When and how did the convention of clapping to show appreciation sharted?

The custom of applauding may be as old and as widespread as humanity, and the variety of its forms is limited only by the capacity for devising means of making a noise (e.g., stomping of feet or rapping of fists or hands on a table). Within each culture, however, it is usually subject to conventions.

The ancient Romans had a set ritual of applause for public performances, expressing degrees of approval: snapping the finger and thumb, clapping with the flat or hollow palm, waving the flap of the toga, for which the emperor Aurelian substituted handkerchiefs that he had distributed to the Roman people. In Roman theatre, at the close of the play, the chief actor called out "Valete et plaudite!", and the audience, guided by an unofficial choregus, chanted their applause antiphonally. This was often organized and paid for.

http://en.wikipedia.org/wiki/Applause#History

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I think maybe back during the Greek and Roman times. There have been so many different ways of making noise to show appreciation. Some use to snap fingers, smack lips. Different cultures can even find clapping as BOOING