805 research outputs found
Do branch lengths help to locate a tree in a phylogenetic network?
Phylogenetic networks are increasingly used in evolutionary biology to
represent the history of species that have undergone reticulate events such as
horizontal gene transfer, hybrid speciation and recombination. One of the most
fundamental questions that arise in this context is whether the evolution of a
gene with one copy in all species can be explained by a given network. In
mathematical terms, this is often translated in the following way: is a given
phylogenetic tree contained in a given phylogenetic network? Recently this tree
containment problem has been widely investigated from a computational
perspective, but most studies have only focused on the topology of the phylo-
genies, ignoring a piece of information that, in the case of phylogenetic
trees, is routinely inferred by evolutionary analyses: branch lengths. These
measure the amount of change (e.g., nucleotide substitutions) that has occurred
along each branch of the phylogeny. Here, we study a number of versions of the
tree containment problem that explicitly account for branch lengths. We show
that, although length information has the potential to locate more precisely a
tree within a network, the problem is computationally hard in its most general
form. On a positive note, for a number of special cases of biological
relevance, we provide algorithms that solve this problem efficiently. This
includes the case of networks of limited complexity, for which it is possible
to recover, among the trees contained by the network with the same topology as
the input tree, the closest one in terms of branch lengths
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 practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees
Reticulate events play an important role in determining evolutionary
relationships. The problem of computing the minimum number of such events to
explain discordance between two phylogenetic trees is a hard computational
problem. Even for binary trees, exact solvers struggle to solve instances with
reticulation number larger than 40-50. Here we present CycleKiller and
NonbinaryCycleKiller, the first methods to produce solutions verifiably close
to optimality for instances with hundreds or even thousands of reticulations.
Using simulations, we demonstrate that these algorithms run quickly for large
and difficult instances, producing solutions that are very close to optimality.
As a spin-off from our simulations we also present TerminusEst, which is the
fastest exact method currently available that can handle nonbinary trees: this
is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All
three methods are based on extensions of previous theoretical work and are
publicly available. We also apply our methods to real data
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