An aquaponics system imitates the natural balance of nutrients that can be found in nature, meaning that you don't have to use fertilizer. In traditional agriculture, crops get their nutrients from the soil they're grown in. Infertile soil from poor conditions or overfarming can deprive plants of the nutrients they need to grow, meaning many large-scale farms have to resort to artifical fertilizers, pesticides, and other chemicals. In an aquaponics system, your plants are fertilized via the fish waste found in the water, and the fish's home is kept healthy by your hungry plants.
However, sometimes additional nutrients are needed if they aren't being produced by your fish, like potassium or phosphorous. You can keep an eye on these nutrient levels through frequent water testing, and monitoring your plants' health. Poor plant growth, or paling/yellowing leaves may be a sign of nitrogen deficiency. This is easily solved by simply adding more fish into your system. Potassium deficiency can result in brown or curling leaves, and is solved by spraying potassium directly onto the leaves of your plants, or by adding over-ripe banana peels or kelp meal concentrate into the biofilter. Stunted growth, or a purple/reddish color could mean that your plants are low in phosphorous, and it may be necessary to add phosphate into your system.
