Exploration 3: Arranging the groups on the ancestry tree so that distance reflects (to some extent) the time since branching
For the previous post I was able to use a (virtual) mobile to depict the diagram of human ancestry from Tishkoff and collaborators down to the level of 4 branches, i.e., AB, CC, DM, and NR. Moreover, I was able to make the distance between any pair of branches, i.e., (DM,NR), (CC,DR), (AB,CR) proportional to the time since they diverged. In the figure below this distance relationship holds for all pairs of branches in the full tree. (Of course, a more refined analysis might allow for different speeds of divergence from the common ancestor down different branches, but this could also be depicted in this same form.)
As in the previous post, the distance relationship between members of a pair does not mean that the distance between every pair of the 18 groups at the base of the mobile—there are 153 such pairings—is equal to the time since their common ancestor. Indeed, the crossing over makes this obvious. It’s easy to see that, for example, the closeness of H and L is not because they share a recent common ancestor. The use of the mobile in the previous post suggests the next step in exploration, namely, one in which crossing over is eliminated by spreading out the groups in two dimensions.