Aquaponics couples aquaculture and hydroponics into one closed loop: fish waste and gill excretion release ammonia into the water; a biofilter's bacteria oxidize it in two steps (nitrification); plants absorb the resulting nitrate as fertilizer and the cleaned water recirculates back to the fish.
Fish tank → NH₃ (ammonia, from waste + respiration)
Biofilter: NH₃ --Nitrosomonas--> NO₂⁻ --Nitrobacter--> NO₃⁻
Grow bed: NO₃⁻ + roots → plant biomass, water clarified
Clarified water → back to fish tank (closed loop, ~90% less water than soil farming)
d[NH₃]/dt = feed·F − k₁·B·[NH₃]
d[NO₂⁻]/dt = k₁·B·[NH₃] − k₂·B·[NO₂⁻]
d[NO₃⁻]/dt = k₂·B·[NO₂⁻] − k₃·P·[NO₃⁻]/([NO₃⁻]+Km)
B = biofilter maturity, P = plant density, Km = uptake saturation constant
- Feed rate — more food means more fish waste and respired ammonia entering the water.
- Bacteria colony maturity — a young biofilm nitrifies slowly; a mature one converts ammonia to nitrite to nitrate fast (k₁, k₂ above).
- Plant density — more roots pull nitrate out of the water faster (k₃ above), the step that actually closes the loop.
- Water flow rate — too slow starves the biofilter of oxygen and substrate; too fast cuts the bacteria's contact time with the water, both hurting conversion efficiency.
If ammonia builds up faster than the biofilter can process it — heavy feeding on an immature colony, or a sparse grow bed leaving nitrate to accumulate — fish health drops. Balance all four controls to keep the system in equilibrium.