On the origins of clapping

This question has been on my mind for a while. I always get chills when I'm in a large group clapping. I find it such a strange behaviour. Whether I clap or not cannot be heard by the performers, because all they hear is the thunderous applause of the group, but I feel compelled to do so. Yet when you add everything up, the loudness gives the performers an indication of how much enjoyment they've provided to the group as a whole. The other thing I find funny is that we do not clap in synchrony: it is totally chaotic. Everyone has their own clapping rhythm, which I assume may change depending on the mood but probably falls within a personal bell curve. The other thing I wonder is who started this tradition. I've seen it in every ethnic group I have encountered while traveling, even remote tribes in the jungle with very little outside contacts. I seems as universal as music. And I suspect it shares common origins, which probably were invented independently multiple times. I have heard that even babies seem to inherently want to clap, in which case it might not need to be invented and could be an innate behavior. However clapping can be substituted with feet stumping, but the idea is the same, a loud noise, with a constant rythm. So does clapping precede music, are they even related? Why the hell do we do it?

Does anybody out there know of a good explanation or theory on the origins of clapping?