In 1999, Joseph Chang, a professor of statistics at Yale University, published a paper in Advances in Applied Probability showing that the most recent common genealogical ancestor in a randomly mating population of size n lived log2 n generations ago, where log2 n is the number of times you have to multiply 2 by itself to equal n. (Thus, log2 n of 1 million is about 20, since 2 to the 20th power is 1,048,576.) I read Chang's paper while I was writing my book, Mapping Human History: Genes, Race, and Our Common Origins, and he and I began working to extend his result to more realistic human populations where mates are not chosen at random.
About that time, I also was reading about small-worlds graphs, which is a branch of mathematics that flourished in the 1990s. In a small-worlds graph, subgraphs consisting of random connections among a cluster of points (random marriages within a population form such a subgraph) are connected to each other by occasional links. It doesn't take many of those occasional links for the entire collection of subgraphs to start behaving like one big randomly connected graph.
I realized that human ancestry could be modeled as a small-worlds graph. Even with very small rates of migration between populations that are separated geographically or socially, the entire population would behave in ways comparable to a randomly connected graph. Thus, ancestry for the population as a whole might conform roughly to Chang's observation about randomly mating populations. That conclusion gave me enough confidence to publish in my book some of the observations I've made in this article.
Meanwhile, Douglas Rohde, a computer scientist who was then at MIT and now works at Google, heard about the research that Chang and I were doing. He built an amazing computer simulation of the world's interlinked populations going back 20,000 years, which produced results comparable to those of Chang's theoreticical approach. The three of us worked together on the results published in the Nature paper.
Computer scientist Mark Humphrys anticipated some of our work on human ancestry in his fascinating "royal descents of famous people" Web site, which I wrote about in the May 2002 Atlantic. Douglas Rohde has summarized his work on human ancestry in an unpublished paper posted at his old MIT Web site. The esteemed geneticist Susumu Ohno also wrote about human ancestry in the Proceedings of the National Academy of Sciences. I used Ohno's paper to conclude that each of us had between 600,000 and 1 million distinct ancestors 20 generations ago.