw, in salad, etc.
Some fish are omnivorous. Tilapia is the typical aquaponics fish, though others are also used. My personal choice is the Rio Grand Cichlid/Texas 'Perch' (NOT a Perch, but actually a native, distant cousin to Tilapia).
Basically, for aquaponics, fish eat and piss and poop in their water, the water is used as hydroponic plant food.
For open-sea pens, multi-trophic aquaponics relies on the same concept, but it's more of an open loop, allowing the water to go pretty much wherever, bring in new nutrients and washing out some nutrients.
Each section of my concept works, and is in practice, in various places. I've just stacked the process, to use the nutrients in a more intensified manner.
Macroalgae-Kelp... Kelp farming and Kelp as fish food is already in use, as is feeding Kelp to Abalone, in floating cages. Abalone yielding Mother of Pearl, the occasional pearl, and some great meat, as well.
( http://videos.howstuffworks.com/discovery/28310-dirty-jobs-feeding-some-abalone-video.htm )
This would be floating above the fish pens.
Top pen would have a feeder species of fish, that consumes kelp. The middle pen (conjoined), holds the market fish, which are routinely fed a portion of the feeder-fish. The bottom pen holds a shellfish/bottom-feeder, such as prawn, crabs, or even lobster. Any dead fish, from the other pens, can be chunked and fed to the bottom pen.
Now, not quite done... As the poop trickles down, it is collected, from beneath the shellfish and pumped back up, as food for the kelp and additional food for the Abalone.
Summing up, by raising kelp, feeding it to Abalone and feeder-fish, the IMTA should produce a reliable source of Mother of Pearl and Abalone meat, a Marketable fish, and a shellfish. By having a number of these, at various stages of development, there is a steady supply to market.