Data for: Branch length transforms using optimal tree metric matching

The abundant discordance between evolutionary relationships across the
genome has rekindled interest in methods for comparing and averaging trees
on a shared leaf set. However, compared to tree topology, where much
progress has been made, handling branch lengths has been more challenging.
Species tree branch lengths can be measured in various units, often
different from gene trees. Moreover, rates of evolution change across the
genome, the species tree, and specific branches of gene trees. These
factors compound the stochasticity of coalescence times and estimation
noise, making branch lengths highly heterogeneous across the genome. For
many downstream applications in phylogenomic analyses, branch lengths are
as important as the topology, and yet, existing tools to compare and
combine weighted trees are limited. In this paper, we address the question
of matching one tree to another, accounting for their branch lengths. We
define a series of computational problems called Topology-Constrained
Metric Matching (TCMM) that seek to transform the branch lengths of a
query tree based on a reference tree. We show that TCMM problems can be
solved in quadratic time and memory using a linear algebraic formulation
coupled with dynamic programming preprocessing. While many applications
can be imagined for this framework, we explore two applications in this
paper: embedding leaves of gene trees in Euclidean space to find outliers
potentially indicative of estimation errors and summarizing gene tree
branch lengths onto the species tree. In these applications, our method,
when paired with existing methods, increases their accuracy at limited
computational expense.