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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. 2^{35} ∼ 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 http://genealogy.stackexchange.com/q/3105/104

– None – 2014-06-11T09:02:12.5202Would you be able to edit your Question to indicate whether you are hoping for global figures, or for a particular country, or ... ? – PolyGeo – 2014-06-11T10:03:46.603

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

mayhave been an article in the (UK) Society of Genealogists' Journal. Does this ring any bells with anyone? – AdrianB38 – 2014-06-11T14:23:15.667Google 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 http://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.

– AdrianB38 – 2014-06-11T14:33:09.923@AdrianB: nope re SoG, and the search facilities on their site are woeful. – None – 2014-06-11T14:40:12.437

I think some of the answers in the discussion by ColeValleyGirl start to address the question and like Verbeia answer mentions there are a lot of undefined criteria to the question. I guess my question is, what is the purpose of what you are trying to utilize the answer, is it for a guide or are you truly trying to look for a "Mathematical Model" that utilizes a series of predictor variables from a large set of predictor variables associated in genealogy. My guess DNA analysis would provide the simplest and most precise answer though more than a mathematical model. – CRSouser – 2014-11-12T21:08:10.470

@HansStricker Since my comment a month ago I found some good papers on this topic, I am working on a summation of those papers and journal articles but I do not believe a linear model

Y = B0 + B1(x1) + B2(X2)^Z1will be part of the answer or are you looking for that level of answer to this question as I could reference some of those but from what I have read no one claims to have a perfect model and use and results will vary? Can you clarify expectation? – CRSouser – 2014-12-12T16:34:30.357