Exploration 4: Arranging the groups on the ancestry tree in two dimensions so that distance reflects the time since branching (somewhat)
The previous post depicted the diagram of human ancestry from Tishkoff and collaborators in a way that made the distance between any pair of branches proportional to the time since they split in two from their most recent common ancestor. This does not mean, however, that the distance between every pair of the 18 groups at the base of the diagram is equal to the time since their common ancestor. By spreading out the tree into a fan, we can do much better on this last count. (Recall: NR stands for the ancestor of groups N through R, where the groups are as labeled across the bottom of the Tishkoff diagram of human ancestry.
This 2-D depiction eliminates the crossing over that made the tree in the previous post difficult to read. However, it is far from perfect. For example, C and N end up close even though their common ancestor was almost as distant in time as could be. A sophisticated algorithm might arrive at a better fan than the first attempt above, but we could never get around the fact that at each branching point, the branches could be flipped (e.g., E or F could be made close to D instead of G). These limitations notwithstanding, the next post employs the 2-D fan to depict something about the genetics omitted so far in these posts.