Phylogenies (evolutionary trees) are basic to thinking about and analyzing differences between species. Statistical, computational, and algorithmic work on them has been ongoing for four decades, with great advances in understanding. Yet no book has summarized this work until now. Inferring Phylogenies explains clearly the assumptions and logic of making inferences about phylogenies, and using them to make inferences about evolutionary processes. It is an essential text and reference for anyone who wants to understand how phylogenies are reconstructed and how they are used. As phylogenies are inferred with various kinds of data, this book concentrates on some of the central ones: discretely coded characters, molecular sequences, gene frequencies, and quantitative traits. Also covered are restriction sites, RAPDs, and microsatellites. Inferring Phylogenies is intended for graduate-level courses, assuming some knowledge of statistics, mathematics (calculus and fundamental matrix algebra), molecular sequences, and quantitative genetics. Parsimony Methods -- Counting Evolutionary Changes -- How Many Trees Are There? -- Finding The Best Tree By Heuristic Search -- Finding The Best Tree : Branch And Bound -- Ancestral States And Branch Lengths -- Variants Of Parsimony -- Compatibility -- Statistical Properties Of Parsimony -- A Digression On History And Philosophy -- Distance Matrix Methods -- Quartets Of Species -- Models Of Dna Evolution -- Models Of Protein Evolution -- Restriction Sites, Rapds, And Microsatellites -- Likelihood Methods -- Hadamard Methods -- Bayesian Inference Of Phylogenies -- Testing Models, Trees And Clocks -- Bootstrap, Jackknife, And Permutation Tests -- Paired Sites Tests -- Invariants -- Brownian Motion And Gene Frequencies -- Quantitative Characters -- Comparative Methods -- Coalescent Trees -- Likelihood Calculations On Coalescents -- Coalescents And Species Trees -- Alignment, Gene Families, And Genomics -- Consensus Trees And Distances Between Trees -- Biogeography, Hosts, And Parasites -- Phylogenies And Paleontology -- Tests Based On Tree Shape -- Drawing Trees -- Phylogeny Software. Joe Felsenstein. Includes Bibliographical References (p. 595-644) And Index. Phylogenies (evolutionary trees) are basic to thinking about and analyzing differences between species. Statistical, computational, and algorithmic work on them has been ongoing for four decades, with great advances in understanding. Yet no book has summarized this work until now. __Phylogenies____Inferring Phylogenies__ Phylogenies, are the basic structures necessary to think about and analyse differences between species. This text covers the statistical, computational and algorithmic work that has taken place in the field over four decades Parsimony methods are the easiest ones to explain; they were also among the first methods for inferring phylogenies.