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Mathematics of evolution and phylogeny /

"This book considers evolution at different scales. The focus is on the mathematical and computational tools and concepts, which form an essential basis of evolutionary studies, indicate their limitations, and give them orientation"--Provided by publisher

Detalles Bibliográficos
Clasificación:	Libro Electrónico
Otros Autores:	Gascuel, Olivier, 1956-
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Oxford ; New York : Oxford University Press, 2005.
Temas:	Evolution (Biology) > Mathematics. Phylogeny > Mathematics. Évolution (Biologie) > Mathématiques. Phylogenèse > Mathématiques. SCIENCE > Life Sciences > Biological Diversity. Mathematics
Acceso en línea:	Texto completo

Tabla de Contenidos:

List of Contributors
1 The minimum evolution distance-based approach of phylogenetic inference
1.1 Introduction
1.2 Tree metrics
1.2.1 Notation and basics
1.2.2 Three-point and four-point conditions
1.2.3 Linear decomposition into split metrics
1.2.4 Topological matrices
1.2.5 Unweighted and balanced averages
1.2.6 Alternate balanced basis for tree metrics
1.2.7 Tree metric inference in phylogenetics
1.3 Edge and tree length estimation
1.3.1 The LS approach
1.3.2 Edge length formulae
1.3.3 Tree length formulae
1.3.4 The positivity constraint
1.3.5 The balanced scheme of Pauplin
1.3.6 Semple and Steel combinatorial interpretation
1.3.7 BME: a WLS interpretation
1.4 The agglomerative approach
1.4.1 UPGMA and WPGMA
1.4.2 NJ as a balanced minimum evolution algorithm
1.4.3 Other agglomerative algorithms
1.5 Iterative topology searching and tree building
1.5.1 Topology transformations.; 1.5.2 A fast algorithm for NNIs with OLS
1.5.3 A fast algorithm for NNIs with BME
1.5.4 Iterative tree building with OLS
1.5.5 From OLS to BME
1.6 Statistical consistency
1.6.1 Positive results
1.6.2 Negative results
1.6.3 Atteson's safety radius analysis
1.7 Discussion
Acknowledgements
2 Likelihood calculation in molecular phylogenetics
2.1 Introduction
2.2 Markov models of sequence evolution
2.2.1 Independence of sites
2.2.2 Setting up the basic model
2.2.3 Stationary distribution
2.2.4 Time reversibility
2.2.5 Rate of mutation
2.2.6 Probability of sequence evolution on a tree
2.3 Likelihood calculation: the basic algorithm
2.4 Likelihood calculation: improved models
2.4.1 Choosing the rate matrix
2.4.2 Among site rate variation
2.4.3 Site-specific rate variation
2.4.4 Correlated evolution between sites
2.5 Optimizing parameters
2.5.1 Optimizing continuous parameters
2.5.2 Searching for the optimal tree.; 2.5.3 Alternative search strategies
2.6 Consistency of the likelihood approach
2.6.1 Statistical consistency
2.6.2 Identifiability of the phylogenetic models
2.6.3 Coping with errors in the model
2.7 Likelihood ratio tests
2.7.1 When to use the asymptotic x2 distribution
2.7.2 Testing a subset of real parameters
2.7.3 Testing parameters with boundary conditions
2.7.4 Testing trees
2.8 Concluding remarks
Acknowledgements
3 Bayesian inference in molecular phylogenetics
3.1 The likelihood function and maximum likelihood estimates
3.2 The Bayesian paradigm
3.3 Prior
3.4 Markov chain Monte Carlo
3.4.1 Metropolis-Hastings algorithm
3.4.2 Single-component Metropolis-Hastings algorithm
3.4.3 Gibbs sampler
3.4.4 Metropolis-coupled MCMC
3.5 Simple moves and their proposal ratios
3.5.1 Sliding window using uniform proposal
3.5.2 Sliding window using normally distributed proposal.; 3.5.3 Sliding window using normal proposal in multidimensions
3.5.4 Proportional shrinking and expanding
3.6 Monitoring Markov chains and processing output
3.6.1 Diagnosing and validating MCMC algorithms
3.6.2 Gelman and Rubin's potential scale reduction statistic
3.6.3 Processing output
3.7 Applications to molecular phylogenetics
3.7.1 Estimation of phylogenies
3.7.2 Estimation of species divergence times
3.8 Conclusions and perspectives
Acknowledgements
4 Statistical approach to tests involving phylogenies
4.1 The statistical approach to phylogenetic inference
4.2 Hypotheses testing
4.2.1 Null and alternative hypotheses
4.2.2 Test statistics
4.2.3 Significance and power
4.2.4 Bayesian hypothesis testing
4.2.5 Questions posed as function of the tree parameter
4.2.6 Topology of treespace
4.2.7 The data
4.2.8 Statistical paradigms
4.2.9 Distributions on treespace
4.3 Different types of tests involving phylogenies.; 4.3.1 Testing t1 versus t2
4.3.2 Conditional tests
4.3.3 Modern Bayesian hypothesis testing
4.3.4 Bootstrap tests
4.4 Non-parametric multivariate hypothesis testing
4.4.1 Multivariate con.dence regions
4.5 Conclusions: there are many open problems
Acknowledgements
5 Mixture models in phylogenetic inference
5.1 Introduction: models of gene-sequence evolution
5.2 Mixture models
5.3 Defining mixture models
5.3.1 Partitioning and mixture models
5.3.2 Discrete-gamma model as a mixture model
5.3.3 Combining rate and pattern-heterogeneity
5.4 Digression: Bayesian phylogenetic inference
5.4.1 Bayesian inference of trees via MCMC
5.5 A mixture model combining rate and pattern-heterogeneity
5.5.1 Selected simulation results
5.6 Application of the mixture model to inferring the phylogeny of the mammals
5.6.1 Model testing
5.7 Results
5.7.1 How many rate matrices to include in the mixture model?; 5.7.2 Inferring the tree of mammals
5.7.3 Tree lengths
5.8 Discussion
Acknowledgements.
6 Hadamard conjugation: an analytic tool for phylogenetics
6.1 Introduction
6.2 Hadamard conjugation for two sequences
6.2.1 Hadamard matrices-a brief introduction
6.3 Some symmetric models of nucleotide substitution
6.3.1 Kimura's 3-substitution types model
6.3.2 Other symmetric models
6.4 Hadamard conjugation-Neyman model
6.4.1 Neyman model on three sequences
6.4.2 Neyman model on four sequences
6.4.3 Neyman model on n + 1 sequences
6.5 Applications: using the Neyman model
6.5.1 Rate variation
6.5.2 Invertibility
6.5.3 Invariants
6.5.4 Closest tree
6.5.5 Maximum parsimony
6.5.6 Parsimony inconsistency, Felsenstein's example
6.5.7 Parsimony inconsistency, molecular clock
6.5.8 Maximum likelihood under the Neyman model
6.6 Kimura's 3-substitution types model
6.6.1 One edge
6.6.2 K3ST for n + 1 sequences.; 6.7 Other applications and perspectives
7 Phylogenetic networks
7.1 Introduction
7.2 Median networks
7.3 Visual complexity of median networks
7.4 Consensus networks
7.5 Treelikeness
7.6 Deriving phylogenetic networks from distances
7.7 Neighbour-net
7.8 Discussion
Acknowledgements
8 Reconstructing the duplication history of tandemly repeated sequences
8.1 Introduction
8.2 Repeated sequences and duplication model
8.2.1 Di.erent categories of repeated sequences
8.2.2 Biological model and assumptions
8.2.3 Duplication events, duplication histories, and duplication trees
8.2.4 The human T-cell receptor Gamma genes
8.2.5 Other data sets, applicability of the model
8.3 Mathematical model and properties
8.3.1 Notation
8.3.2 Root position
8.3.3 Recursive de.nition of rooted and unrooted duplication trees
8.3.4 From phylogenies with ordered leaves to duplication trees.; 8.3.5 Topñdown approach and leftñright properties of rooted duplication trees
8.3.6 Counting duplication histories
8.3.7 Counting simple event duplication trees
8.3.8 Counting (unrestricted) duplication trees
8.4 Inferring duplication trees from sequence data
8.4.1 Preamble
8.4.2 Computational hardness of duplication tree inference
8.4.3 Distance-based inference of simple event duplication trees
8.4.4 A simple parsimony heuristic to infer unrestricted duplication trees
8.4.5 Simple distance-based heuristic to infer unrestricted duplication trees
8.5 Simulation comparison and prospects
Acknowledgements
9 Conserved segment statistics and rearrangement inferences in comparative genomics
9.1 Introduction
9.2 Genetic (recombinational) distance
9.3 Gene counts
9.4 The inference problem
9.5 What can we infer from conserved segments?
9.6 Rearrangement algorithms
9.7 Loss of signal
9.8 From gene order to genomic sequence.; 9.8.1 The Pevzner-Tesler approach
9.8.2 The re-use statistic r
9.8.3 Simulating rearrangement inference with a block-size threshold
9.8.4 A model for breakpoint re-use
9.8.5 A measure of noise?
9.9 Between the blocks
9.9.1 Fragments
9.10 Conclusions
Acknowledgements
10 The inversion distance problem
10.1 Introduction and biological background
10.2 De.nitions and examples
10.3 Anatomy of a signed permutation
10.3.1 Elementary intervals and cycles
10.3.2 E.ects of an inversion on elementary intervals and cycles
10.3.3 Components
10.3.4 Effects of an inversion on components
10.4 The HannenhalliñPevzner duality theorem
10.4.1 Sorting oriented components
10.4.2 Computing the inversion distance
10.5 Algorithms
10.6 Conclusion
Glossary
11 Genome rearrangements with gene families
11.1 Introduction
11.2 The formal representation of the genome
11.3 Genome rearrangement
11.4 Multigene families.; 11.5 Algorithms and models
11.5.1 Exemplar distance
11.5.2 Phylogenetic analysis
11.6 Genome duplication
11.6.1 Formalizing the problem
11.6.2 Methodology
11.6.3 Analysing the yeast genome
11.6.4 An application on a circular genome
11.7 Duplication of chromosomal segments
11.7.1 Formalizing the problem
11.7.2 Recovering an ancestor of a semi-ambiguous genome
11.7.3 Recovering an ancestor of an ambiguous genome
11.7.4 Recovering the ancestral nodes of a species tree
11.8 Conclusion.
12 Reconstructing phylogenies from gene-content and gene-order data
12.1 Introduction: phylogenies and phylogenetic data
12.1.1 Phylogenies
12.1.2 Phylogenetic reconstruction
12.2 Computing with gene-order data
12.2.1 Genomic distances
12.2.2 Evolutionary models and distance corrections
12.2.3 Reconstructing ancestral genomes
12.3 Reconstruction from gene-order data
12.3.1 Encoding gene-order data into sequences.; 12.3.2 Direct optimization
12.3.3 Direct optimization with a metamethod: DCM-GRAPPA
12.3.4 Handling unequal gene content in reconstruction
12.4 Experimentation in phylogeny
12.4.1 How to test?
12.4.2 Phylogenetic considerations
12.5 Conclusion and open problems
13 Distance-based genome rearrangement phylogeny
13.1 Introduction
13.2 Whole genomes and events that change gene orders
13.2.1 Inversions and transpositions
13.2.2 Representations of genomes
13.2.3 Edit distances between genomes: inversion and breakpoint distances
13.2.4 The Nadeau-Taylor model and its generalization
13.3 Distance-based phylogeny reconstruction
13.3.1 Additive and near-additive matrices
13.3.2 The two steps of a distance-based method
13.3.3 Method of moments estimators
13.4 Empirically Derived Estimator
13.4.1 The method of moments estimator: EDE
13.4.2 The variance of the inversion and EDE distances.; 13.5 IEBP: "Inverting the expected breakpoint distance"
13.5.1 The method of moments estimator, Exact-IEBP
13.5.2 The method of moments estimator, Approx-IEBP
13.5.3 The variance of the breakpoint and IEBP distances
13.6 Simulation studies
13.6.1 Accuracy of the evolutionary distance estimators
13.6.2 Accuracy of NJ and Weighbor using IEBP and EDE
13.7 Summary
Acknowledgements
14 How much can evolved characters tell us about the tree thatgenerated them?
14.1 Introduction
14.2 Preliminaries
14.2.1 Phylogenetic trees
14.2.2 Markov processes on trees
14.3 Information-theoretic bounds: ancestral states and deep divergences
14.3.1 Reconstructing deep divergences
14.3.2 Connection with information theory
14.4 Phase transitions in ancestral state and tree reconstruction
14.4.1 The logarithmic conjecture
14.4.2 Reconstructing forests
14.5 Processes on an unbounded state space: the random cluster model
14.6 Large but finite state spaces
14.7 Concluding comments.

Mathematics of evolution and phylogeny /

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