Spaces of phylogenetic networks from generalized nearest-neighbor interchange operations

Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are used to represent the evolution of species which have undergone reticulate evolution. In this paper we consider spaces of such networks defined by some novel local operations that we introduce for converting one phylogenetic network into another. These operations are modeled on the well-studied nearest-neighbor interchange operations on phylogenetic trees, and lead to natural generalizations of the tree spaces that have been previously associated to such operations. We present several results on spaces of some relatively simple networks, called level-1 networks, including the size of the neighborhood of a fixed network, and bounds on the diameter of the metric defined by taking the smallest number of operations required to convert one network into another. We expect that our results will be useful in the development of methods for systematically searching for optimal phylogenetic networks using, for example, likelihood and Bayesian approaches.

[1]  Francesc Rosselló,et al.  All that Glisters is not Galled , 2009, Mathematical biosciences.

[2]  M. Steel,et al.  Unicyclic Networks: Compatibility and Enumeration , 2006, TCBB.

[3]  Charles Semple,et al.  On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance , 2005 .

[4]  L. Nakhleh,et al.  A Metric on the Space of Reduced Phylogenetic Networks , 2010, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[5]  R. Radice,et al.  A Bayesian Approach to Phylogenetic Networks , 2011 .

[6]  Philippe Gambette,et al.  On encodings of phylogenetic networks of bounded level , 2009, Journal of mathematical biology.

[7]  Yang Ding,et al.  On agreement forests , 2011, J. Comb. Theory, Ser. A.

[8]  J. Tromp,et al.  On the nearest neighbour interchange distance between evolutionary trees. , 1996, Journal of theoretical biology.

[9]  M. Steel,et al.  Subtree Transfer Operations and Their Induced Metrics on Evolutionary Trees , 2001 .

[10]  Christophe Paul,et al.  The Structure of Level-k Phylogenetic Networks , 2009, CPM.

[11]  V Moulton,et al.  Likelihood analysis of phylogenetic networks using directed graphical models. , 2000, Molecular biology and evolution.

[12]  T. Tuller,et al.  Inferring phylogenetic networks by the maximum parsimony criterion: a case study. , 2006, Molecular biology and evolution.

[13]  Sagi Snir,et al.  Maximum likelihood of phylogenetic networks , 2006, Bioinform..

[14]  Kevin J. Liu,et al.  Maximum likelihood inference of reticulate evolutionary histories , 2014, Proceedings of the National Academy of Sciences.

[15]  V. Moulton,et al.  Bounding the Number of Hybridisation Events for a Consistent Evolutionary History , 2005, Journal of mathematical biology.

[16]  Daniel H. Huson,et al.  Phylogenetic Networks: Contents , 2010 .

[17]  B. Dasgupta,et al.  On distances between phylogenetic trees , 1997, SODA '97.

[18]  Bernard M. E. Moret,et al.  Phylogenetic Inference , 2011, Encyclopedia of Parallel Computing.

[19]  Steven Skiena,et al.  Sorting with Fixed-length Reversals , 1996, Discret. Appl. Math..

[20]  Dan Gusfield,et al.  ReCombinatorics: The Algorithmics of Ancestral Recombination Graphs and Explicit Phylogenetic Networks , 2014 .

[21]  Leo van Iersel,et al.  A Practical Algorithm for Reconstructing Level-1 Phylogenetic Networks , 2009, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[22]  G. Moore,et al.  An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets. , 1973, Journal of theoretical biology.

[23]  Vincent Moulton,et al.  A parsimony-based metric for phylogenetic trees , 2015, Adv. Appl. Math..

[24]  Katharina T. Huber,et al.  Encoding and Constructing 1-Nested Phylogenetic Networks with Trinets , 2012, Algorithmica.

[25]  Katherine St. John,et al.  Hamiltonian Walks of Phylogenetic Treespaces , 2013, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[26]  Christophe Paul,et al.  Quartets and Unrooted phylogenetic Networks , 2012, J. Bioinform. Comput. Biol..

[27]  Louis J. Billera,et al.  Geometry of the Space of Phylogenetic Trees , 2001, Adv. Appl. Math..

[28]  R. Pendavingh,et al.  Reconstructing a Phylogenetic Level-1 Network from Quartets , 2013, Bulletin of Mathematical Biology.

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

[30]  Anne-Mieke Vandamme,et al.  The Phylogenetic Handbook: A Practical Approach to Phylogenetic Analysis and Hypothesis Testing , 2009 .

[31]  W. H. Day.  Properties of the nearest neighbor interchange metric for trees of small size , 1983 .

[32]  Wing-Kin Sung,et al.  Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network , 2006, SIAM J. Comput..

[33]  Gabriel Cardona,et al.  Comparison of Tree-Child Phylogenetic Networks , 2009, TCBB.

[34]  Daniel H. Huson,et al.  Phylogenetic Networks - Concepts, Algorithms and Applications , 2011 .

[35]  Taoyang Wu,et al.  On the Neighborhoods of Trees , 2013, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[36]  Gabriel Cardona,et al.  Comparison of Galled Trees , 2009, IEEE/ACM Transactions on Computational Biology and Bioinformatics.