Biological evolution is the phenomenon concerning how species are born, are transformed or disappear over time. Its study relies on sophisticated methods that involve both mathematical modeling of the biological processes at play and the design of efficient algorithms to fit these models to genetic and morphological data. Models and Methods for Biological Evolution outlines the main methods to study evolution and provides a broad overview illustrating the variety of formal approaches used, notably including combinatorial optimization, stochastic models and statistical inference techniques. Some of the most relevant applications of these methods are detailed, concerning, for example, the study of migratory events of ancient human populations or the progression of epidemics. This book should thus be of interest to applied mathematicians interested in central problems in biology, and to biologists eager to get a deeper understanding of widely used techniques of evolutionary data analysis.

Table of Contents:
Preface xiii Gilles DIDIER and Stéphane GUINDON Chapter 1 Trees: Combinatorics and Models 1 Gilles DIDIER and Stéphane GUINDON 1.1 Introduction 1 1.2 Preliminary definitions 2 1.3 Counting trees 4 1.3.1 Fully labeled non-rooted trees 4 1.3.2 Binary trees with labeled leaves 6 1.3.3 Binary trees with labeled leaves and ordered internal nodes 7 1.3.4 Number of orders of internal nodes of a given tree 8 1.3.5 Directed binary trees 9 1.4 Probabilities of trees resulting from branching processes 9 1.5 Birth-death processes 12 1.5.1 Probability density of a birth-death tree 15 1.6 The coalescent 18 1.6.1 Links with "classical" models in population genetics 19 1.6.2 Moran's model 19 1.6.3 The Wright-Fisher model 21 1.6.4 Generic model 21 1.6.5 Coalescent-generated tree probability density 23 1.7 Conclusion 23 1.8 References 25 Chapter 2 Models of Sequences and Discrete Traits Evolution 27 Étienne PARDOUX 2.1 Introduction 27 2.2 Discrete set-valued continuous-time Markov process 28 2.2.1 Poisson processes 28 2.2.2 Finite set-valued continuous-time Markov process 29 2.3 Models of DNA sequence evolution 32 2.3.1 The Jukes-Cantor model 32 2.3.2 The Kimura model 33 2.3.3 The Felsenstein model 33 2.3.4 The HKY model 34 2.3.5 The general time reversible model 35 2.4 Models of rate evolution along the sequence 35 2.4.1 Independent and identically distributed rates along the sequence 35 2.4.2 Hidden Markov model 36 2.5 Models of discrete trait evolution 37 2.6 References 38 Chapter 3 Evolutionary Models of Continuous Traits 39 Paul BASTIDE, Mahendra MARIADASSOU and Stéphane ROBIN 3.1 Motivations 39 3.1.1 Comparative methods 40 3.1.2 Studies of evolutionary phenomena 41 3.2 Brownian motion 42 3.2.1 Description 43 3.2.2 Phylogenetic regression and statistical transformations 44 3.2.3 Recursive algorithms for inference 47 3.3 Multivariate analysis 48 3.3.1 Description 48 3.3.2 Phylogenetic contrasts 49 3.3.3 Phylogenetic PCA 49 3.4 Gaussian models 51 3.4.1 Some limits of the Brownian motion 51 3.4.2 Ornstein-Uhlenbeck process 52 3.4.3 Biological interpretations and caveats 56 3.4.4 Further Gaussian processes 58 3.4.5 Heterogeneous evolution 60 3.4.6 Observation models 64 3.4.7 Model selection 66 3.5 Extensions and generalizations 67 3.5.1 Non-Gaussian models 67 3.5.2 Tree-trait interactions 67 3.5.3 Interactions between species 68 3.5.4 Trait of high dimension 69 3.6 Useful references 69 3.7 Acknowledgements 70 3.8 References 71 Chapter 4 Correlated Evolution: Models and Methods 79 Guillaume ACHAZ and Julien Y DUTHEIL 4.1 Introduction 79 4.2 Correlated evolution between traits 82 4.2.1 Species are not independent 82 4.2.2 The phylogenetically independent contrasts 84 4.2.3 Extending the linear model to account for phylogeny 86 4.2.4 Correlation between discrete traits 91 4.2.5 Examples of correlated traits 92 4.2.6 Jointly modeling traits and sequences 93 4.3 Correlated evolution within genomes 94 4.3.1 Within genes, between nucleotides 94 4.3.2 Within proteins, between amino acids 96 4.3.3 Within genomes, between genes 101 4.4 Genetics is also correlated evolution 103 4.4.1 In individuals 103 4.4.2 In pedigrees 104 4.4.3 In the population 106 4.5 Conclusion 109 4.6 References 110 Chapter 5 A Century of Genomic Rearrangements 117 Anne BERGERON and Krister M SWENSON 5.1 Introduction 117 5.2 Orderings of genes and the rearrangements that act on them 118 5.2.1 Basic representations and definitions 119 5.2.2 DCJ operations and the breakpoint graph 121 5.3 Counting DCJ scenarios 125 5.3.1 Scenarios for a balanced cycle of length 2m 125 5.3.2 The (many) cycle decompositions of a breakpoint graph 126 5.4 Chromosomal contact data and weighted scenarios 129 5.4.1 A model incorporating chromosomal contacts 129 5.4.2 Planar trees and an algorithm for exploring them 131 5.4.3 Planar trees 132 5.5 Conclusion 136 5.6 References 138 Chapter 6 Phylogenetic Inference: Distance-Based Methods 141 Fabio PARDI 6.1 Introduction 141 6.2 Mathematical basis 143 6.3 Distance estimation 146 6.3.1 Estimating distances from aligned sequences 146 6.3.2 Other approaches to estimate distances 148 6.4 Tree inference 150 6.4.1 Fitting branch lengths with least squares 151 6.4.2 Scoring trees: from least squares to minimum evolution 153 6.4.3 NJ and other agglomerative algorithms 154 6.4.4 Beyond distances 157 6.5 Conclusion 158 6.6 References 159 Chapter 7 Computing Inference in Phylogenetic Trees 165 Laurent GUÉGUEN 7.1 Inferences and modeling 165 7.1.1 Inferences 165 7.1.2 Parsimony and likelihood 166 7.1.3 Maximum parsimony 166 7.2 Dynamic programming 169 7.2.1 Over the branches 170 7.2.2 Over the nodes 171 7.2.3 Over the tree 171 7.2.4 At the root 172 7.2.5 Recursion relations 172 7.2.6 Complexity reduction 174 7.2.7 Root management 175 7.3 Maximum parsimony 177 7.3.1 Ancestral interference 179 7.4 Likelihood 179 7.4.1 Root management 182 7.4.2 Computation at the nodes 182 7.4.3 Maximization, differentiation 184 7.4.4 Ancestral interference 188 7.5 References 190 Chapter 8 The Bayesian Paradigm in Molecular Phylogeny 193 Nicolas RODRIGUE 8.1 Introduction 193 8.2 General principles of the Bayesian approach in phylogeny 194 8.2.1 Markov chain Monte Carlo sampling 197 8.2.2 Summary of posterior distribution and sampling 200 8.3 Demarginalization of the likelihood function 200 8.3.1 Parameter expansion 200 8.3.2 Data augmentation 202 8.4 Bayesian selection of substitution models 203 8.4.1 Relative model comparison via the Bayes factor 204 8.4.2 Absolute evaluation of models via predictive posterior simulation 206 8.5 Impacts and future directions 207 8.6 References 208 Chapter 9 Measures of Branch Support in Phylogenetics 213 Olivier GASCUEL and Frédéric LEMOINE 9.1 Introduction 213 9.2 Local supports: parametric and non-parametric aLRT 215 9.2.1 Null branch test and its limitations 215 9.2.2 Local aLRT test, parametric version 217 9.2.3 Local aLRT test, SH-like nonparametric version 218 9.2.4 Comparison with an example of aLRT support and bootstrap 219 9.3 Phylogenetic bootstrap 221 9.3.1 Statistic bootstrap 221 9.3.2 The Felsenstein bootstrap 221 9.3.3 Transfer bootstrap 223 9.3.4 Comparison with an example of bootstrap supports 226 9.4 Bayesian supports 228 9.4.1 Principle, use of Markov Monte Carlo chains 228 9.4.2 Local Bayesian support 230 9.4.3 Comparison of Bayesian supports with an example 231 9.5 Discussion 231 9.6 References 234 Chapter 10 Fossils and Phylogeny 237 Michel LAURIN 10.1 Inferences on topology 237 10.1.1 First approaches 237 10.1.2 Traits usable in paleontology 239 10.1.3 First quantitative approach: phenetics 241 10.1.4 Stratophenetics 242 10.1.5 Cladistics 242 10.1.6 Model-based approaches: likelihood, Bayesian approaches 243 10.1.7 Fossils and molecular data 245 10.2 Dating the tree of life 245 10.2.1 First qualitative approaches 245 10.2.2 First statistical approaches 246 10.2.3 Molecular dating 247 10.2.4 Tip dating 249 10.2.5 Birth-death model-based dating 250 10.3 Conclusion 252 10.4 References 252 Chapter 11 Phylodynamics 259 Samuel ALIZON 11.1 Reconciling ecology, evolution and mathematics 259 11.2 Data and processors 260 11.2.1 New generation sequencing 261 11.2.2 PCR and capture 261 11.3 Infection phylogenies 262 11.3.1 Link to transmission chains 262 11.3.2 Dating and evolutionary rates 263 11.3.3 Biological applications of time calibration 264 11.4 Phylodynamics 265 11.4.1 A field in search of definition 265 11.4.2 As closely as possible to epidemiology 266 11.4.3 Coalescent 267 11.4.4 Birth-death models 269 11.4.5 Limitations of likelihood approaches 269 11.4.6 ABC phylodynamics 270 11.5 Infection phylogeography 271 11.6 Infection and viral life history traits 272 11.7 Perspectives and challenges 273 11.8 References 275 Chapter 12 Inference of Demographic Processes in Human Populations 283 Frédéric AUSTERLITZ 12.1 Introduction 283 12.2 Demographic inferences from population genetics data 286 12.2.1 Reconstruction of the history of Central African Pygmies 286 12.2.2 Inference of the history of populations in Central Asia 288 12.2.3 Impact of lifestyle on population growth dynamics 288 12.3 Inferring human expansions from next-generation sequence data 291 12.4 Reconstructing population dynamics from genetic and cultural data 294 12.4.1 Simultaneous analysis of genetic and linguistic diversity 294 12.4.2 Detecting the intergenerational transmission of reproductive success 295 12.5 Conclusion 296 12.6 References 297 List of Authors 303 Index 305