Genders <= 2? Why?

By focusing on the number of individuals (genders) required for reproduction we can distinguish species into three classes: those that require one individual (self-reproducers), those that require two (pair reproducers), and those that require three or more (group reproducers). The question is thus: are there group reproducer species? why?

We usually refer to the first class as asexuals, the second as sexuals, and it is a major puzzle of evolutionary biology to account for the existence of the latter^ D, WP^. Like the bee that fluttered in the face of our best aerodynamic theories, sexuals mate impudently in the face of our best evolutionary theories.

But sexuals exist. Everywhere, in fact, at our order of magnitude. So we can’t just sweep pair reproducers aside and carry on our happy, simple theorizing of a self-reproducing world.

Asking the group reproducer question, on the other hand, I’ve been surprised by people to whom it comes as a revelation that the class is obviously empty. I don’t think it is. Obvious, that is. Life on earth does some pretty fucked up stuff, natural gangbanging doesn’t strike me as particularly eccentric. Asimov describes a group reproducer species in great detail in The God Themselves and neither the author nor I (before) ever thought the point merited any explanation.

And if there are no group reproducers (or precious few) their non-existence (or extreme dearth) is as much a fact in need of explanation as their existence (or abundance).