Phylogenetics'Phylogenetics' is the reconstruction and analysis of phylogenetic (evolutionary) trees and networks based on inherited characteristics. It is a flourishing area of interaction between mathematics, statistics, computer science and biology. The main role of phylogenetic techniques lies in evolutionary biology, where it is used to infer historical relationships between species. However, the methods are also relevant to a diverse range of fields including epidemiology, ecology, medicine, as well as linguistics and cognitive psychology This book is intended for biologists interested in the mathematical theory behind phylogenetic methods, and for mathematicians, statisticians, and computer scientists eager to learn about this emerging area of discrete mathematics. 'Phylogenetics' in the 24th volume in the Oxford Lecture Series in Mathematics and its Applications. This series contains short books suitable for graduate students and researchers who want a well-written account of mathematics that is fundamental to current to research. The series emphasises future directions of research and focuses on genuine applications of mathematics to finance, engineering and the physical and biological sciences. |
Contents
Preliminaries | 1 |
Trees and splits | 46 |
Compatibility of characters | 66 |
6579H4 | 83 |
Maximum parsimony | 86 |
4 | 95 |
14 | 106 |
7 | 108 |
18 | 143 |
Treebased metrics | 145 |
Markov models on trees | 183 |
Tree reconstruction for the general Markov process | 191 |
6 | 198 |
References | 218 |
25 | 221 |
| 227 | |
Common terms and phrases
algorithm bijection binary characters binary phylogenetic tree biology Buneman character distribution chordal graph collection of phylogenetic completes the proof construction convex Corollary defined definitive denote the set describe displays dissimilarity map easily checked edge-weighted equidistant representation equivalence Example excess-free follows four-point condition full character Furthermore graph G induced int(C interior edge interior vertex intersection graph interval graph isomorphic label set leaf labelled Lemma Markov process Mathematics maximum parsimony maximum parsimony tree metric space minimal minimum extension N2-model non-empty NP-complete pair parsimony score path phylogenetic invariants polynomial polynomial-time algorithm problem proof of Theorem Proposition quartet trees result root vertex rooted binary phylogenetic rooted phylogenetic tree rooted tree semi-labelled tree set of X-splits shown in Fig species split stationary process Steel subgraph supertree method Suppose Székely tree metric representation ultrametric unique unrooted V₁ vertex set vertices weighting X-tree X-tree and let