133 research outputs found
An analytical comparison of coalescent-based multilocus methods: The three-taxon case
Incomplete lineage sorting (ILS) is a common source of gene tree incongruence
in multilocus analyses. A large number of methods have been developed to infer
species trees in the presence of ILS. Here we provide a mathematical analysis
of several coalescent-based methods. Our analysis is performed on a three-taxon
species tree and assumes that the gene trees are correctly reconstructed along
with their branch lengths
Alignment-free phylogenetic reconstruction: Sample complexity via a branching process analysis
We present an efficient phylogenetic reconstruction algorithm allowing
insertions and deletions which provably achieves a sequence-length requirement
(or sample complexity) growing polynomially in the number of taxa. Our
algorithm is distance-based, that is, it relies on pairwise sequence
comparisons. More importantly, our approach largely bypasses the difficult
problem of multiple sequence alignment.Comment: Published in at http://dx.doi.org/10.1214/12-AAP852 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Phylogenetic mixtures: Concentration of measure in the large-tree limit
The reconstruction of phylogenies from DNA or protein sequences is a major
task of computational evolutionary biology. Common phenomena, notably
variations in mutation rates across genomes and incongruences between gene
lineage histories, often make it necessary to model molecular data as
originating from a mixture of phylogenies. Such mixed models play an
increasingly important role in practice. Using concentration of measure
techniques, we show that mixtures of large trees are typically identifiable. We
also derive sequence-length requirements for high-probability reconstruction.Comment: Published in at http://dx.doi.org/10.1214/11-AAP837 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Phase transition in the sample complexity of likelihood-based phylogeny inference
Reconstructing evolutionary trees from molecular sequence data is a
fundamental problem in computational biology. Stochastic models of sequence
evolution are closely related to spin systems that have been extensively
studied in statistical physics and that connection has led to important
insights on the theoretical properties of phylogenetic reconstruction
algorithms as well as the development of new inference methods. Here, we study
maximum likelihood, a classical statistical technique which is perhaps the most
widely used in phylogenetic practice because of its superior empirical
accuracy.
At the theoretical level, except for its consistency, that is, the guarantee
of eventual correct reconstruction as the size of the input data grows, much
remains to be understood about the statistical properties of maximum likelihood
in this context. In particular, the best bounds on the sample complexity or
sequence-length requirement of maximum likelihood, that is, the amount of data
required for correct reconstruction, are exponential in the number, , of
tips---far from known lower bounds based on information-theoretic arguments.
Here we close the gap by proving a new upper bound on the sequence-length
requirement of maximum likelihood that matches up to constants the known lower
bound for some standard models of evolution.
More specifically, for the -state symmetric model of sequence evolution on
a binary phylogeny with bounded edge lengths, we show that the sequence-length
requirement behaves logarithmically in when the expected amount of mutation
per edge is below what is known as the Kesten-Stigum threshold. In general, the
sequence-length requirement is polynomial in . Our results imply moreover
that the maximum likelihood estimator can be computed efficiently on randomly
generated data provided sequences are as above.Comment: To appear in Probability Theory and Related Field
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