The link between Desmond and his ancestral assassins, Altaïr and Ezio, was thought to be that of a bloodline. Guess we were working with only half a script? Speaking to Kotaku, script writer Darby McDevitt (Assassin's Creed: Revelations) revealed that Altaïr and Ezio don't share a family link. How in the world is that possible when we thought the Animus pulls from one's subconscious mind?
Whether or not this is a significant arc to the overall plot of the series, we don't know, but it's always interesting to learn something new about your favorite video game characters.