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Every so often, an individual is born who stands out a little from the rest of his people. This individual displays characteristics associated with a different kind of creature, such as a dragon, giant, celestial, or demon. Such a character is said to have a bloodline.
Bloodlines can exist for any number of reasons. Perhaps the character has an unusual ancestor, such as a dragon who took alternate form to live among humans or elves. The character might be a throwback to an earlier age, when all species were more closely related. The bloodline might be the result of unusual supernatural energies present during conception, pregnancy, or birth. It could also be an omen sent by the gods, part of an ancient prophecy or dire legend. The DM should decide the truth behind the bloodline, though the character need not know why he is different.