Go off your tree

Does anybody out there know the origin of the phrase 'to go off your tree', a curiously antipodean phrase (Oz or NZ), meaning to become extremely irate about some matter or other.
Cheers mates

No, but to confuse matters further here in the UK we have two similar phrases - "to go off on one", meaning to lose one's temper and start ranting, and "to fall out of one's tree", humorously meaning to go mad or insane.

I wonder if there's a connection?