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

Alignment-Free Phylogenetic Reconstruction

14th Annual International Conference, RECOMB 2010, Lisbon, Portugal, April 25-28, 2010. ProceedingsWe introduce the first polynomial-time phylogenetic reconstruction algorithm under a model of sequence evolution allowing insertions and deletions (or indels). Given appropriate assumptions, our algorithm requires sequence lengths growing polynomially in the number of leaf taxa. Our techniques are distance-based and largely bypass the problem of multiple alignment

The matroid structure of representative triple sets and triple-closure computation

The closure cl (R) of a consistent set R of triples (rooted binary trees on three leaves) provides essential information about tree-like relations that are shown by any supertree that displays all triples in . In this contribution, we are concerned with representative triple sets, that is, subsets R' of R with cl (R') = cl . In this case, R' still contains all information on the tree structure implied by R, although R' might be significantly smaller. We show that representative triple sets that are minimal w.r.t. inclusion form the basis of a matroid. This in turn implies that minimal representative triple sets also have minimum cardinality. In particular, the matroid structure can be used to show that minimum representative triple sets can be computed in polynomial time with a simple greedy approach. For a given triple set R that “identifies” a tree, we provide an exact value for the cardinality of its minimum representative triple sets. In addition, we utilize the latter results to provide a novel and efficient method to compute the closure cl (R) of a consistent triple set R that improves the time complexity (R Lr 4) of the currently fastest known method proposed by Bryant and Steel (1995). In particular, if a minimum representative triple set for R is given, it can be shown that the time complexity to compute cl (R) can be improved by a factor up to R Lr . As it turns out, collections of quartets (unrooted binary trees on four leaves) do not provide a matroid structure, in general

Reconstructing phylogenies from noisy quartets in polynomial time with a high success probability

<p>Abstract</p> <p>Background</p> <p>In recent years, quartet-based phylogeny reconstruction methods have received considerable attentions in the computational biology community. Traditionally, the accuracy of a phylogeny reconstruction method is measured by simulations on synthetic datasets with known "true" phylogenies, while little theoretical analysis has been done. In this paper, we present a new model-based approach to measuring the accuracy of a quartet-based phylogeny reconstruction method. Under this model, we propose three efficient algorithms to reconstruct the "true" phylogeny with a high success probability.</p> <p>Results</p> <p>The first algorithm can reconstruct the "true" phylogeny from the input quartet topology set without quartet errors in <it>O</it>(<it>n</it>²) time by querying at most (<it>n </it>- 4) log(<it>n </it>- 1) quartet topologies, where <it>n </it>is the number of the taxa. When the input quartet topology set contains errors, the second algorithm can reconstruct the "true" phylogeny with a probability approximately 1 - <it>p </it>in <it>O</it>(<it>n</it>⁴log <it>n</it>) time, where <it>p </it>is the probability for a quartet topology being an error. This probability is improved by the third algorithm to approximately <inline-formula><m:math name="1748-7188-3-1-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:semantics><m:mrow><m:mfrac><m:mn>1</m:mn><m:mrow><m:mn>1</m:mn><m:mo>+</m:mo><m:msup><m:mi>q</m:mi><m:mn>2</m:mn></m:msup><m:mo>+</m:mo><m:mfrac><m:mn>1</m:mn><m:mn>2</m:mn></m:mfrac><m:msup><m:mi>q</m:mi><m:mn>4</m:mn></m:msup><m:mo>+</m:mo><m:mfrac><m:mn>1</m:mn><m:mrow><m:mn>16</m:mn></m:mrow></m:mfrac><m:msup><m:mi>q</m:mi><m:mn>5</m:mn></m:msup></m:mrow></m:mfrac></m:mrow><m:annotation encoding="MathType-MTEF"> MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSaaaeaacqaIXaqmaeaacqaIXaqmcqGHRaWkcqWGXbqCdaahaaqabeaacqaIYaGmaaGaey4kaSYaaSaaaeaacqaIXaqmaeaacqaIYaGmaaGaemyCae3aaWbaaeqabaGaeGinaqdaaiabgUcaRmaalaaabaGaeGymaedabaGaeGymaeJaeGOnaydaaiabdghaXnaaCaaabeqaaiabiwda1aaaaaaaaa@3D5A@</m:annotation></m:semantics></m:math></inline-formula>, where <inline-formula><m:math name="1748-7188-3-1-i2" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:semantics><m:mrow><m:mi>q</m:mi><m:mo>=</m:mo><m:mfrac><m:mi>p</m:mi><m:mrow><m:mn>1</m:mn><m:mo>−</m:mo><m:mi>p</m:mi></m:mrow></m:mfrac></m:mrow><m:annotation encoding="MathType-MTEF"> MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemyCaeNaeyypa0tcfa4aaSaaaeaacqWGWbaCaeaacqaIXaqmcqGHsislcqWGWbaCaaaaaa@3391@</m:annotation></m:semantics></m:math></inline-formula>, with running time of <it>O</it>(<it>n</it>⁵), which is at least 0.984 when <it>p </it>< 0.05.</p> <p>Conclusion</p> <p>The three proposed algorithms are mathematically guaranteed to reconstruct the "true" phylogeny with a high success probability. The experimental results showed that the third algorithm produced phylogenies with a higher probability than its aforementioned theoretical lower bound and outperformed some existing phylogeny reconstruction methods in both speed and accuracy.</p

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters