Statistical Methods in Molecular Evolution, edited by Rasmus Nielsen, contains a wide survey of current research in molecular evolution. It is organized into sections—introduction, program ‘‘tutorials,’’ models, and inference—a setup that constitutes a gentle introduction to the topic for mathematically inclined readers. For practical biologists, the start might be somewhat more challenging, although the introduction is tailored to a mixed audience. All chapters are written by researchers with active research projects in the areas they write about. I address each chapter with a short comment. Introduction. The introductory material sets the stage for all further chapters. Without going into too much depth, the authors give a broad overview of topics such as Markov chain-based substitution models, likelihood concept, Markov chain Monte Carlo (MCMC) methods, and population genetic aspects of molecular evolution. (1) ‘‘Markov Models in Evolution:’’ Galtier, Gascuel, and Jean-Marie give a crash course on Markov models that will leave mathematicians happily humming along and many biologists struggling with the mathematical syntax. The discussion of population models of DNA, RNA, and protein sequence evolution is concise but lacks the presentation of the transition probabilities for some of the models. Readers who want to familiarize themselves with these models still need to read Felsenstein (2004) and Swofford et al. (1996). (2) ‘‘Introduction to Applications of the Likelihood Function in Molecular Evolution:’’ Buschbom and von Haeseler give an overview of the likelihood principle. Several examples of application of the maximum-likelihood principle—from simple one-parameter inferences to complicated many-parameter problems, such as finding the best tree given a set of sampled sequences—are given. The difficulties inherent in likelihood ratio testing receive too little attention. It would have been useful to read about difficulties with testing of hypotheses, taking into account boundary conditions of the parameters. For example, how should one test if a branch length in a phylogenetic tree is zero? And should this be used as a means of judging support for the tree? Given that this book will have a much higher profile than a single paper, coverage of such topics would have been helpful to many readers. (3) ‘‘Introduction to Markov Chain Monte Carlo Methods in Molecular Evolution:’’ Larget gives a brief introduction to MCMC sampling, using a Bayesian approach exclusively.
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