A distance metric for a class of tree-sibling phylogenetic networks

Abstract

Motivation: The presence of reticulate evolutionary events in phylogenies turn phylogenetic trees into phylogenetic networks. These events imply in particular that there may exist multiple evolutionary paths from a non-extant species to an extant one, and this multiplicity makes the comparison of phylogenetic networks much more difficult than the comparison of phylogenetic trees. In fact, all attempts to define a sound distance measure on the class of all phylogenetic networks have failed so far. Thus, the only practical solutions have been either the use of rough estimates of similarity (based on comparison of the trees embedded in the networks), or narrowing the class of phylogenetic networks to a certain class where such a distance is known and can be efficiently computed. The first approach has the problem that one may identify two networks as equivalent, when they are not; the second one has the drawback that there may not exist algorithms to reconstruct such networks from biological sequences.Results: We present in this article a distance measure on the class of semi-binary tree-sibling time consistent phylogenetic networks, which generalize tree-child time consistent phylogenetic networks, and thus also galled-trees. The practical interest of this distance measure is 2-fold: it can be computed in polynomial time by means of simple algorithms, and there also exist polynomial-time algorithms for reconstructing networks of this class from DNA sequence data.Availability: The Perl package , included in the BioPerl bundle, implements many algorithms on phylogenetic networks, including the computation of the distance presented in this article.Contact: gabriel.cardona@uib.esSupplementary information: Some counterexamples, proofs of the results not included in this article, and some computational experiments are available at Bioinformatics online.

Regular Networks Can be Uniquely Constructed from Their Trees

“…It is commonly assumed that the networks are rooted acyclic digraphs [23], [16], [17], [15]. Restrictions that appear tractable and yield interesting results include time consistency [16], [7], roughly that the parents of a hybrid be contemporaneous. Others include restrictions on the children of vertices, for example tree-child networks [6] or tree-sibling networks [7].…”

“…Restrictions that appear tractable and yield interesting results include time consistency [16], [7], roughly that the parents of a hybrid be contemporaneous. Others include restrictions on the children of vertices, for example tree-child networks [6] or tree-sibling networks [7]. Certain unique reconstructions for normal networks are given in [25].…”

Properties of Normal Phylogenetic Networks

“…If this condition were true for all U and v, then from knowledge of N and U = E(i), we could always pinpoint the unique vertex v where the character i originated, since U ∈ gc(v). Even in the simple example of Figure 3, however, this strong condition does not hold since U = {3} is in both gc (13) and gc (3); and similarly U = {6} is in both gc(15) and gc (6).…”

“…In normal networks, every vertex not in X has a child which is not a hybrid vertex. Related restrictions on networks include the "tree-sibling" networks [18], [10], and [6].…”

Evolutionary Phylogenetic Networks: Models and Issues

“…Recently, several results have appeared on measures for comparing phylogenetic network topologies and quantifying their dissimilarities; we refer the reader to [3,8,9,10,11,14,15,70,76,79]. Further, some proposals have been made on representing phylogenetic networks for I/O operations using an extended Newick, or eNewick, format; e.g., see [12,13,71,101].…”