The Atavism of the Mazoku (魔族大隔世 Mazoku Dai Kakusei?, translated as Demon Race Great Atavism) is when atavism (a trait that recurs in a descendant after skipping generations and even resulting in a reversion to the primitive characteristics of a remote ancestor) occurs as a result of a demon deliberately rendering its genes a recessive trait until that code can express itself in a descendant strong enough to succeed it, effectively creating a demon sleeper agent. This, understandably, is an extreme example.
When Yusuke Urameshi had died for the first time, he was not strong enough for this recessive strain to express itself. Ironically, through his employment as Spirit Detective, he became strong enough for this demonic trait to 'accept' him and express itself after he died in his second battle against Shinobu Sensui.
As revealed by Ootake, leader of the Special Defense Force, it was forty-four generations prior to Yusuke's birth, about seven-hundred years ago, when Raizen had impregnated Yusuke's ancestral mother.