Meaningfulness of the lattice distance for inference

Determine whether the lattice distance defined through least upper bounds on the lattice of multifurcating ranked tree shapes constitutes a meaningful metric for phylogenetic inference and related analyses.

Background

The paper defines a lattice distance between two multifurcating ranked tree shapes as the sum of their respective distances to their least upper bound. The authors establish that this function is a valid distance metric and note that it can be computed in less than cubic time.

They also identify a limitation: the distance is not highly granular and is constrained by the numbers of internal nodes. Whether this computationally efficient metric captures biologically or statistically meaningful differences between trees for inference and analysis is explicitly left unresolved.