Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
ALLARDYCE
As described in historical dictionaries
Patronymica Britannica (1860)
ALLARDYCE.* " This family," says Nisbet, " got a charter from King William, of the lands of Albretlds in the sheriffdom of Kincardine, .... now Allardice, M'hich has ever since been the surname of the family."