Exploration 1: Rearranging the horizontal sequence of a tree diagram
(Continuing from the previous post, we consider alternative depictions of human genetic variation keeping in mind the question, “Can any depiction of genetic relationships among humans allow simultaneously for similarity, diversity, ancestry, and admixture?”)
The diagram of human ancestry from Tishkoff and collaborators branches out like an upside-down tree from a common ancestral group into 18 groups today. (The diagram shows some cross-links that indicate gene-flow between populations, but we will ignore these for the time being.)
(Source: Michael C. Campbell1 and Sarah A. Tishkoff, 2010, “The Evolution of Human Genetic and Phenotypic Variation in Africa,” Current Biology 20, R166–R173. Letters at the bottom added for the purposes of referring to the groups in this series of blog posts.)
Now, the branches at any fork can be flipped so the next diagram conveys the same information about ancestry and branching.
Notice that the second variant does not convey the impression that the branch that in ancestral to the non-Africans, i.e., NR, is more different from the branches ancestral to the African groups, i.e., AB, CC, DM, than these branches are from each other. Although the lineage that ended up at CC (the ancestor of group C) branched off earlier than the lineage leading to NR, there is nothing in the ancestry diagram that says it should be more similar genetically to AB than to NR.
If we exclude diagrams with crossing over of branches, such as the one below, there are four distinct reorderings of the four branches that preserve the sequence of the branchings. There are 2 to the power 16 = 65536 reorderings of the full set of the 18 current groups. The point is not that we need to find one correct ordering from among such a large set. The lesson is 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. (In this light, diagrams with crossing over should be excluded because they suggest that the two branches at a fork are further away from each other than to one of the earlier branches, which goes against the information contained in the sequence of branches.)
It is not easy, however, to convince one’s brain not to give significance to these horizontal positions. This cognitive weakness gives rise to the explorations in the next posts.