Hi, this is my first message here. I've been playing this game recently and I just have a quick question.
Does anybody know the minimum set of fish that will yield every possible one in just one generation?

Welcome to the forums!

I suppose it's theoretically possible to produce a set of fish that could do what you're asking, but I don't know of anyone in this community that has attempted to determine what those fish would be. That set of fish would have to contain fish from several iterations of breeding (i.e. generations), or as they are referred to in the game: common, unusual, and rare fish. Most people who opt to be structured in their breeding (as opposed to relying on random breeding and luck) have found that there are a handful of fishies that will allow you to breed all other species, but in multiple generations, rather than one.

Twinfin Shark, Twinfin Spotanus, Silky Shark, Silky Spotanus.

I throw the greenfins in with the ones above, and then add all three fins of the beta ... twin, silky and green. Only three breedings to any fish using those. But to do it all in one breeding? That's beyond me. The way I breed the final three fish are breed from the third generation, so there wouldn't be any way to do it in one. ... It would be interesting, though, if there were some that could breed a whole batch with one crossing ... but you'd still have to find a way to get those.

I suspect that the minimum set of fish that will produce all 441 possible species in one generation is more than will fit in a game.

But I think adding Hornets and Arrowfish will reduce the number of generations needed.

After that I would add Finless, Wasps, Quicksilvers and Goldsharks.

I think that will reduce the number of generations needed to 2. If I did the chart right, adding in Speckled, Canary, Leaffish, and Fire-arrows is all that remains to be needed.

So that is:

fins:
Silky
Twinfin
Greenfin
Hornet
Finless
Wasp
Speckled
Canary

bodies:
Shark
Spotanus
Beta
Arrowfish
Quicksilver
Goldshark
Leaffish
Fire-Arrow

if you make all combinations of these, that produces 64 fish. There is probably some redundancy, but I haven't worked out which combos can be removed.

HTH.