An Approach to Minimize Crossings in Phylogenetic Trees

Visualization of phylogenetic trees became popular and has been widely used in biology, taxonomy, cloud computing, and bioinformatics. Different phylogenetic trees can be built based on different measures and methods. As a result, the problem became obvious when deciding which tree is better and most visually appealing. This often involves comparing two phylogenetic trees to each other. The main goal of this paper is to display a pair of alternative phylogenetic trees together while minimizing the number of crossings among the branches of both trees. This paper summarizes different tools and techniques used in visualizing phylogenetic trees in different studies and describes their limitations. After surveying different studies involved in crossings minimization, a naive algorithm to minimize the number of crossings is proposed.

[1]  Donald K. Berry,et al.  Parallel Implementation and Performance of FastDNAml - A Program for Maximum Likelihood Phylogenetic Inference , 2001, ACM/IEEE SC 2001 Conference (SC'01).

[2]  Michael Kaufmann,et al.  Comparing trees via crossing minimization , 2005, J. Comput. Syst. Sci..

[3]  John Alan Robinson,et al.  Novel Techniques for Visualizing Biological Information , 1997, ISMB.

[4]  Derek A. Ruths,et al.  Arbor 3D: an interactive environment for examining phylogenetic and taxonomic trees in multiple dimensions , 2000, Bioinform..

[5]  Tobias Schreck,et al.  Interactive visual comparison of multiple trees , 2011, 2011 IEEE Conference on Visual Analytics Science and Technology (VAST).

[6]  G. Dunn,et al.  An Introduction to Mathematical Taxonomy , 1983 .

[7]  Clark F. Olson,et al.  Parallel Algorithms for Hierarchical Clustering , 1995, Parallel Comput..

[8]  Serdar Tasiran,et al.  TreeJuxtaposer: scalable tree comparison using Focus+Context with guaranteed visibility , 2003, ACM Trans. Graph..

[9]  Michael Kaufmann,et al.  Fixed parameter algorithms for one-sided crossing minimization revisited , 2003, J. Discrete Algorithms.

[10]  Katherine St. John,et al.  Untangling Tanglegrams: Comparing Trees by Their Drawings , 2009, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[11]  D. Bryant Building trees, hunting for trees, and comparing trees : theory and methods in phylogenetic analysis , 1997 .

[12]  Sean R. Eddy,et al.  ATV: display and manipulation of annotated phylogenetic , 2001, Bioinform..

[13]  Erich Bornberg-Bauer,et al.  TreeWiz: interactive exploration of huge trees , 2002, Bioinform..

[14]  Tim Dwyer,et al.  Optimal Leaf Ordering for Two and a Half Dimensional Phylogenetic Tree Visualisation , 2004, InVis.au.

[15]  Shigeo Abe DrEng Pattern Classification , 2001, Springer London.

[16]  Abdullah Zawawi Talib,et al.  Display-based approaches for Phylogenetic tree visualisation , 2010, 2010 International Conference on Distributed Frameworks for Multimedia Applications.

[17]  William B. Cowan,et al.  Human Perception of Laid-Out Graphs , 1998, Graph Drawing.

[18]  D. Robinson Comparison of labeled trees with valency three , 1971 .

[19]  Che-Lun Hung,et al.  Open Reading Frame Phylogenetic Analysis on the Cloud , 2013, International journal of genomics.

[20]  Nina Amenta,et al.  Case study: visualizing sets of evolutionary trees , 2002, IEEE Symposium on Information Visualization, 2002. INFOVIS 2002..

[21]  Paul R. Calder,et al.  Visualising phylogenetic trees , 2006, AUIC.

[22]  S. Balaji,et al.  PALI: a database of alignments and phylogeny of homologous protein structures , 2001, Bioinform..

[23]  Savrina F. Carrizo Phylogenetic Trees: An Information Visualisation Perspective , 2004, APBC.

[24]  D. Maddison,et al.  Mesquite: a modular system for evolutionary analysis. Version 2.6 , 2009 .

[25]  Abdullah Zawawi Talib,et al.  A New Framework for Phylogenetic Tree Visualization , 2011, IVIC.

[26]  Vladimir Makarenkov,et al.  T-REX: reconstructing and visualizing phylogenetic trees and reticulation networks , 2001, Bioinform..

[27]  Alexander Wolff,et al.  Drawing (Complete) Binary Tanglegrams , 2010, Algorithmica.