RESEARCH ON ANCESTRY

It’s a hard question to answer. It depends on the detailed migration, mating, and survival patterns of humans over hundreds and thousands of years. But in 1999 a professor of statistics at Yale, Joe Chang, published a paper proving that the number of generations back to the MRCA in a randomly mating population is surprisingly small. (Here’s how small, for those who remember a little high school mathematics. Joe Chang proved that the number of generations back to the most recent common ancestor in a randomly mating population is very closely approximated by the base two logarithm of the size of the population. So, for a population of a million people, it takes 20 generations to reach the MCRA—or about 500 years—because 2 to the 20th power is about a million. For a randomly mating population of a billion people, it takes 30 generations—750 years—because 2 to the 30th power is a billion.)

The problem is that human populations don’t mate randomly. Random mating means that anyone has an equal chance of marrying and having children with anyone else in the world. But people are much more likely to have children with people they know, who live near them, who speak the same language, or are from the same social class. The nonrandom nature of human mating is what makes the problem so hard.

The key to the problem lies in what are known as small world networks. A small world network typically consists of clusters of objects (whether points on a paper, networked computers, interacting proteins, or whatever) that share many interconnections. These clusters are in turn linked to other clusters by occasional interconnections that occur more or less at random. The remarkable thing about a small world network is that even when the clusters are loosely connected, the network as a whole can exhibit behavior much like that of a single tightly connected cluster.