This study introduces a large-scale, detailed computer model of recent human history which suggests that the common ancestor of everyone alive today very likely lived between 2,000 and 5,000 years ago. Furthermore, the model indicates that nearly everyone living a few thousand years prior to that time is either the ancestor of no one or of all living humans.
And this essay on the same topic. This is well worth reading as it will take about five minutes and makes all the main points.
The model is simplistic, and doesn't take into account widespread migration (which would obviously increase genetic mixing). However, I think the overall idea is correct. The population in the past was very low: at the time of Henry the 8th, in a period of peace and prosperity and improved food production, England had two or three million people. In the Middle Ages it was a lot lower. I have read a study which claimed that more or less everyone in Britain is descended from more or less everyone who was alive in the Middle Ages. Or more accurately, about a third of the population have left no issue (because of celibacy, infertility, or disease) and the remaining two-thirds (perhaps less than a million people of each sex) are the ancestors of everyone in Britain (except very recent migrants). All of us, royal, aristocratic, bourgeois and prole.
nwhyte points out that The Queen is the direct female descendent of Mary Garritt, the wife of Thomas Webb, a surveyor in Stow-on-the-Wold in the mid-18th century. Who were her cousins, and who are their offspring? For cultural reasons we trace direct descent via the oldest surviving son. But all the other descendants, girls, younger sons, unknown and illegitimate children, all go their way with the same genes, and mix them into the overall gene pool.
watervole posts an interesting poll about what kind of science mistakes you can tolerate in an SF story. For me, biological mistakes are the hardest to tolerate. My biggest niggle is an ecosystem that doesn't make sense (no energy input). Anyway, I also find genetic fallacies hard to take, and for me this is possibly the biggest problem I have with Tolkein's universe. Tolkein confuses the noble lineage as defined in social terms with genetic descent. He talks about Elvish descent, and noble houses stretching back thousands of years. It's all bull. Really, everyone is descended from everyone. There are no special genes for special families.
I'm using noble family and royal family as examples, but it applies to everything. There are no clever families, no beautiful or strong families, no master race, no professional classes, no super-genes. It's just a total mix-up.
I am amused to discover that my blood group (B) was brought to Europe by the Huns, so that like the character in Hitch-hiker's Guide I am the direct descendent of Attila the Hun. Well, I might be. But almost certainly everyone else is too. And we are all descendants of of Muhammed, and Charlemagne and everyone else.
I'm obviously not excluding my lj-friends of non-European descent from this commonality, as the paper linked at the top explains.