Predestination paradox

Suppose a man travels back in time and impregnates his great-great grandmother. The grandmother would thus give birth to one of the man's great grandparents, who would then give birth to his grandmother or father, who would then be able to give birth to one of the man's parents, and finally to the man himself. As a result, the man's very existence would be pre-determined by his time traveling adventure, and therein lies the paradox.

The Predesination paradox is very closely related to the Grandfather paradox. Please see that page for a more detailed analysis of possible genetic paradoxes posed by time travel.