Genealogy and genetic ancestry are different from each other

Graham Coop runs a valuable blog on population genetics that worth wide publicity. Here is a snippet:

In the last post, I described how your vast number of ancestors meant that you were descended from nearly everyone in the world more than a few thousand years back. But you are only a genetic descendant of a relatively few of those individuals, as most have left no trace in your genome. For example, you might be able to trace a particular route through your pedigree to Charlemagne, as can almost any one with European ancestry, but there’s less than a 1/100 million chance that you’re a genetic descendant of Charlemagne due to that particular connection through your pedigree. Forty generations back most of your genome traces back to a random subset of around twenty-six hundred individuals out of all your millions of ancestors. It’s unlikely that Charlemagne is one of them.