Preliminaries |
Graphs and their role in biology / 1: |
Graphs / 1.1: |
Trees and forests / 1.2: |
Intersection graphs / 1.3: |
Applications of graphs in biology / 1.4: |
Exercises / 1.5: |
X-trees and phylogenetic trees / 2: |
X-trees / 2.1: |
Rooted X-trees / 2.2: |
Ranked trees and the coalescent process / 2.3: |
Tree shapes / 2.4: |
Randomly generated trees / 2.5: |
Tree rearrangement operations / 2.6: |
Reticulate evolution and co-phylogeny / 2.7: |
Phylogenetic forests / 2.8: |
Trees and splits / 2.9: |
Splits-Equivalence Theorem / 3.1: |
A partial order on X-trees / 3.2: |
Compatibility of X-trees / 3.3: |
The splits metric / 3.4: |
Hierarchies, clusters, and splits / 3.5: |
Consensus trees / 3.6: |
Cyclic split systems and weak hierarchies / 3.7: |
The Buneman graph / 3.8: |
Compatibility of characters / 3.9: |
Characters and convexity / 4.1: |
Character compatibility (perfect phylogeny) / 4.2: |
Strongly compatible characters / 4.3: |
Complexity of determining character compatibility / 4.4: |
Maximum compatibility / 4.5: |
Generalized characters and directional constraints / 4.6: |
Defining an X-tree by characters / 4.7: |
Maximum parsimony / 4.8: |
Classical parsimony / 5.1: |
Optimization on a fixed tree / 5.2: |
Extensions of classical parsimony / 5.3: |
Maximum parsimony trees / 5.4: |
Networks of maximum parsimony trees / 5.5: |
Combinatorial statistics of parsimony / 5.6: |
Subtrees and supertrees / 5.7: |
Restricted subtrees / 6.1: |
Maximum agreement subtrees / 6.2: |
Compatibility of semi-labelled trees / 6.3: |
A reconstruction algorithm for rooted trees / 6.4: |
Complexity analysis / 6.5: |
Supertree methods / 6.6: |
Closure and correction operations / 6.7: |
Defining a tree by subtrees / 6.8: |
Phylogenetic patchworks / 6.9: |
Tree-based metrics / 6.10: |
Dissimilarity maps and tree metrics / 7.1: |
Ultrametrics / 7.2: |
Reconstruction methods / 7.3: |
Split decomposition theory / 7.4: |
Ordinal methods / 7.5: |
Group-valued, non-symmetric dissimilarities / 7.6: |
Perturbing tree metrics / 7.7: |
Markov models on trees / 7.8: |
Matrix algebra / 8.1: |
Markov processes on trees and graphs / 8.2: |
Phylogenetic models of character evolution / 8.3: |
Tree reconstruction for the general Markov process / 8.4: |
Stationary and reversible models / 8.5: |
The Hadamard representation / 8.6: |
The 'Felsenstein zone' / 8.7: |
Rate variation across characters / 8.8: |
Model-based reconstruction methods / 8.9: |
Algebraic properties of Markov processes on trees / 8.10: |
References / 8.11: |
Commonly used symbols |
Index |
Preliminaries |
Graphs and their role in biology / 1: |
Graphs / 1.1: |
Trees and forests / 1.2: |
Intersection graphs / 1.3: |
Applications of graphs in biology / 1.4: |