Are fiddler crabs social creatures?

I was given 2 fiddler crabs for my birthday, a male and a female, but the female died maybe about 2 months after I got them. I'm not entirely sure what killed her, but the male seems to be in perfect health, except that I often find him doing what appears to be some kind of mating dance where he very rigidly moves his larger claw back and forth for hours at a time. I'm wondering if he actually needs a new "mate" or not, or if he's perfectly happy to be alone in his tank.