Do you have any idea, why do people concentrate on aquaponics, not aeroponics? Is it just simply easier to implement, or better researched? Or is it actually better (higher yield, closed-loop system, ...)?
Sibling is correct. Aquaponics is a (partially) closed loop system where fish provide nitrogen for the roots, and the plants clean the water for the fish. You still need to feed the fish and sometimes balance the water pH.
I've experimented with both. Aeroponics is a LOT more complicated- you really need a high-pressure system if you want good results (fogponics with an ultrasonic humidifier doesn't work well enough). And a high pressure system has to worry about clogs in the nozzles, and it has more moving parts, and some of those parts need to be well sealed.... vs. hydroponics which can be as complicated as turning on and off an aquarium pump.