73 research outputs found
A quadratic kernel for computing the hybridization number of multiple trees
It has recently been shown that the NP-hard problem of calculating the
minimum number of hybridization events that is needed to explain a set of
rooted binary phylogenetic trees by means of a hybridization network is
fixed-parameter tractable if an instance of the problem consists of precisely
two such trees. In this paper, we show that this problem remains
fixed-parameter tractable for an arbitrarily large set of rooted binary
phylogenetic trees. In particular, we present a quadratic kernel
A first step towards computing all hybridization networks for two rooted binary phylogenetic trees
Recently, considerable effort has been put into developing fast algorithms to
reconstruct a rooted phylogenetic network that explains two rooted phylogenetic
trees and has a minimum number of hybridization vertices. With the standard
approach to tackle this problem being combinatorial, the reconstructed network
is rarely unique. From a biological point of view, it is therefore of
importance to not only compute one network, but all possible networks. In this
paper, we make a first step towards approaching this goal by presenting the
first algorithm---called allMAAFs---that calculates all
maximum-acyclic-agreement forests for two rooted binary phylogenetic trees on
the same set of taxa.Comment: 21 pages, 5 figure
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 (NNI) 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
On the existence of funneled orientations for classes of rooted phylogenetic networks
Recently, there has been a growing interest in the relationships between
unrooted and rooted phylogenetic networks. In this context, a natural question
to ask is if an unrooted phylogenetic network U can be oriented as a rooted
phylogenetic network such that the latter satisfies certain structural
properties. In a recent preprint, Bulteau et al. claim that it is computational
hard to decide if U has a funneled (resp. funneled tree-child) orientation, for
when the internal vertices of U have degree at most 5. Unfortunately, the proof
of their funneled tree-child result appears to be incorrect. In this paper, we
present a corrected proof and show that hardness remains for other popular
classes of rooted phylogenetic networks such as funneled normal and funneled
reticulation-visible. Additionally, our results hold regardless of whether U is
rooted at an existing vertex or by subdividing an edge with the root
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