Phylogeny. Discrete and random processes in evolution (Q2828468)

The author describes some of the key problems in phylogenetics. He defines this scientific area as ``the theory of reconstructing and analyzing trees or more complex networks from data observed in the present.''NEWLINENEWLINEIn Chapter 1, basic concepts are presented: generic and key notation, graphs and trees, phylogenetic trees.NEWLINENEWLINEChapter 2 describes some combinatorial features of phylogenetic trees, encoding by set systems, enumeration, properties of tree shape, and metrics on trees. Counting trees, rooted and unrooted trees, tree rearrangement metrics, and consensus functions are studied.NEWLINENEWLINEIn Chapter 3, the author discusses discrete properties of phylogenetic trees that arise under random models of evolution. Particularly, he describes tree shapes, including evolving trees, measuring, and modelling tree shape.NEWLINENEWLINEIn Chapter 4, results of exploration trees in terms of their substructures are given.NEWLINENEWLINEChapter 5 studies the way in which trees can display discrete data and focuses on tree reconstruction from data, which may not perfectly fit tree characters, homoplasy, and minimal evolution trees, including trees for a sequence of characters.NEWLINENEWLINEChapter 6 ``allows edges of a tree to have length, a seemingly minor embellishment which leads to enhanced theory for tree reconstruction, geometric modeling, and biodiversity conversation.'' The author defines metrics from trees with edge lengths, and describes three distance-based tree reconstruction methods. At the end of the chapter, a generalization and geometry approaches are presented; this part of the book ends with a description of phylogenetic diversity.NEWLINENEWLINEIn Chapter 7, the author discusses stochastic models which can describe the evolution of discrete characters as they evolve along the branches of evolutionary trees from some unknown ancestral state. Using such models, simple empirical distances can be transformed in such a way that methods like NJ applied to these transformed distances are statistically consistent estimators of phylogenies and branch length. He describes nonhomogeneous Markov chains, Hadamard story and phylogenetic mixture models.NEWLINENEWLINEIn Chapter 8, the author continues the application of Markov processes to trees, focusing on the points of view of information theory and algebra. In these two chapters about Markov processes on trees, many topics have been omitted, including bootstrap, model selection, the theory underlying the VCVC machinery in Bayesian phylogenetics, and the evolution of continuous characters based on stochastic models.NEWLINENEWLINEChapter 9 presents results ``of speciation and extinction models for phylogenies, and the predictions these make regarding the trees' shape. Also was investigated random processes under which gene and species trees can disagree.''NEWLINENEWLINEIn Chapter 10, the author considers a framework allowing more complex representations of evolutionary relationships. The author indicates that a directed network can provide an explicit representation of evolution where there has been reticulation. In this part, the main concepts and results as well as a number of recent developments are described.