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

A list of parameterized problems in bioinformatics

In this report we present a list of problems that originated in bionformatics. Our aim is to collect information on such problems that have been analyzed from the point of view of Parameterized Complexity. For every problem we give its definition and biological motivation together with known complexity results.Postprint (published version

A Comparison of Two Versions of Modified Mercalli Intensity for Earthquake Exposure Assessment

The U.S. Geological Survey conducted an earthquake exposure assessment for the State of Washington using peak ground acceleration (PGA) shaking from the USGS ShakeMap Project grouped to approximate Modified Mercalli Intensity (MMI) classes. Since ShakeMap datasets also have data representing official MMI classes, a companion exposure assessment was performed to determine whether MMI-grouped PGA data and official MMI data are interchangeable. Along with the exposure assessment, a spatial sampling process was used to further check how MMI-grouped PGA and official MMI data compared. Results indicated that significant variations existed spatially between the two ShakeMap datasets; generalizations by ShakeMap in creating their publically available data as well as the formulae ShakeMap\u27s model uses to calculate MMI from PGA and peak ground velocity generally explain the variations. Though the two datasets differ significantly spatially, these results simply demonstrated that MMI-grouped PGA and official MMI are not interchangeable and did not identify one dataset as more appropriate than another for exposure assessments

The development and application of metaheuristics for problems in graph theory: A computational study

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.It is known that graph theoretic models have extensive application to real-life discrete optimization problems. Many of these models are NP-hard and, as a result, exact methods may be impractical for large scale problem instances. Consequently, there is a great interest in developing e±cient approximate methods that yield near-optimal solutions in acceptable computational times. A class of such methods, known as metaheuristics, have been proposed with success. This thesis considers some recently proposed NP-hard combinatorial optimization problems formulated on graphs. In particular, the min- imum labelling spanning tree problem, the minimum labelling Steiner tree problem, and the minimum quartet tree cost problem, are inves- tigated. Several metaheuristics are proposed for each problem, from classical approximation algorithms to novel approaches. A compre- hensive computational investigation in which the proposed methods are compared with other algorithms recommended in the literature is reported. The results show that the proposed metaheuristics outper- form the algorithms recommended in the literature, obtaining optimal or near-optimal solutions in short computational running times. In addition, a thorough analysis of the implementation of these methods provide insights for the implementation of metaheuristic strategies for other graph theoretic problems

Dual-Aspect Meter: A Theory of Metrical Consonance, Dissonance, Weight, and Variety

The core argument of the dissertation emerges as a synthesis of ideas introduced in the first four chapters. Resonances with recent metrical theories are explored in chapter 1. Chapter 2 problematizes modern and historical theories through a phenomenological examination of meter and phenomenal accent in a few baroque sarabandes. Meter in these pieces is shown to involve entrainment to both a beat hierarchy and a recurrent weight profile, clarifying that metrical dissonance is fundamentally an expressive category, not a phenomenal category. Chapters 3 and 4 articulate a theory of weight, reviewing and refining phenomenal-accent theory, developing a notion of musical mass, and offering a simple preference-rule system for the comparison of weight between musical moments. Chapter 5 synthesizes the arguments of chapters 2–4, positing a general theory of metrical experience situated on a spectrum of perceived rhythmic consistency. I argue that a listener’s metrical attitude necessarily involves entrainment to or projection of both beat hierarchy and weight profile. The notion of dual entrainment developed in chapter 2 is thus supplemented by single entrainment and dual projection, all of which are categories of dual-aspect meter. The theory’s analytical and hermeneutic utility is demonstrated through a combined metrical and narrative analysis in appendix 1

Inferring Processes of Coevolutionary Diversification in a Community of Panamanian Strangler Figs and Associated Pollinating Wasps

The fig and pollinator wasp obligate mutualism is diverse (~750 described species), ecologically important, and ancient (~80-90 Ma), providing model systems for generating and testing many questions in evolution and ecology. Once thought to be a prime example of strict one-to-one cospeciation, current thinking suggests that genera of pollinator wasps coevolve with corresponding subsections of figs, but the degree to which cospeciation or other processes contributes to the association at finer scales is unclear. Here we use genome-wide sequence data from a community of Panamanian strangler figs (Ficus subgenus Urostigma, section Americana) and associated fig wasp pollinators (Pegoscapus spp.) to infer the process of coevolutionary diversification in this obligate mutualism. Using a model-based approach adapted from the study of gene family evolution, our results indicate pervasive and ongoing host switching of pollinator wasps at this fine phylogenetic and regional scale. Although the model estimates a modest amount of cospeciation, simulations reveal this signal to be consistent with levels of co-association expected under a model of free host switching. Our findings provide an outline for testing how ecological and evolutionary processes can be modeled to evaluate the history of association of interacting lineages in a phylogenetic framework