What is the Jacobsen index?

The Jacobsen index of a phylogenetic tree is a measure of its branchiness, or the degree to which the tree contains short internal branches. It is defined as the ratio of the total tree length (the sum of the lengths of all the branches in the tree) to the minimum possible tree length, which is the length of a tree with the same number of taxa and no internal branches (all taxa are connected directly to the root).

A high Jacobsen index indicates a tree with many short internal branches, which may be the result of a rapid radiation of taxa or a high rate of character evolution. A low Jacobsen index indicates a tree with few short internal branches, which may be the result of a slow radiation of taxa or a low rate of character evolution.

The Jacobsen index is often used to compare the relative branchiness of different phylogenetic trees, and can be used to assess the fit of different evolutionary models to a given dataset.