Disclosed is an aquaponics system with minimal outflows of waste. A stream of waste water from aquatic animals is mineralized in a waste conversion unit having algae and bacteria located on multiple horizontal plates through which the stream of waste water flows. The stream of waste leaving the waste conversion unit passes through troughs upon which plants are hydroponically grown by absorbing the mineralized waste. The water leaving the troughs is returned to the tank holding the aquatic animals and the cycle is repeated. The system may be augmented with an air source, a light source, and a nutrient source in the waste conversion unit to further enhance the breakdown of the animal waste. Additionally, floating trays may be utilized in the troughs to support a wide range of plants hydroponically grown in the troughs.