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The hybrids were a humanoid species directly descended from those Isu who chose to interbreed with their human workforce. As a result of this interbreeding, hybrids were born without the artifical neurotransmitters that forced humanity's subservience to their Piece of Eden-wielding Isu overlords.
Over the subsequent generations, the hybrids and their offspring were assimilated into the general human population. Consequently, the concentration of Isu DNA in their own genome became diluted with each generation. Certain bloodlines directly descended from the hybrids, however, possessed fractionally higher levels of Isu DNA in their genome—resting somewhere between the 0.0002% of normal humans, to the 5 or 6% of Sages—which allowed their scions to naturally access Eagle Vision, to more fully interact with Pieces of Eden, much like their ancestors had, and in the case of Sages meant that they would serve as a reincarnation of Aita. 
Also as shown by Pythagoras, Kassandra and Deimos hybrids with high concentrations of Isu DNA were stronger, faster, smarter and more durable than regular humans. This along with their access to the powers of pieces of Eden such as Kassandra's spear and Deimos sword, leads them to be seen as Demigods.