Quantitative Biology > Populations and Evolution
[Submitted on 19 Oct 2013 (v1), last revised 20 Oct 2015 (this version, v2)]
Title:Discriminative Measures for Comparison of Phylogenetic Trees
View PDFAbstract:In this paper we introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity $d_{nav}$ counts the steps along a "combing" of the Nearest Neighbor Interchange (NNI) graph of binary hierarchies, providing an efficient approximation to the (NP-hard) NNI distance in terms of "edit length". At the same time, a closed form formula for $d_{nav}$ presents it as a weighted count of pairwise incompatibilities between clusters, lending it the character of an edge dissimilarity measure as well. A relaxation of this formula to a simple count yields another measure on all trees --- the crossing dissimilarity $d_{CM}$. Both dissimilarities are symmetric and positive definite (vanish only between identical trees) on binary hierarchies but they fail to satisfy the triangle inequality. Nevertheless, both are bounded below by the widely used Robinson-Foulds metric and bounded above by a closely related true metric, the cluster-cardinality metric $d_{CC}$. We show that each of the three proposed new dissimilarities is computable in time $O(n^2)$ in the number of leaves $n$, and conclude the paper with a brief numerical exploration of the distribution over tree space of these dissimilarities in comparison with the Robinson-Foulds metric and the more recently introduced matching-split distance.
Submission history
From: Omur Arslan [view email][v1] Sat, 19 Oct 2013 05:03:23 UTC (1,165 KB)
[v2] Tue, 20 Oct 2015 14:10:43 UTC (800 KB)
Current browse context:
q-bio.PE
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.