# Average number of ancestors [duplicate]

Every individual has two parents, four grand-parents and so on. This would yield an astronomical number of ancestors even after a small number of generations, e.g. 235 ∼ 34 billions. The solution to this paradox is called pedigree collapse which takes into account that some of the ancestors in the binary Ahnentafel are identical, i.e. one and the same subject. This leads to a decrease of the number of ancestors of a given generation.

Are there any empirical statistics about the average number of ancestors of generation -1, -2, -3, etc. in a given population.

The average number of parents is exactly 2, the average number of grand-parents is slightly less than 4, and so on.

Which mathematical model might yield sensible numbers? Does anyone know a reference?

• We've talked about pedigree collapse here genealogy.stackexchange.com/q/3105/104
– user104
Commented Jun 11, 2014 at 9:02
• Would you be able to edit your Question to indicate whether you are hoping for global figures, or for a particular country, or ... ?
– PolyGeo
Commented Jun 11, 2014 at 10:03
• I have a feeling that somewhere, some years ago, I saw an article attempting to analyse (though perhaps not quantify) the amount of pedigree collapse. It may have been an article in the (UK) Society of Genealogists' Journal. Does this ring any bells with anyone? Commented Jun 11, 2014 at 14:23
• Google does not immediately provide an obvious model but I suspect it might help if I knew what words to search for... However, Andrew Millard's article on this link community.dur.ac.uk/a.r.millard/genealogy/EdwardIIIDescent.php - while it aims at the inverse problem as it were - seems to provide a few names, phrases and concepts to search for. Commented Jun 11, 2014 at 14:33
• @AdrianB: nope re SoG, and the search facilities on their site are woeful.
– user104
Commented Jun 11, 2014 at 14:40