Hydroponics, to put it very simply, is soil-free agriculture. Plants are grown in either a support medium such as expanded clay or floating trays. Nutrients are supplied via water directly to the plants' roots through a drip or flood type irrigation system. The advantages of this lies in nearly weed and disease free growing conditions and crop density. An acre of land growing corn could be converted to an intense hydroponic system, exponentially increasing food production and efficiency.
With hydroponics however, difficulties arise in the procurement of fertilizer mixes for the plants. In addition, being an open cycle, nutrients must be continually brought in from outside sources, leading to dependence and a lack of self-sufficiency and independence.
The solution to this problem is the combination of aquaculture (artificial raising of fish, mollusc, or crustacean species, generally) with hydroponics into a system that directly mimics nature - Aquaponics
I'll use a basic example to illustrate the concept. Several tanks are set-up, each containing a colony of fish species, which may include tilapia, catfish, carp, freshwater muscles, and crawfish. The fish are fed a plant-protein based diet, which can theoretically be grown on site. I'll explain this later.
Water from the tanks is pumped into long grow tanks, each with floating trays of crops. Beneficial bacteria living throughout the system convert waste nitrites into nitrates which nourish the plants. These crops can include leafy crops, cucumbers, melons, and tomatoes. With a very dense stocking of fish, virtually any type of crop could be grown.
The water is filtered by the plants and returned back to the fish tanks, completing the system.
Now back to the fish diet. Technically it can be obtained very easily from an outside source, but this would make it an open system. There are several solutions to this problem. One would be to set-up growing tanks for algae or plant-based foods, which could then be condensed and fed to the fish.
I imagine combining this system with vertical farming could potentially lead to a dramatic change in the way we get our food. In addition, principles discovered from Earth-based hydroponics systems could be invaluable in the search for methods of sustaining long-term space missions requiring production of food.
(The previous images are copyright Nelson and Pade, Inc. For more information, they've got a great website that explains pretty much anything you need to know about aquaponics - www.aquaponics.com.
Also check out www.backyardaquaponics.com.)