Reconstructing Evolution: New Mathematical and Computational Advances

Contents
List of Contributors
I: Evolution in Populations
	1 Trees of genes in populations
		1.1 Introduction
		1.2 Effects of evolutionary forces on coalescent trees
		1.3 Inference methods
		1.4 Programmes
		1.5 The wave of the future
	2 The evolutionary analysis of measurably evolving populations using serially sampled gene sequences
		2.1 Introduction
		2.2 Constructing phylogenetic trees from serially sampled data
		2.3 Maximum-likelihood estimation of evolutionary rates
		2.4 The serial coalescent
		2.5 Estimating population size and substitution rates under the s-coalescent
		2.6 Estimating migration rates
		2.7 Where to next
II: Models of sequence evolution
	3 Modelling the variability of evolutionary processes
		3.1 Introduction
		3.2 Mathematical tools and concepts
		3.3 Biological data sets
		3.4 The models in action: analysis of protein coding sequences
		3.5 Discussion
	4 Phylogenetic invariants
		4.1 Introduction
		4.2 Phylogenetic models on a tree
		4.3 Edge invariants and matrix rank
		4.4 Vertex invariants and tensor rank
		4.5 Algebraic geometry and computational algebra
		4.6 Invariants for specific models
		4.7 Invariants and statistical tests
		4.8 Invariants and maximum-likelihood
		4.9 Invariants and identifiability of complex models
		4.10 Other directions
		4.11 Concluding remarks
III: Tree shape, speciation, and extinction
	5 Some models of phylogenetic tree shape
		5.1 Introduction
		5.2 Background
		5.3 Yule and Hey models
		5.4 λ = function(trait)
		5.5 λ = function(age)
		5.6 λ = function(time)
		5.7 The neutral model
		5.8 λ = function(N)
		5.9 Concluding remarks
		5.10 Appendix
	6 Phylogenetic diversity: from combinatorics to ecology
		6.1 Introduction and terminology
		6.2 Definitions and combinatorial properties
		6.3 Biodiversity conservation
		6.4 Loss of phylogenetic diversity under extinction models
		6.5 Tree reconstruction using PD
		6.6 Concluding comments
IV: Trees from subtrees and characters
	7 Fragmentation of large data sets in phylogenetic analyses
		7.1 Introduction
		7.2 Basic definitions
		7.3 Strategies for handling fragmentation of data sets
		7.4 Conclusions
	8 Identifying and defining trees
		8.1 Introduction
		8.2 From biology to mathematics
		8.3 Defining trees in terms of chordal graphs
		8.4 Defining trees in terms of closure rules
		8.5 Identifying trees in terms of chordal graphs
		8.6 Identifying trees in terms of quartets
		8.7 Conclusion
V: From trees to networks
	9 Split networks and reticulate networks
		9.1 Introduction
		9.2 Consensus networks and super networks
		9.3 Split networks from sequences and distances
		9.4 Hybridization and reticulate networks
		9.5 Recombination networks
	10 Hybridization networks
		10.1 Introduction
		10.2 Hybridization networks
		10.3 A characterization of MINIMUM HYBRIDIZATION
		10.4 Algorithmic applications of agreement forests
		10.5 Recombination networks
		10.6 Hybridization networks in real time
		10.7 Computational complexity
		10.8 Concluding remarks
Index
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