[QUOTE="Evangelicalhumanist, post: 6883471, member: 47768]
On the other hand, basic mathematics tells me that every single one of us on this planet has a common ancester, father or mother, who lived 100,000 years ago. The relationship would be, of course, somewhat remote. I'm not quite sure what it means to be an 87th cousin, 43 times removed.
Not possible. Some lines of descent died out. My Y chromosome dies with me. But my nephew (my brother’s son) has two sons. I have a half brother who has a son. It’s entirely possible my paternal male cousin has a son. Now, if my nephews don’t have anymore sons, the line that was me, my father, my grandfather, great-grandfather, great-great-grandfather, etc. dies. If my grandfather had brothers who had sons who had sons, etc. then my Y-DNA continues.
The short answer is that it’s a branching tree. Some branches die, others become vines.[/QUOTE]
The mathematics may be a bit daunting, but your reasoning doesn't hold. Yes, it is true that about 20% of everybody from about 1,000 years ago is the ancestor of nobody alive today -- their line died out. (For now, let's just talk about people of European descent.)
But the converse is much more interesting for you -- if you happen to be alive today! The remaining 80% of those living 1,000 years ago are all the ancestors of everyone alive today.
Let's do some numbers. Assume that the average length of a "generation" is about 25 years. It was shorter a long time ago, a little longer now, but that doesn't matter. Now, it is also true that everybody has 2 parents, 4 grandparents, 8 great-grandparents, 16 great-greats...and so forth. Now in 1,000 years, we could have had probably about 250 generations. Now that means that if you could follow every genealogical line, you would have had 1,809,251,394,333,065,553,493,296,640,760,748,560,207,343,510,400,633,813,116,524,750,123,642,650,624 !!!!
Only the tiniest, tiniest fraction of that number has ever lived on this planet, and therefore it is absolutely certain that each and every one of us shares ancestry with everybody who was alive 1,000 years ago. So I can conclude (assuming that you are of European descent) that you and I are both related -- in several lines of descent -- to Holy Roman Emperor Charlemagne.[/QUOTE]
You’re not understanding haplogroups, and getting autosomal chromosomes confused with haplogroups. My Y haplogroup is T, which originated in the Middle East. So, I am not of European descent. Haplogroup T is extremely rare and not found in northern and Central Europe, except possibly by Mediterraneans or Middle Easterners who now live there. Charlemagne’s Y haplogroup was R1b. We do not descend from the same paternal line. But even if one of my ancient Middle Eastern ancestors produced a child with a European, the genetic admixture is impossible to trace back to any particular person. In every generation the relation are halved. My nephews and I share 12.5% (+/-) DNA. Go back to great grandparents and the percentage is less. Four times great grandparents, and the relationship is negligible.
Autosomal chromosomes are those that give us our characteristics. But over the course of only a few generations they become so “diluted” that without a paper trail it’s virtually impossible to trace ancestry more than 500 years or so. That’s why DNA testing companies make that disclaimer. It’s wishful thinking that so many people are related to or descended from Charlemagne, Chinggis Khan, Ragnar Loðbrök or any other famous person or royalty.