Exploration 6: Superimposing changes in genetic location on an ancestry diagram, a simulation
In the previous post, the depiction of a 2-D ancestry “fan” plus “aprons” allowed us to represent within group variation as well as branching. Whereas in a branching diagram we sought to minimize the crossing over of branches 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” (see earlier post), with the inclusion of aprons that overlap we can embrace branches that cross over. Consider the following simulation, which also allows for evolution along branches to happen at different rates.
In a branching process, each group breaks into two. Imagine that the new groups are small so that by genetic drift, that is, by chance, all members end up with the same variant a some genetic locus (position on the genome), that is, this locus does not contribute genetic variation. (See an analogy given in the wikipedia entry on genetic drift.) The population eventually grows larger and genetic drift ceases to be significant. Each of the new groups then represents a subset of the variation existing in their common ancestor group. If we discount new mutations for now, none of the branched-off groups can have more genetic variation than groups from which they are descended.
The following diagram uses a random simulation to generate directions of branching and the distances of each branch from its most recent common ancestor. The two dimensions stand for the genetic variation of the whole set of populations. No aprons are drawn around the midpoints of the groups, but it should be noted that the variation of the original population spans a space five times as wide as the area shown in the diagram.
The following slide show builds up the messy web branching from one group (AR) to two (AB and NR), and so on, step by step.
Of course, this is only a simulation. The actual genetic data might yield a 2-D web that is quite different. Nevertheless, in the next post, we add aprons to the simulation to complete a picture of similarity, diversity, and ancestry.