Adam Rutherford in Nautilus:
We are all special, which also means that none of us is. This is merely a numbers game. You have two parents, four grandparents, eight great-grandparents, and so on. Each generation back the number of ancestors you have doubles. But this ancestral expansion is not borne back ceaselessly into the past. If it were, your family tree when Charlemagne was Le Grand Fromage would harbor around 137,438,953,472 individuals on it—more people than were alive then, now, or in total. What this means is that pedigrees begin to fold in on themselves a few generations back, and become less arboreal, and more a mesh or weblike. You can be, and in fact are, descended from the same individual many times over. Your great-great-great-great-great-grandmother might hold that position in your family tree twice, or many times, as her lines of descent branch out from her, but collapse onto you. The further back through time we go, the more these lines will coalesce on fewer individuals. “Pedigree” is a word derived from the middle French phrase “pied de grue”—the crane’s foot—as the digits and hallux spread from a single joint at the bottom of the tibia, roughly equivalent to our ankle. This branching describes one or a few generations of a family tree, but it’s wholly inaccurate as we climb upward into the past. Rather, each person can act as a node into whom the genetic past flows, and from whom the future spills out, if indeed they left descendants at all.
This I find relatively easy to digest. The simple logic is that there are more living people on Earth now than at any single moment in the past, which means that many fewer people act as multiple ancestors of people alive today. But how can we say with utter confidence that any individual European is, like Christopher Lee, directly descended from the great European conciliator?
The answer came before high-powered DNA sequencing and ancient genetic analysis. Instead it comes from mathematics. Joseph Chang is a statistician from Yale University and wished to analyze our ancestry not with genetics or family trees, but just with numbers. By asking how recently the people of Europe would have a common ancestor, he constructed a mathematical model that incorporated the number of ancestors an individual is presumed to have had (each with two parents), and given the current population size, the point at which all those possible lines of ascent up the family trees would cross. The answer was merely 600 years ago. Sometime at the end of the 13th century lived a man or woman from whom all Europeans could trace ancestry, if records permitted (which they don’t). If this sounds unlikely or weird, remember that this individual is one of thousands of lines of descent that you and everyone else has at this moment in time, and whoever this unknown individual was, they represent a tiny proportion of your total familial webbed pedigree. But if we could document the total family tree of everyone alive back through 600 years, among the impenetrable mess, everyone European alive would be able to select a line that would cross everyone else’s around the time of Richard II.