508 research outputs found
A New Quartet Tree Heuristic for Hierarchical Clustering
We consider the problem of constructing an an optimal-weight tree from the
3*(n choose 4) weighted quartet topologies on n objects, where optimality means
that the summed weight of the embedded quartet topologiesis optimal (so it can
be the case that the optimal tree embeds all quartets as non-optimal
topologies). We present a heuristic for reconstructing the optimal-weight tree,
and a canonical manner to derive the quartet-topology weights from a given
distance matrix. The method repeatedly transforms a bifurcating tree, with all
objects involved as leaves, achieving a monotonic approximation to the exact
single globally optimal tree. This contrasts to other heuristic search methods
from biological phylogeny, like DNAML or quartet puzzling, which, repeatedly,
incrementally construct a solution from a random order of objects, and
subsequently add agreement values.Comment: 22 pages, 14 figure
A Fast Quartet Tree Heuristic for Hierarchical Clustering
The Minimum Quartet Tree Cost problem is to construct an optimal weight tree
from the weighted quartet topologies on objects, where
optimality means that the summed weight of the embedded quartet topologies is
optimal (so it can be the case that the optimal tree embeds all quartets as
nonoptimal topologies). We present a Monte Carlo heuristic, based on randomized
hill climbing, for approximating the optimal weight tree, given the quartet
topology weights. The method repeatedly transforms a dendrogram, with all
objects involved as leaves, achieving a monotonic approximation to the exact
single globally optimal tree. The problem and the solution heuristic has been
extensively used for general hierarchical clustering of nontree-like
(non-phylogeny) data in various domains and across domains with heterogeneous
data. We also present a greatly improved heuristic, reducing the running time
by a factor of order a thousand to ten thousand. All this is implemented and
available, as part of the CompLearn package. We compare performance and running
time of the original and improved versions with those of UPGMA, BioNJ, and NJ,
as implemented in the SplitsTree package on genomic data for which the latter
are optimized.
Keywords: Data and knowledge visualization, Pattern
matching--Clustering--Algorithms/Similarity measures, Hierarchical clustering,
Global optimization, Quartet tree, Randomized hill-climbing,Comment: LaTeX, 40 pages, 11 figures; this paper has substantial overlap with
arXiv:cs/0606048 in cs.D
Using ESTs for phylogenomics: Can one accurately infer a phylogenetic tree from a gappy alignment?
<p>Abstract</p> <p>Background</p> <p>While full genome sequences are still only available for a handful of taxa, large collections of partial gene sequences are available for many more. The alignment of partial gene sequences results in a multiple sequence alignment containing large gaps that are arranged in a staggered pattern. The consequences of this pattern of missing data on the accuracy of phylogenetic analysis are not well understood. We conducted a simulation study to determine the accuracy of phylogenetic trees obtained from gappy alignments using three commonly used phylogenetic reconstruction methods (Neighbor Joining, Maximum Parsimony, and Maximum Likelihood) and studied ways to improve the accuracy of trees obtained from such datasets.</p> <p>Results</p> <p>We found that the pattern of gappiness in multiple sequence alignments derived from partial gene sequences substantially compromised phylogenetic accuracy even in the absence of alignment error. The decline in accuracy was beyond what would be expected based on the amount of missing data. The decline was particularly dramatic for Neighbor Joining and Maximum Parsimony, where the majority of gappy alignments contained 25% to 40% incorrect quartets. To improve the accuracy of the trees obtained from a gappy multiple sequence alignment, we examined two approaches. In the first approach, alignment masking, potentially problematic columns and input sequences are excluded from from the dataset. Even in the absence of alignment error, masking improved phylogenetic accuracy up to 100-fold. However, masking retained, on average, only 83% of the input sequences. In the second approach, alignment subdivision, the missing data is statistically modelled in order to retain as many sequences as possible in the phylogenetic analysis. Subdivision resulted in more modest improvements to alignment accuracy, but succeeded in including almost all of the input sequences.</p> <p>Conclusion</p> <p>These results demonstrate that partial gene sequences and gappy multiple sequence alignments can pose a major problem for phylogenetic analysis. The concern will be greatest for high-throughput phylogenomic analyses, in which Neighbor Joining is often the preferred method due to its computational efficiency. Both approaches can be used to increase the accuracy of phylogenetic inference from a gappy alignment. The choice between the two approaches will depend upon how robust the application is to the loss of sequences from the input set, with alignment masking generally giving a much greater improvement in accuracy but at the cost of discarding a larger number of the input sequences.</p
Learning mutational graphs of individual tumour evolution from single-cell and multi-region sequencing data
Background. A large number of algorithms is being developed to reconstruct
evolutionary models of individual tumours from genome sequencing data. Most
methods can analyze multiple samples collected either through bulk multi-region
sequencing experiments or the sequencing of individual cancer cells. However,
rarely the same method can support both data types.
Results. We introduce TRaIT, a computational framework to infer mutational
graphs that model the accumulation of multiple types of somatic alterations
driving tumour evolution. Compared to other tools, TRaIT supports multi-region
and single-cell sequencing data within the same statistical framework, and
delivers expressive models that capture many complex evolutionary phenomena.
TRaIT improves accuracy, robustness to data-specific errors and computational
complexity compared to competing methods.
Conclusions. We show that the application of TRaIT to single-cell and
multi-region cancer datasets can produce accurate and reliable models of
single-tumour evolution, quantify the extent of intra-tumour heterogeneity and
generate new testable experimental hypotheses
The Binary Perfect Phylogeny with Persistent characters
The binary perfect phylogeny model is too restrictive to model biological
events such as back mutations. In this paper we consider a natural
generalization of the model that allows a special type of back mutation. We
investigate the problem of reconstructing a near perfect phylogeny over a
binary set of characters where characters are persistent: characters can be
gained and lost at most once. Based on this notion, we define the problem of
the Persistent Perfect Phylogeny (referred as P-PP). We restate the P-PP
problem as a special case of the Incomplete Directed Perfect Phylogeny, called
Incomplete Perfect Phylogeny with Persistent Completion, (refereed as IP-PP),
where the instance is an incomplete binary matrix M having some missing
entries, denoted by symbol ?, that must be determined (or completed) as 0 or 1
so that M admits a binary perfect phylogeny. We show that the IP-PP problem can
be reduced to a problem over an edge colored graph since the completion of each
column of the input matrix can be represented by a graph operation. Based on
this graph formulation, we develop an exact algorithm for solving the P-PP
problem that is exponential in the number of characters and polynomial in the
number of species.Comment: 13 pages, 3 figure
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