|A clever wren|
In human music, what they are doing is called hocketing. Here's a snappy definition from Oxford Music Online:
"(Lat. hoquetus, (h)oketus, (h)ochetus; from Fr. hoquet, Old Fr. hoquet, hoket, ocquet, etc., related to English hickock, hicket, hiccup, and similar onomatopoeic word formations in Celtic, Breton, Dutch etc., meaning bump, knock, shock, hitch, hiccup; attempts at etymological derivation from the Arabic must be regarded as unsuccessful).
The medieval term for a contrapuntal technique of manipulating silence as a precise mensural value in the 13th and 14th centuries. It occurs in a single voice or, most commonly, in two or more voices, which display the dovetailing of sounds and silences by means of the staggered arrangement of rests; a ‘mutual stop-and-go device’ (F.Ll. Harrison). Medieval authors.... mentioned the existence of this practice in popular music."
If you have a library card, you can access Oxford Music Online to discover more obfuscatory explanations and listen to some examples. And please desist from any attempts to prove etymological derivation from the Arabic - you will only be ridiculed.
Here's a clip of the Dirty Projectors demonstrating it very beautifully. Feel free to watch the whole video - I couldn't manage more than 10 seconds of the incoherent young man (there seems to be something about hocketing which encourages over-elaboration) and fast-forwarded to the singers, who start at 7.17 ish.
And here's Meredith Monk and Theo Bleckmann with a longer and more complex example.
Hocketing happens all over the world - the panpipes of the Southern Andes are played that way, although the panpipes of Ecuador (where the wrens were recorded (blimey, try saying that with your teeth out)) are not.
My initial research has not revealed the originator of the practice in humans and I suspect that is unknowable, as it is so old. I like to think that whoever it was, or they were, the inspiration came from listening to the birds.
Thanks for popping in - the salon is always open.