Hi Ludi, I noticed no one had answered you yet, so as an amateur mycologist I thought I'd give it a shot.
Fungi do need lots of
water, but most edible mushrooms will not be very happy in a constantly soggy or flooded environment. Other sorts of microbes like bacteria, yeasts, and molds will thrive better in those conditions and would quickly out-compete your intended species. However, I don't think all hope is lost, as long as you're willing to experiment and improvise.
There are a couple ways I can see mushrooms being used in some capacity within an aquaponics system. Without knowing size and location specifications, these are my immediate thoughts. I might come up with some more later:
-As a living filter of some sort.
Paul Stamets has written a good bit about mushroom mycelium's "mycofiltration" properties, particularly in his book "Mycelium Running" (which is a good read for anyone interested in incorporating mushrooms into
permaculture landscapes). Mycelium-infused substrates like
straw or wood chips are so tightly-knit that silt and minerals, as well as pathogens, are filtered out while water is able to trickle through. This has been shown to lower the fecal coliform levels 100-fold in water downstream from farm animal waste runoff. I think the hardship you might find here is keeping the substrate from becoming too wet. In the above circumstances, the mushroom patch was large and intercepted the runoff of rainwater between the animal areas and the nearby bay. It did not have water constantly running through it, so air could easily permeate the substrate. This could possibly be simulated in a flood and drain system, but I honestly have no idea. If you do decide to try this, I recommend growing oyster mushrooms (
Pleurotus ostreatus) on pasteurized straw. Oysters are easy to grow: very hardy, fast growers, and they'll eat just about any plant product. If it ends up working well, you may want to move on to the garden giant (
Stropharia rugoso annulata), which grows best outside on hardwood chips, probably makes a better filter, and is tastier than oysters.
-As a source of fish food. Stamets has noted that garden giant specimens that grow past prime eating sizes eventually become infested with
maggots (yuck, right?). He would often pick these and toss them into his trout
pond, where the drowning maggots would struggle free from the mushroom, only to be promptly eaten by the fish. These fish quickly learned that ramming their heads into the mushroom would dislodge the maggots more quickly, so tossing a couple of these into the
pond would inevitably create quite a splashfest!
That's actually all I can think of off the top of my head. I thought I might have more ideas while writing this, but the main issue is that mushrooms don't like being
wet, just moist. I'm not sure an aquaponics system would be the right place for controlled mushroom growth, but I'll keep pondering it and let you know.