Ancestor Paradox

[Pharaoh Cat]

Having read the entire thread and being a mathematician, I'm not sure what the question is.  I'd be glad to help out, but I'm not sure what's being asked.  Let me try a couple explanations and see if I can avoid striking out.

I would say you hit a home run!  Thank you!

[keithpenrod]

Another way to think of it is like this: suppose that you have (for simplicity) a 1% chance of having one ancestor match up with another person's ancestor.  Then you have a 2% chance for one of your parents to match, since you have 2 parents, and 4% for grandparents, and so on.  Thus, 7 generations back you'd be guaranteed to match ancestors with someone else. 

Obviously, it's much more complicated than that, but I hope it helps illustrate the idea.  When you're listing 8 people (great grandparents) you have a small probability of matching one of those 8 with an ancestor from someone else's pedigree.  But when you're listing 1024, then your probability increases greatly. 

So, even if all of your 10th-great grandparents are all different from each other (which I doubt), there are 4,096 of them and if you list those 4,096 for all people in the world, you're bound to find several people who are listed in multiple people's pedigrees.

[xSilverPhinx]

Is it really so odd to think that people married their cousins much more often than they do now? That would mean a whole line of ancestors getting crossed.

[pytheas]

Part of the paradox can be resolved by considering the tribal nature of earlier generations.  There was probably a much higher incidence of what we would refer to today as "incest" during those times. So you would probably find, for example, that one level 10-great grandfather was the father of more than one of your level 9-great grandparents.  That would cut down on the required number of ancestors somewhat.  If you started with a bottleneck of one woman, for example, such as "Mitochondrial Eve" 200,000 years ago  (see article on her at  http://www.sciencedaily.com/releases/2010/08/100817122405.htm )  , all current humans might come from her.  This means that, of necessity, there was "incest" at probably multiple levels downstream from her (using "incest" not in a legal or moral sense).  That cuts down on the total number of required ancestors.  Am I making sense?

Cut even more with Adam Y patrilinear heritage which is more recent. although i knew the 60000 example I see it has been revised to 142000 years ago
http://en.wikipedia.org/wiki/Y-chromosomal_Adam

the ancestor paradox is that although we are all related, we dont seem to acknowledge it and feel that way...