Spaces of phylogenetic networks from generalized nearest-neighbor interchange operations
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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.
KeywordsPhylogenetic networks Spaces of phylogenetic trees Phylogenetic tree metrics Nearest-neighbor interchange (NNI)
Mathematics Subject Classification05C90 92D15
The authors thank the organizers of the workshop “Utilizing Genealogical Phylogenetic Networks in Evolutionary Biology: Touching the Data” at the Lorentz Center (the Netherlands) where the ideas for this paper were first discussed. We also thank the anonymous referee for very careful reading and helpful suggestions on the first version of this manuscript.
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