STATISTICAL METHODS IN (MOLECULAR) EVOLUTION1

Abstract

Statistical Methods in Molecular Evolution, edited by Ras-mus Nielsen, contains a wide survey of current research inmolecular evolution. It is organized into sections—introduc-tion, program ‘‘tutorials,’’ models, and inference—a setupthat constitutes a gentle introduction to the topic for math-ematically inclined readers. For practical biologists, the startmight be somewhat more challenging, although the intro-duction is tailored to a mixed audience. All chapters arewritten by researchers with active research projects in theareas they write about. I address each chapter with a shortcomment.Introduction. The introductory material sets the stage forall further chapters. Without going into too much depth, theauthors give a broad overview of topics such as Markovchain-based substitution models, likelihood concept, Markovchain Monte Carlo (MCMC) methods, and population geneticaspects of molecular evolution. (1) ‘‘Markov Models in Evo-lution:’’ Galtier, Gascuel, and Jean-Marie give a crash courseon Markov models that will leave mathematicians happilyhumming along and many biologists struggling with themathematical syntax. The discussion of population modelsof DNA, RNA, and protein sequence evolution is concise butlacks the presentation of the transition probabilities for someof the models. Readers who want to familiarize themselveswith these models still need to read Felsenstein (2004) andSwofford et al. (1996). (2) ‘‘Introduction to Applications ofthe Likelihood Function in Molecular Evolution:’’Buschbomand von Haeseler give an overview of the likelihood prin-ciple. Several examples of application of the maximum-like-lihood principle—from simple one-parameter inferences tocomplicated many-parameter problems, such as finding thebest tree given a set of sampled sequences—are given. Thedifficulties inherent in likelihood ratio testing receive toolittle attention. It would have been useful to read about dif-ficulties with testing of hypotheses, taking into accountboundary conditions of the parameters. For example, howshould one test if a branch length in a phylogenetic tree iszero? And should this be used as a means of judging supportfor the tree? Given that this book will have a much higherprofile than a single paper, coverage of such topics wouldhave been helpful to many readers. (3) ‘‘Introduction to Mar-kov Chain Monte Carlo Methods in Molecular Evolution:’’Larget gives a brief introduction to MCMC sampling, usinga Bayesian approach exclusively. The Gibbs sampler, a spe-cial case of the Metropolis-Hastings (MH) sampler, is ex-plained in detail. Regarding phylogenetics and population