4,209 research outputs found
Spectral analysis and a closest tree method for genetic sequences
We describe a new method for estimating the evolutionary tree linking a collection of species from their aligned four-state genetic sequences. This method, which can be adapted to provide a branch-and-bound algorithm, is statistically consistent provided the sequences have evolved according to a standard stochastic model of nucleotide mutation. Our approach exploits a recent group-theoretic description of this model
Combinatorics of least squares trees
A recurring theme in the least squares approach to phylogenetics has been the
discovery of elegant combinatorial formulas for the least squares estimates of
edge lengths. These formulas have proved useful for the development of
efficient algorithms, and have also been important for understanding
connections among popular phylogeny algorithms. For example, the selection
criterion of the neighbor-joining algorithm is now understood in terms of the
combinatorial formulas of Pauplin for estimating tree length.
We highlight a phylogenetically desirable property that weighted least
squares methods should satisfy, and provide a complete characterization of
methods that satisfy the property. The necessary and sufficient condition is a
multiplicative four point condition that the the variance matrix needs to
satisfy. The proof is based on the observation that the Lagrange multipliers in
the proof of the Gauss--Markov theorem are tree-additive. Our results
generalize and complete previous work on ordinary least squares, balanced
minimum evolution and the taxon weighted variance model. They also provide a
time optimal algorithm for computation
On the optimality of the neighbor-joining algorithm
The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy
algorithm for finding the balanced minimum evolution (BME) tree associated to a
dissimilarity map. From this point of view, NJ is ``optimal'' when the
algorithm outputs the tree which minimizes the balanced minimum evolution
criterion. We use the fact that the NJ tree topology and the BME tree topology
are determined by polyhedral subdivisions of the spaces of dissimilarity maps
to study the optimality of the neighbor-joining
algorithm. In particular, we investigate and compare the polyhedral
subdivisions for . A key requirement is the measurement of volumes of
spherical polytopes in high dimension, which we obtain using a combination of
Monte Carlo methods and polyhedral algorithms. We show that highly unrelated
trees can be co-optimal in BME reconstruction, and that NJ regions are not
convex. We obtain the radius for neighbor-joining for and we
conjecture that the ability of the neighbor-joining algorithm to recover the
BME tree depends on the diameter of the BME tree
A parallel genetic algorithm for the Steiner Problem in Networks
This paper presents a parallel genetic algorithm to the
Steiner Problem in Networks. Several previous papers
have proposed the adoption of GAs and others
metaheuristics to solve the SPN demonstrating the
validity of their approaches. This work differs from them
for two main reasons: the dimension and the
characteristics of the networks adopted in the experiments
and the aim from which it has been originated. The reason
that aimed this work was namely to build a comparison
term for validating deterministic and computationally
inexpensive algorithms which can be used in practical
engineering applications, such as the multicast
transmission in the Internet. On the other hand, the large
dimensions of our sample networks require the adoption
of a parallel implementation of the Steiner GA, which is
able to deal with such large problem instances
Polyhedral geometry of Phylogenetic Rogue Taxa
It is well known among phylogeneticists that adding an extra taxon (e.g.
species) to a data set can alter the structure of the optimal phylogenetic tree
in surprising ways. However, little is known about this "rogue taxon" effect.
In this paper we characterize the behavior of balanced minimum evolution (BME)
phylogenetics on data sets of this type using tools from polyhedral geometry.
First we show that for any distance matrix there exist distances to a "rogue
taxon" such that the BME-optimal tree for the data set with the new taxon does
not contain any nontrivial splits (bipartitions) of the optimal tree for the
original data. Second, we prove a theorem which restricts the topology of
BME-optimal trees for data sets of this type, thus showing that a rogue taxon
cannot have an arbitrary effect on the optimal tree. Third, we construct
polyhedral cones computationally which give complete answers for BME rogue
taxon behavior when our original data fits a tree on four, five, and six taxa.
We use these cones to derive sufficient conditions for rogue taxon behavior for
four taxa, and to understand the frequency of the rogue taxon effect via
simulation.Comment: In this version, we add quartet distances and fix Table 4
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