Of course just as many people might trace their lineage back to Charlemagne, or Genghis, there are also some likely unknowns who cast similar genetic shadows over the future - some unknown peasant father and/or mother, who had numerous children, healthy, good looking, both sons and daughters, whose descendants spread out just as widely. We just don't know their names. The nobility, even minor nobility, shows up in church and civil records; the farmer doesn't. Perhaps DNA analysis might at some point in the future reveal his existence, even if tentatively.
(It is one of the striking things about doing this kind of research - how many people left so little trace other than through their children. Even their names are missing. I wish I had a at least a page, or even a paragraph, of information about each - I'm sure their challenges weren't fundamentally so different from ours.)
So - is there any way to quantify any of this, even crudely?
The resulting model might be one of relatively static pools of population, connected by some punctuated diffusion. This might not match historical reality exactly (say, an individual might have married into an immigrant family in his town, then his descendants might have moved back to the source of the immigration), but it might be a useful model nevertheless. It seems ripe for mathematical modeling.