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Phylogenetics. (English) Zbl 1043.92026
Oxford Lecture Series in Mathematics and its Applications 24. Oxford: Oxford University Press (ISBN 0-19-850942-1/hbk). xiii, 239 p. (2003).
This book, which is based on the authors’ lectures at the University of Canterburry, New Zealand, deals with the mathematical foundations of phylogenetics – the theory of reconstruction and analysis of evolutionary trees based on inherited characteristics of species. The fundamental question in phylogenetics is how to use the present-day characteristics of a group of species to infer their historical relationships. In the past, phylogenetic methods were based on morphological and physiological characters of species, later on molecular data, i.e., protein sequences, genetic sequences and most recently whole genome data. The aim of this book is to outline the mathematical concepts used in phylogenetics within a rather general mathematical framework.
The first part of the book (chapters 1 to 3) provides a set-theoretic and graph-theoretic background including the notions of phylogenetic trees, X-trees, rooted X-trees, and the relations between X-trees and certain types of collections of bipartitions. Chapter 4 is concerned with the formal description of characters and compatibility of characters. The classical maximum parsimony method, a popular technique for reconstructing phylogenetic trees from characters, as well as some extensions, are described in chapter 5. Chapter 6 deals with the problem of combining several trees for overlapping sets of species into a single phylogenetic tree. In chapter 7, reconstruction methods for trees with weighted edges are considered which are based on distance measures beetween species. Finally, the last chapter 8 deals with Markov processes on phylogenetic trees and associated tree reconstruction methods.
The mathematics presented in this graduate-level book is mainly discrete mathematics and probability theory. At the end of each chapter there are specialzed topics as well as an extensive number of exercises. The book affords a good insight into the mathematical theory behind phylogentic methods in the focus of mathematics, statistics, computer science and biology.

92D15 Problems related to evolution
05C05 Trees
05C90 Applications of graph theory
92B10 Taxonomy, cladistics, statistics in mathematical biology