I'm still trying to work out the algorithm on what fish are being fed and how much they drop. I've had two pearls drop, but not on a reliable basis where you could say "feed this fish this particular food and 20% of the time you get a pearl." There's a lot of fish in Aqua Pets to work through, and I'm trying several foods each day, which means it's kind of slow to get a real list. I'm not keeping everything (I generally get rid of shrimp and crabs) -- tonight I'm trying out an "organic morsels" tank.
I'm not sure if Bionic Panda's actually figuring a weighted "rareness" factor on the food because it seems as if rare fish and common fish drop similar amounts of coinage.
Here's the list so far of what food the Aqua Pets animals that I've fished up prefer: