So the lone trumpet snail that appeared in my aquarium last week has been hard at work. Today I noticed some small white specks in the gravel that, upon closer inspection, were oddly... snail-shaped. Now, after a few minutes of examining the tank, I count over 50 small snails crawling around on the gravel. There's no turning back now.
There's really no good way to deal with a snail infestation in an aquarium. The only way to really get rid of them is to boil everything in the tank for awhile. This, of course, kills the fish and the plants as well as the snails. There are loaches and various other fish that will eat small snails, but they are all much too large for a 10 gallon aquarium. The only real option is population control by periodically removing the snails from the tank and giving them a new home in the toilet. So it looks like from now on my weekly tank maintenance is going to be that much more of a pain in the arse.
Addendum: There's also some kind of small white worm, several of them, crawling around on the glass. They're only a few millimeters in length... no idea what they are or where they came from.

