Also the clean water and healthy fish is a testament to the cycle. It's the same concept that I use to filter all of my ponds, plants to remove the fish poop and return clean water. I keep small fish in the outside ponds because I don't want birds taking off with larger fish and thus I don't have enough fish poop to feed a lot of plants. Carp are good producers of fertilizer as are koi and large goldfish, but they are also easy, attractive targets for herons and other fishing birds. Perhaps with screening you could keep the carp? I think most aquaponics use tilapia because they are better eating.
In my case, the fish are more like pets and not for food, and I have to give the plants additional fertilizer. I had a pond in Calif that was well balanced and I didn't have to fertilize the plants, but I did have to feed the fish. It was covered though and I had koi and Wakin goldfish in it - large poop producers. In my current largest pond, I don't have to feed the fish, the plants and insects produce enough food for the small guppies and mollies that I have in there and the 5 or 6 angel fish keep the fish from over producing. I do feed the plants though. It's one or the other, there is no absolutely perfect balance.