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Order-Dependent dissimilarity measures on phylogenetic trees.

Simone Linz1, Katherine St John2,3, Charles Semple4

  • 1School of Computer Science, University of Auckland, Auckland, New Zealand.

Journal of Mathematical Biology
|March 17, 2026
PubMed
Summary
This summary is machine-generated.

Three new vector representations for phylogenetic trees (ordered leaf attachment, Phylo2Vec, HOP) offer computable dissimilarity measures. When minimized over all orderings, the hybrid number equals HOP, while specific orderings link temporal tree-child hybrid number to all three vector measures.

Keywords:
Order-dependent measuresPhylogenetic treesVector representations

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Area of Science:

  • Computational Biology
  • Phylogenetics
  • Data Science

Background:

  • Vector representations like ordered leaf attachment, Phylo2Vec, and HOP are emerging for rooted phylogenetic trees.
  • These methods depend on the ordering of the leaf set X.
  • Dissimilarity measures can be derived from these vector representations for a fixed leaf ordering.

Purpose of the Study:

  • To compare novel vector-based dissimilarity measures with established phylogenetic distances.
  • To investigate the relationships between ordered leaf attachment, Phylo2Vec, HOP, rooted subtree prune and regraft (rSPR) distance, hybrid number, and temporal tree-child hybrid number.
  • To determine how minimizing over different leaf orderings affects these comparisons.

Main Methods:

  • Calculated polynomial-time computable dissimilarity measures for rooted phylogenetic X-trees T and T' based on ordered leaf attachment, Phylo2Vec, and HOP.
  • Compared these vector-based measures against rSPR, hybrid number, and temporal tree-child hybrid number.
  • Analyzed measures minimized over all possible leaf orderings and those induced by common cherry-picking sequences.

Main Results:

  • No direct relationship was found between rSPR and the three vector-based measures.
  • When minimized over all orderings, the hybrid number equals the HOP measure and provides an upper bound for ordered leaf attachment and Phylo2Vec.
  • When minimized over orderings from common cherry-picking sequences, the temporal tree-child hybrid number equals all three vector-based measures.

Conclusions:

  • Vector representations offer novel, order-dependent dissimilarity metrics for phylogenetic trees.
  • The hybrid number and HOP measure show a direct equivalence under global ordering minimization.
  • Specific common orderings establish a strong link between temporal tree-child hybrid number and the studied vector representations, suggesting potential for efficient tree comparison.