A note on the path interval distance

• Path interval distance analyzed as a method for comparing phylogenetic trees.
• Path interval distance captures global similarities between tree topologies.
• Random trees are not likely to be maximally distant under the path interval distance.

The path interval distance accounts for global congruence between locally incongruent trees. We show that the path interval distance provides a lower bound for the nearest neighbor interchange distance. In contrast to the Robinson–Foulds distance, random pairs of trees are unlikely to be maximally distant from one another under the path interval distance. These features indicate that the path interval distance should play a role in phylogenomics where the comparison of trees on a fixed set of taxa is becoming increasingly important.