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I'm new to all this myself but found the info link on the main page here helpful. http://theaquaponicsource.com/rules-of-thumb/
Some other info I collected off of one of the threads for catfish. "1 (adult) catfish per 20 gallons of grow bed with 10 gallons of fish tank per fish."
This figure seems a little low to me since I'm as interested in eating the fish as I am the produce.
@Diana See Aquaponic Gardening by Sylvia Bernstein p.216 1:1 ratio by volume Grow bed to fish tank to start
I'm the one who likes to recommend lots of fish tank and filtration for the channel catfish. (They can grow quite large quite fast and if you overstock them, you risk having disease outbreaks.)
If you are going to simply pump from your fish tank up to a grow bed and let the water drain back to the fish tank, the water level in the fish tank will fluctuate and you can only really do the 1:1 ratio to keep that fluctuation from getting too extreme if you are going to flood and drain your grow bed.
So for a 20 gallon fish tank you won't be able to do more than about 20 gallons of grow bed if doing the simple system.
If you also incorporate a sump tank, you could have more grow bed (basically dependent on how big your sump tank is to handle the flood and drain and how much space you want to devote to it.) With only 20 gallons of fish tank you really can't grow out edible fish so you just need to make sure not to stock too many fish or make sure the amount of fish you stock is appropriate to the amount of filtration.
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