Hidden inbreeding, also called
unconscious inbreeding, occurs when a
child is produced by a man and a woman
unaware that they are already
related to each other. While technically
we are all related, this refers to a
relationship close enough to have potential
detrimental effects for the
offspring.
One example of this is the inbreeding that occurred from the seventeenth through twentieth centuries on Martha's Vineyard, which resulted in a large deaf population on the island. The Vineyard community was very isolated for most of that time, and as a result the only taboo marriages were between aunts and nephews, uncles and nieces, and siblings - first cousins and beyond were fair game. By the 1970s, members of one clan insisted they were unrelated despite sharing a last name, yet those people could be traced back to the same individual from the original group of settlers on the island.
Source: Groce, Nora Ellen. Everyone Here Spoke Sign Language. Page 44.