3,608 research outputs found
A Practical Algorithm for Reconstructing Level-1 Phylogenetic Networks
Recently much attention has been devoted to the construction of phylogenetic
networks which generalize phylogenetic trees in order to accommodate complex
evolutionary processes. Here we present an efficient, practical algorithm for
reconstructing level-1 phylogenetic networks - a type of network slightly more
general than a phylogenetic tree - from triplets. Our algorithm has been made
publicly available as the program LEV1ATHAN. It combines ideas from several
known theoretical algorithms for phylogenetic tree and network reconstruction
with two novel subroutines. Namely, an exponential-time exact and a greedy
algorithm both of which are of independent theoretical interest. Most
importantly, LEV1ATHAN runs in polynomial time and always constructs a level-1
network. If the data is consistent with a phylogenetic tree, then the algorithm
constructs such a tree. Moreover, if the input triplet set is dense and, in
addition, is fully consistent with some level-1 network, it will find such a
network. The potential of LEV1ATHAN is explored by means of an extensive
simulation study and a biological data set. One of our conclusions is that
LEV1ATHAN is able to construct networks consistent with a high percentage of
input triplets, even when these input triplets are affected by a low to
moderate level of noise
Reconstructing a phylogenetic level-1 network from quartets
We describe a method that will reconstruct an unrooted binary phylogenetic
level-1 network on n taxa from the set of all quartets containing a certain
fixed taxon, in O(n^3) time. We also present a more general method which can
handle more diverse quartet data, but which takes O(n^6) time. Both methods
proceed by solving a certain system of linear equations over GF(2).
For a general dense quartet set (containing at least one quartet on every
four taxa) our O(n^6) algorithm constructs a phylogenetic level-1 network
consistent with the quartet set if such a network exists and returns an (O(n^2)
sized) certificate of inconsistency otherwise. This answers a question raised
by Gambette, Berry and Paul regarding the complexity of reconstructing a
level-1 network from a dense quartet set
A Perl Package and an Alignment Tool for Phylogenetic Networks
Phylogenetic networks are a generalization of phylogenetic trees that allow
for the representation of evolutionary events acting at the population level,
like recombination between genes, hybridization between lineages, and lateral
gene transfer. While most phylogenetics tools implement a wide range of
algorithms on phylogenetic trees, there exist only a few applications to work
with phylogenetic networks, and there are no open-source libraries either.
In order to improve this situation, we have developed a Perl package that
relies on the BioPerl bundle and implements many algorithms on phylogenetic
networks. We have also developed a Java applet that makes use of the
aforementioned Perl package and allows the user to make simple experiments with
phylogenetic networks without having to develop a program or Perl script by
herself.
The Perl package has been accepted as part of the BioPerl bundle. It can be
downloaded from http://dmi.uib.es/~gcardona/BioInfo/Bio-PhyloNetwork.tgz. The
web-based application is available at http://dmi.uib.es/~gcardona/BioInfo/. The
Perl package includes full documentation of all its features.Comment: 5 page
Reconstructing phylogenetic level-1 networks from nondense binet and trinet sets
Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set T of binary binets or trinets over a taxon set X, and constructing such a network whenever it exists. We show that this is NP-hard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an O(3^{|X|} poly(|X|)) time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted 1 phylogenetic networks
Uniqueness, intractability and exact algorithms: reflections on level-k phylogenetic networks
Phylogenetic networks provide a way to describe and visualize evolutionary
histories that have undergone so-called reticulate evolutionary events such as
recombination, hybridization or horizontal gene transfer. The level k of a
network determines how non-treelike the evolution can be, with level-0 networks
being trees. We study the problem of constructing level-k phylogenetic networks
from triplets, i.e. phylogenetic trees for three leaves (taxa). We give, for
each k, a level-k network that is uniquely defined by its triplets. We
demonstrate the applicability of this result by using it to prove that (1) for
all k of at least one it is NP-hard to construct a level-k network consistent
with all input triplets, and (2) for all k it is NP-hard to construct a level-k
network consistent with a maximum number of input triplets, even when the input
is dense. As a response to this intractability we give an exact algorithm for
constructing level-1 networks consistent with a maximum number of input
triplets
On Computing the Maximum Parsimony Score of a Phylogenetic Network
Phylogenetic networks are used to display the relationship of different
species whose evolution is not treelike, which is the case, for instance, in
the presence of hybridization events or horizontal gene transfers. Tree
inference methods such as Maximum Parsimony need to be modified in order to be
applicable to networks. In this paper, we discuss two different definitions of
Maximum Parsimony on networks, "hardwired" and "softwired", and examine the
complexity of computing them given a network topology and a character. By
exploiting a link with the problem Multicut, we show that computing the
hardwired parsimony score for 2-state characters is polynomial-time solvable,
while for characters with more states this problem becomes NP-hard but is still
approximable and fixed parameter tractable in the parsimony score. On the other
hand we show that, for the softwired definition, obtaining even weak
approximation guarantees is already difficult for binary characters and
restricted network topologies, and fixed-parameter tractable algorithms in the
parsimony score are unlikely. On the positive side we show that computing the
softwired parsimony score is fixed-parameter tractable in the level of the
network, a natural parameter describing how tangled reticulate activity is in
the network. Finally, we show that both the hardwired and softwired parsimony
score can be computed efficiently using Integer Linear Programming. The
software has been made freely available
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