Height-to-Length Ratio

The ratio of the tree height to the sum of the lengths of all the branches of a tree ranges from \(1/n\) to \(1/2\), where \(n\) is the number of leaves. The extreme case of \(1/2\) is approached when a tree has two long branches and many short ones. In genealogies of lineages sampled from a population, a high height-to-length ratio is typical of a pair of separate populations with a low migration rate between them. Lineages have a recent common ancestor within each separate population, and these two ancestors have their own common ancestor only much farther back in the past. See Arbisser et al. (2018) for details.

Photo: Noah Rosenberg, December 2, 2016