The answer to this question has two components. For each generation, there are the number of possible unique ancestors and the number of actual unique ancestors.

The number of possible ancestors doubles with every generation. You have two possible parents, four possible grandparents, eight possible 1st great-grandparents, sixteen possible 2nd great-grandparents, and so on.

Eventually, the number of potential ancestors in a generation exceeds the number of people alive on Earth in that generation. Therefore, it is not possible for every ancestor to be unique within a pedigree. The genealogist Robert C. Gunderson coined this as pedigree collapse.

For example, if someone’s parents are 2nd cousins, the number of possible 2nd great-grandparents is sixteen. However, the number of actual unique 2nd great-grandparents is only fourteen. In the pedigree chart below, the parent of the father’s father’s father and the parents of the mother’s mother’s father are the same couple.

A Classic Pedigree Chart

A Classic Pedigree Chart
(Click for Full Size)

A Chart with Pedigree Collapse

A Chart with Pedigree Collapse
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The amount of pedigree collapse seen in an individual pedigree depends on local marriage patterns. In a recent paper (Lachance et al 2009), the authors calculated the number of actual ancestors over ten generations using different degrees of relatedness. This table summarizes the results.

(click image for full size)

*Outbred -Your relatives themselves were not related.