For every system, the nutrients in the water come from the fish feed, not the fish. The nutrient profile of the feed is manufactured explicitly for a select species or several species that have similar nutrient demands. In general, as long as you stick to recommended feeding rates, and use a nutrient complete fish feed, it will provide 10/13 of the essential nutrients for plants; limiting nutrients which need to be supplemented in various forms include Potassium, Calcium, and Iron.
Roughly 50% of all nutrients excreted by the fish are bound up in the fecal waste and are unavailable to the plant without further biological breakdown; this includes a large percentage of your calcium, potassium, iron, and phosphorus, If broken down and readded to your system you can reduce the number of additives needed.
For more information, check out our Feed Rate to Grow Space Calculator Blog, which goes into great detail on some of the basics on nutrient dynamics in aquaponics.