Exploration 2: Arranging the groups on the ancestry tree so that distance reflects (to some extent) the time since branching
The order of the 18 current human groups at the base of the diagram of human ancestry from Tishkoff and collaborators is only 1 of 65536 possible orderings that preserve the same sequence of branchings from a common ancestral group 150,000 years ago. The image that comes to mind is of a mobile with each pair of branches able to revolve around the position of its most recent common ancestor, which will itself be moving as it revolves with another branch around its common ancestor. I found a wonderful website for building mobiles, http://www.nga.gov/kids/zone/mobile.htm, and was able to use it to replicate the Tishkoff diagram down to the level of 4 branches, i.e., AB, CC, DM, and NR.
In this mobile, 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. This differs from the original Tishkoff diagram, which has, for example, A, B, and C close together at the bottom even though the common ancestor of A and B, i.e., AB, branched off 150,000 years ago from the ancestor of C, i.e., CC. This is plenty of time for genetic divergence to occur.
The distance relationship between members of a pair does not mean that the distance between every pair of the four groups at the base of the mobile is equal to the time since their common ancestor. Mostly, the mobile serves to remind us “that no lessons should be drawn from the order along the bottom of a branching diagram that is not already contained in the sequence of branches above” (see previous post).
The mobile software allows one to view the mobile from above as well as from the side. In the following snapshots from above, the red ball is AB, the lime one is CC, and the blue and purple are DM and NR. (The relative size of the balls has no significance.)
I haven’t constructed a mobile for the whole ancestry tree, but the next post extends the feature of the mobile that had the distance between any pair of branches proportional to the time since they diverged.