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This question has been asked a lot of times before; do a search and you'll find lots of discussion on the subject, basically they go something like this:
Smaller fish have higher metabolic rate than larger fish (just like children), so smaller fish are fed smaller amounts of feed more regularly, but in terms of body weight they consume a much higher percentage than larger fish which have fewer but larger feeds each day.
e.g.
20 fry @ 20grams each, fed 10% of total body weight daily is 40grams per day, over 5-6 feeding sessions, so small quantities of nutrient are entering the system more frequently
a few moths later...
20 fish @ 500g, fed 1% of total body weight daily is 100grams per day, in one or maybe two feeding sessions, so more nutrient is actually entering the system, but in bursts, which a matured system can cope with.
[Exact quantities are dependent on species and food quality]
You might be thinking the example 40g of feed wont be enough to sustain plants, and you may be right, but there is still a lot of mineral nutrient in that 40g. If there isn't enough, it's usually only one or two minerals/elements missing, such as iron, magnesium or potassium (the things which growing plants use most of) which can be easily supplemented.
As for the supply of nitrates, smaller fish have higher respiratory rates than larger fish and are generally more active, darting here and there where big fish are generally lazy and loiter in one spot for most of the time, so the ammonia release from a swarm of active fingerlings for bacterial conversion into nitrites and nitrates is (almost) commensurate with slovenly larger fish (or close enough for our purposes anyway).
I know it's only a generalisation, but if you want to see how "close to the money" this assumption is, read through the forum for all the sad stories of people killing their fish through over-population and under-filtration, "because the fish are only small now". The waste produced by those small fish was enough to kill them, so there's plenty enough there to support some plants.
AP systems are frequently "over supplied" with nutrients as can be shown by the number of algal blooms and reports of nitrate readings 100+. There are more discussions on the maximum number of fish, unfortunately the discussions on the forum for the minimum number of fish are much fewer, but they are out there. Joel, Faye and the BYAP team et al. have demonstrated that just a couple of fish can support a few large GBs of healthy thriving plants.
Armed with a test kit and close observation of your plants and fish, you'll be able to tell if the quantity and activity of your fish, and the feeding regime are sufficient for your plants; if not, supplement (usually with something like Seasol (Australia, PowerFeed internationally?)) and/or specific elements such as chelated iron (for Fe deficiencies), potassium bicarbonate (for K deficiencies) etc.
Remember too, that at the start, your fish are only going to be small, but so too are your plants (unless you're replanting established plants into your new system). All through the life of your system, you'll be balancing the differing requirements of fish and plants, all growing at different rates; there is rarely a "steady state".
HTH.
(BTW: the example above was as used in a new system, 1000L FT, 2 x 500L GB, 20 trout yearlings initially of about 20g each; fish and plant growth were spectacular, as expected.)
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Backyard Aquaponics
