114 research outputs found
Graph Triangulations and the Compatibility of Unrooted Phylogenetic Trees
We characterize the compatibility of a collection of unrooted phylogenetic
trees as a question of determining whether a graph derived from these trees ---
the display graph --- has a specific kind of triangulation, which we call
legal. Our result is a counterpart to the well known triangulation-based
characterization of the compatibility of undirected multi-state characters
Improved Lower Bounds on the Compatibility of Multi-State Characters
We study a long standing conjecture on the necessary and sufficient
conditions for the compatibility of multi-state characters: There exists a
function such that, for any set of -state characters, is
compatible if and only if every subset of characters of is
compatible. We show that for every , there exists an incompatible set
of -state
characters such that every proper subset of is compatible. Thus, for every .
This improves the previous lower bound of given by Meacham (1983),
and generalizes the construction showing that given by Habib and
To (2011). We prove our result via a result on quartet compatibility that may
be of independent interest: For every integer , there exists an
incompatible set of
quartets over
labels such that every proper subset of is compatible. We contrast this
with a result on the compatibility of triplets: For every , if is
an incompatible set of more than triplets over labels, then some
proper subset of is incompatible. We show this upper bound is tight by
exhibiting, for every , a set of triplets over taxa such
that is incompatible, but every proper subset of is compatible
Inferring Species Trees from Incongruent Multi-Copy Gene Trees Using the Robinson-Foulds Distance
We present a new method for inferring species trees from multi-copy gene
trees. Our method is based on a generalization of the Robinson-Foulds (RF)
distance to multi-labeled trees (mul-trees), i.e., gene trees in which multiple
leaves can have the same label. Unlike most previous phylogenetic methods using
gene trees, this method does not assume that gene tree incongruence is caused
by a single, specific biological process, such as gene duplication and loss,
deep coalescence, or lateral gene transfer. We prove that it is NP-hard to
compute the RF distance between two mul-trees, but it is easy to calculate the
generalized RF distance between a mul-tree and a singly-labeled tree. Motivated
by this observation, we formulate the RF supertree problem for mul-trees
(MulRF), which takes a collection of mul-trees and constructs a species tree
that minimizes the total RF distance from the input mul-trees. We present a
fast heuristic algorithm for the MulRF supertree problem. Simulation
experiments demonstrate that the MulRF method produces more accurate species
trees than gene tree parsimony methods when incongruence is caused by gene tree
error, duplications and losses, and/or lateral gene transfer. Furthermore, the
MulRF heuristic runs quickly on data sets containing hundreds of trees with up
to a hundred taxa.Comment: 16 pages, 11 figure
Extracting Conflict-free Information from Multi-labeled Trees
A multi-labeled tree, or MUL-tree, is a phylogenetic tree where two or more
leaves share a label, e.g., a species name. A MUL-tree can imply multiple
conflicting phylogenetic relationships for the same set of taxa, but can also
contain conflict-free information that is of interest and yet is not obvious.
We define the information content of a MUL-tree T as the set of all
conflict-free quartet topologies implied by T, and define the maximal reduced
form of T as the smallest tree that can be obtained from T by pruning leaves
and contracting edges while retaining the same information content. We show
that any two MUL-trees with the same information content exhibit the same
reduced form. This introduces an equivalence relation in MUL-trees with
potential applications to comparing MUL-trees. We present an efficient
algorithm to reduce a MUL-tree to its maximally reduced form and evaluate its
performance on empirical datasets in terms of both quality of the reduced tree
and the degree of data reduction achieved.Comment: Submitted in Workshop on Algorithms in Bioinformatics 2012
(http://algo12.fri.uni-lj.si/?file=wabi
A Simple Characterization of the Minimal Obstruction Sets for Three-State Perfect Phylogenies
Lam, Gusfield, and Sridhar (2009) showed that a set of three-state characters
has a perfect phylogeny if and only if every subset of three characters has a
perfect phylogeny. They also gave a complete characterization of the sets of
three three-state characters that do not have a perfect phylogeny. However, it
is not clear from their characterization how to find a subset of three
characters that does not have a perfect phylogeny without testing all triples
of characters. In this note, we build upon their result by giving a simple
characterization of when a set of three-state characters does not have a
perfect phylogeny that can be inferred from testing all pairs of characters
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