are we all descended from Charlemagne?

Perhaps this has been discussed elsewhere on geni but:

From http://itotd.com/articles/226/most-recent-common-ancestors/

"Yale statistician Joseph Chang wrote a 1999 paper entitled “Recent Common Ancestors of All Present-Day Individuals.” If his many pages of equations, theorems, and proofs are to be believed—and even Chang says his figures probably don’t account for all the facts—we could have a most recent common ancestor who lived as recently as A.D. 1200. More recent research and computer simulations have pushed that date back to perhaps A.D. 300, but that’s still a far cry from 60,000 years ago.
...
Chang’s paper proves something much more surprising. According to his calculations, there was a date in the not-too-distant past at which all individuals were either ancestors of everyone alive today, or ancestors of no one alive today. This date varies depending on what portion of the population you look at, but for Europe, it would seem to be in the neighborhood of A.D. 800—the year Charlemagne, king of the Franks, became emperor of Rome. And because Charlemagne is known to be the ancestor of some people alive today, that must mean he was the ancestor of all people of European descent. Of course, we pick on Charlemagne because he’s so well known, but he doesn’t have any special status as a common ancestor. In reality, about 80% of the people living in Europe at Charlemagne’s time were also ancestors of everyone from the West".

and another online blog post at http://shakespearessister.blogspot.com/2008/03/get-along-kid-charle...
discusses how all north europeans are descended from Charlemagne and Mohammed

"But of course, this leads to fun with math. It only takes 15 generations -- about 300 years' time -- to get you to 32,768 ancestors in that generation. 30 generations -- 600 years' time -- and you have 230 ancestors, or 1,073,741,824. Go back to 1 C.E. and you've got 2100 ancestors in that generation, or roughly 1.2 nonillion ancestors.

Of course, that's roughly 500 billion billion times the number of people who have ever lived"

and from http://www.gly.uga.edu/railsback/GenealComp1.html

"Now let's go back to someone's claim to be descended from Charlemagne. Charlemagne lived about 1200 years ago, which turns out to be about 40 generations back in most lineages. 240 is a little over one trillion. This means that, if our claimant filled out an ancestry chart back the forty generations to about 800AD, he or she would have to list a trillion names in that fortieth generation back.

If you've been following the math, you'll have noticed a problem. The present total human population of the world is about six billion. Scholars estimate that world population in 800AD was a lot lower, around 300 million. Even if we're generous by a factor of more than three and assume world population in 800 AD was a billion, that would only be one-thousandth of the people needed to fill in the trillion spaces in the ancestry chart. The name of each person alive in 800AD would have to appear, on average, one thousand times in the fortieth generation of our claimant's chart.

If we're more realistic about where people's ancestors lived and how much they crossed geographic barriers, populations of potential ancestors get even smaller. If world population in 800AD was 300 million, most people are probably descended from a pool that was at most a third of the world's population, or about 100 million in 800 AD. With that in mind, the number of potential ancestors is only one ten-thousandth of the number of spaces in the chart forty generations back.

This tremendous shortfall of potential ancestors implies that almost anyone alive and reproducing in our area of geographic interest in 800AD had a high probability of being an ancestor, that persons descended from one geographic area have to have many ancestors in common, and that, among any one person's ancestors, intermarriage of cousins was almost inevitable. The three apparent improbabilities discussed at the beginning of this essay (famous ancestry, extensive cousinhood, and self-cousinhood) now seem like inevitabilities."

There was a thinning of the herd through disease, mishap and mayhem. Take your figures on compounding Charlemagne and subtract the western population to find the net result of those who didn't make it.