# Nodal distances for rooted phylogenetic trees

@article{Cardona2010NodalDF, title={Nodal distances for rooted phylogenetic trees}, author={Gabriel Cardona and Merc{\`e} Llabr{\'e}s and Francesc Rossell{\'o} and Gabriel Valiente}, journal={Journal of Mathematical Biology}, year={2010}, volume={61}, pages={253-276} }

Dissimilarity measures for (possibly weighted) phylogenetic trees based on the comparison of their vectors of path lengths between pairs of taxa, have been present in the systematics literature since the early seventies. For rooted phylogenetic trees, however, these vectors can only separate non-weighted binary trees, and therefore these dissimilarity measures are metrics only on this class of rooted phylogenetic trees. In this paper we overcome this problem, by splitting in a suitable way each…

## 28 Citations

Comparing Phylogenetic Trees by Matching Nodes Using the Transfer Distance Between Partitions

- BiologyJ. Comput. Biol.
- 2017

A new metric for rooted trees-the Matching Pair (MP) distance is defined, which uses the concept of the minimum-weight perfect matching in a complete bipartite graph constructed from partitions of all pairs of leaves of the compared phylogenetic trees.

A partial order and cluster-similarity metric on rooted phylogenetic trees

- Computer ScienceJournal of mathematical biology
- 2020

A new cluster-similarity metric on rooted phylogenetic tree space that has an associated local operation, allowing for easy calculation of neighbourhoods, a trait that is desirable for MCMC calculations is introduced.

On a matching distance between rooted phylogenetic trees

- Computer ScienceInt. J. Appl. Math. Comput. Sci.
- 2013

This paper defines and explores in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees, but the distance evaluation is more complex.

Metrics for Phylogenetic Networks II: Nodal and Triplets Metrics

- BiologyIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2009

This paper generalizes to phylogenetic networks two metrics that have already been introduced in the literature for phylogenetic trees: the nodal distance and the triplets distance and proves that they are metrics on any class of tree-child time consistent phylogenetics networks on the same set of taxa, as well as some basic properties for them.

Optimal Completion and Comparison of Incomplete Phylogenetic Trees Under Robinson-Foulds Distance

- Computer ScienceCPM
- 2021

This work provides the first polynomial-time algorithms for the above problem under the widely used Robinson-Foulds (RF) distance measure and shows that completion-based RF distance can lead to very different inferences regarding phylogenetic similarity compared to traditional RF distance.

Algorithms for Computing Cluster Dissimilarity between Rooted PhylogeneticTrees

- Biology
- 2015

A new dissimilarity measure for comparing rooted trees and three algorithms to efficiently compute it, which operates on clusters of compared trees as in the case of standard Robinson-Foulds distance, but extracts more subtle differences between clusters, and thus may offer better discrimination than the Robinson-Fs distance.

TreeCmp: Comparison of Trees in Polynomial Time

- Computer ScienceEvolutionary Bioinformatics Online
- 2012

When a phylogenetic reconstruction does not result in one tree but in several, tree metrics permit finding out how far the reconstructed trees are from one another. They also permit to assess the…

## References

SHOWING 1-10 OF 44 REFERENCES

THE TRIPLES DISTANCE FOR ROOTED BIFURCATING PHYLOGENETIC TREES

- Biology
- 1996

The triples distance is investigated as a measure of the distance between two rooted bifurcating phylogenetic trees and a normal approximation is proved under the class of label-invariant models on the distribution of trees.

Encoding phylogenetic trees in terms of weighted quartets

- BiologyJournal of mathematical biology
- 2008

Here, a new characterisation for arbitrary phylogenetic trees is provided, that is, phylogenetic Trees all of whose internal vertices have degree 3 are provided.

Geometry of the Space of Phylogenetic Trees

- MathematicsAdv. Appl. Math.
- 2001

We consider a continuous space which models the set of all phylogenetic trees having a fixed set of leaves. This space has a natural metric of nonpositive curvature, giving a way of measuring…

Subtree Transfer Operations and Their Induced Metrics on Evolutionary Trees

- Computer Science
- 2001

The problem of computing the minimum number of TBR operations required to transform one tree to another can be reduced to a problem whose size is a function just of the distance between the trees, and thereby establish that the problem is fixed-parameter tractable.

Nodal distance algorithm: calculating a phylogenetic tree comparison metric

- Biology, Computer ScienceThird IEEE Symposium on Bioinformatics and Bioengineering, 2003. Proceedings.
- 2003

The nodal distance algorithm provides a method for comparing large sets of phylogenetic trees in a reasonable amount of time and has significantly less computation time than the most widely used comparison method, the partition metric.

Distributions of Tree Comparison Metrics—Some New Results

- Mathematics, Environmental Science
- 1993

Measures of dissimilarity (metrics) for comparing trees are important tools in the quantitative analysis of evolutionary trees, but many of their properties are incompletely known. The present paper…

DETECTING PHYLOGENETIC RELATIONS OUT FROM SPARSE CONTEXT TREES

- Computer Science
- 2008

The Phyl-SPST package is implemented to compute the distance between the sparse context trees estimated with the SPST algorithm, and this approach is applied to reconstruct a phylogenetic tree of protein sequences in the globin family of vertebrates.

The number of evolutionary trees

- Computer Science
- 1978

The method is extended to count trees some of whose interior nodes may be labelled, to double-check algorithms and notation systems, and to frighten taxonomists.

Molecular phylogenetic analyses and real-life data

- BiologyComput. Sci. Eng.
- 2005

Since the 1960s, researchers have published numerous studies addressing the problems of molecular phylogenetic analysis methods in theory and practice, but challenges still remain.

Properties of the distance matrix of a tree

- Mathematics, Computer Science
- 1969

The purpose of this note is to exhibit certain interesting algebraic properties of the distance matrix of a tree, and two algorithms for tree realization emerge from these properties.