Source-linked AI summary
A tree metric using structure and length to capture distinct phylogenetic signals
Michelle Kendall, Caroline Colijn
TL;DR
Inferred trees can conflict across estimation methods and data sources, motivating quantitative comparison. This paper introduces a metric for rooted, labeled trees that captures structure and branch lengths; its projections correspond better to true distances than RF and BHV, and posterior islands typically merge as λ approaches 1.
Problem
Inferred trees can conflict across estimation methods and data sources, so comparing trees is important for identifying distinct evolutionary signals.
Source: §1 · p. 1Method
The paper introduces a metric combining tree structure and branch lengths for rooted trees with the same set of taxa.
Source: §1 · p. 1, §2.1 · p. 5, §2.3 · p. 7Results
The metric's MDS projections correspond better to true distances than RF and BHV, and posterior islands typically merge as λ approaches 1.
Source: §3.1 · p. 8, §3.2 · p. 9Takeaways & Limitations
The geometric median tree selects a sampled tree closest to the average vector as a representative of a group of trees.
Source: §3.3 · p. 10The metric compares trees only when they have the same taxa; overlapping trees can be compared after restricting them to shared taxa.
Source: §2.3 · p. 7
Abstract
from arXiv · showhide
Phylogenetic trees are a central tool in understanding evolution. They are typically inferred from sequence data, and capture evolutionary relationships through time. It is essential to be able to compare trees from different data sources (e.g. several genes from the same organisms) and different inference methods. We propose a new metric for robust, quantitative comparison of rooted, labeled trees. It enables clear visualizations of tree space, gives meaningful comparisons between trees, and can detect distinct islands of tree topologies in posterior distributions of trees. This makes it possible to select well-supported summary trees. We demonstrate our approach on Dengue fever phylogenies.
1 Introduction
Inferred trees can conflict across estimation methods and data sources, making quantitative comparison important. The paper introduces a metric that captures tree structure and branch lengths and outlines applications to visualizing tree space, detecting islands, and selecting summary trees.
1 Introduction
- The metric addresses comparisons where estimation methods or data sources produce conflicting phylogenies, reflecting multiple sources of uncertainty in inferred trees.Source: §1 · p. 1
- Existing visualizations do not support detailed comparison of large tree groups, while RF/NNI distances can behave counterintuitively.Trees differing in the placement of one tip can be a maximal NNI distance apart.Source: §1 · p. 1
- The proposed metric captures both tree structure and branch lengths, defining a tree space for low-dimensional visualization and biologically meaningful differences.Source: §1 · p. 1
- The paper proves the distance is a metric and applies it to tree-space visualization, island detection in Dengue phylogenies, and summary-tree selection.Source: §1 · p. 1
2 Metrics
The paper defines and proves a metric blending root-based topology and branch-length representations; λ tunes their contributions, while comparisons with existing metrics clarify its scope.
2.1 Our metric: definition and proof
- Each rooted tree is represented by m, encoding MRCA edge counts, and M, encoding root-to-MRCA path lengths and pendant lengths; λ blends the two vectors.The vectors are compared using Euclidean distance.Source: §2.1 · pp. 2–3
- At λ=0, zero distance identifies matching topology; for λ>0, zero distance requires identical topology and branch lengths.The proof is presented for binary trees, with extension to nonbinary trees described as straightforward.Source: §2.1 · pp. 3, 5
- The metric is fundamentally for rooted trees: rerooting the same unrooted tree can yield positive distance, larger when the chosen roots are farther apart.The authors say unrooted topologies can be checked by rooting both trees on the edge to the same tip.Source: §2.1 · p. 5
2.2 The role of λ
- λ sets the relative contribution of topology and branch lengths, but their influence depends on branch-length scale because m counts edges and M measures lengths.When branch lengths are much larger than 1, M can dominate even at relatively small λ; when lengths are much smaller, λ near 1 may be needed.Source: §2.2 · p. 5
- Rescaling lengths may make changes in dλ more gradual, but can obscure biologically relevant rate differences between genes.The example given is trees from one gene having branches typically twice as long as those from another.Source: §2.2 · pp. 5–6
2.3 Other metrics on labeled phylogenetic trees
- Unlike unrooted RF and path-difference metrics, this metric emphasizes root-to-MRCA relationships; unlike BHV, it lets users balance topology against branch lengths.The authors note that RF and path-difference metrics capture different tree characteristics, while BHV does not offer this user-selected balance.Source: §2.3 · pp. 6–7
- The metric compares trees with the same taxa; for partially overlapping trees, the authors suggest comparing subtrees restricted to shared taxa.Comparisons between trees with different taxa are not captured by this metric.Source: §2.3 · p. 7
3 Exploring tree space
This section uses MDS to visualize tree spaces and detect topology islands, then uses the metric to select central summary trees.
3.1 Visualizing tree space
- Across all 945 T6 shapes and label permutations, the metric preserves symmetry while RF and BHV projections suggest false islands; Shepard plots show better distance correspondence.The metric’s Euclidean nature suits low-dimensional projections, though projected distances can be much smaller than true distances.Source: §3.1 · pp. 7–8, Figure 4 · p. 8
3.2 Islands in tree space
- On Dengue posteriors, islands are clearer under GTR + Γ + I with a relaxed clock than GTR + CP with a strict clock; repeated first-setting runs recover the same islands.The MCC tree lies in the largest island or cluster in both settings.Source: §3.2 · p. 9, Figure 5 · p. 10
- As λ approaches 1, topology islands typically merge and the posterior becomes unimodal, although topology-focused outcomes such as ancestral character reconstruction can be affected by islands.Source: §3.2 · p. 9
3.3 Summary trees
- The geometric median selects sampled tree(s) nearest the mean vector, avoiding unsampled MCC trees and negative branch lengths; within islands, it lies close to the MCC tree.The minimal distance to the average vector measures how close the selected tree is to the posterior average.Source: §3.3 · pp. 9–10
4 Concluding remarks
The metric supports flexible comparisons of rooted, labeled trees and can be extended to emphasize a particular tip. Its uses range from comparing estimates and detecting evolutionary patterns to analyzing other kinds of trees.
4 Concluding remarks
- Weighting the m and M entries for a focal tip can make distances emphasize that tip’s placement over ancestry patterns among other tips.The passage gives placing new outbreak cases on an existing phylogeny as a possible use.Source: §4 · p. 11
- For rooted, labeled trees with the same tips, the metric can compare estimates across methods or data and provide a heuristic for convergence.Source: §4 · p. 11
- The metric can reveal likely evolutionary patterns, identify informative sites whose removal substantially changes a phylogeny, and compare trees from other scientific disciplines.Examples include decision trees, network spanning trees, hierarchical clustering trees, and language trees.Source: §4 · p. 11