title: On the quirks of maximum parsimony and likelihood on phylogenetic networks.
abstract: Maximum parsimony is one of the most frequently-discussed tree reconstruction methods in phylogenetic estimation. However, in recent years it has become more and more apparent that phylogenetic trees are often not sufficient to describe evolution accurately. For instance, processes like hybridization or lateral gene transfer that are commonplace in many groups of organisms and result in mosaic patterns of relationships cannot be represented by a single phylogenetic tree. This is why phylogenetic networks, which can display such events, are becoming of more and more interest in phylogenetic research. It is therefore necessary to extend concepts like maximum parsimony from phylogenetic trees to networks. Several suggestions for possible extensions can be found in recent literature, for instance the softwired and the hardwired parsimony concepts. In this paper, we analyze the so-called big parsimony problem under these two concepts, i.e. we investigate maximum parsimonious networks and analyze their properties. In particular, we show that finding a softwired maximum parsimony network is possible in polynomial time. We also show that the set of maximum parsimony networks for the hardwired definition always contains at least one phylogenetic tree. Lastly, we investigate some parallels of parsimony to different likelihood concepts on phylogenetic networks.
authors.affiliation: Statistics New Zealand, Wellington, New Zealand. Electronic address: chris.bryant@stats.govt.nz.
authors.forename: Christopher
authors.initials: C
authors.lastname: Bryant
authors.affiliation: Department for Mathematics and Computer Science, Ernst Moritz Arndt University, Greifswald, Germany. Electronic address: email@mareikefischer.de.
authors.forename: Mareike
authors.initials: M
authors.lastname: Fischer
authors.affiliation: Department of Computer Science, University of Auckland, New Zealand. Electronic address: s.linz@auckland.ac.nz.
authors.forename: Simone
authors.initials: S
authors.lastname: Linz
authors.affiliation: School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand. Electronic address: charles.semple@canterbury.ac.nz.
authors.forename: Charles
authors.initials: C
authors.lastname: Semple
mesh_terms: D000818:Animals; D005075:Biological Evolution; D053263:Gene Regulatory Networks; D006801:Humans; D016013:Likelihood Functions; D008957:Models, Genetic; D010802:Phylogeny
keywords: Hardwired; Likelihood; Parsimony; Phylogenetic networks; Softwired