Phylogenetic Trees and Molecular Evolution: A Hands-on Introduction with Uncertainty Quantification Corrected

Preface
	Why This Book?
		Brief Description
		Why the Subtitle ``A Hands-On Introduction with Uncertainty Quantification Corrected?\'\'
	Chapter-by-Chapter Synopsis
	Acknowledgments
Contents
1 Introduction to Phylogenetic Trees
	1.1 What Are Phylogenetic Trees All About?
	1.2 Assumptions Behind Models of Molecular Phylogenetics
		1.2.1 Common Ancestry
		1.2.2 Molecular Clock Hypothesis
		1.2.3 Statistical Assumptions
	1.3 Exercises
2 Adaptation of the Molecular Clock: A Divergence Time Story
	2.1 1960s: Starting the Clock
	2.2 1970s: Neutralism Versus Selectionism
	2.3 1980s: Fluctuating Rates
	2.4 1990s: Confronting the Fossil Record
	2.5 2000s: Molecular Punctuated Equilibrium
	2.6 2010s: Integration of Data
	2.7 2020s: Time Will Tell
	2.8 Excursus: Models with Molecular Evolution over All Time Scales
		2.8.1 Why Models with Evolution over All Time Scales?
		2.8.2 Fractal point process models
		2.8.3 Fractal-Rate Poisson Models
			2.8.3.1 Generic Fractal-Rate Poisson Model
			2.8.3.2 Gaussian Models of Rates
			2.8.3.3 Diffusion Models of Rates
		2.8.4 Multiplicative Model of Molecular Evolution
	2.9 Exercises
	2.10 Bibliographic Notes
3 Estimating Phylogenetic Trees
	3.1 Substituter: The Poisson Game (3 Sequences of 12 Nucleotides Each)
		3.1.1 Rules for Simulation Mode
			3.1.1.1 Simulating Sequences
			3.1.1.2 Sharing Selected Sequences with the Opposing Team
		3.1.2 Rules for Estimation Mode
			3.1.2.1 Distance-Based Tree Estimation
			3.1.2.2 Estimating a Tree from Protein Sequences
			3.1.2.3 Estimating a Tree from DNA Sequences
	3.2 Relations of Different Types of Trees
	3.3 Software for Tree Estimation
	3.4 Sources of Uncertainty in Tree Estimates
		3.4.1 Uncertainty About Common Ancestry
		3.4.2 Uncertainty About the Topology
		3.4.3 Uncertainty About the Branch Lengths
		3.4.4 Uncertainty About the Substitution Model
		3.4.5 Uncertainty About the Tree Estimation Method
		3.4.6 Uncertainty About the Statistical Method and Prior Probabilities
	3.5 Excursus: Models of Nucleotide Substitution
		3.5.1 Background Terminology
		3.5.2 Discrete-Time Models [§13.2]ewens2001statistical
		3.5.3 Continuous-Time Models [§13.3]ewens2001statistical
		3.5.4 Further Reading
	3.6 Exercises
4 Estimating Divergence Times
	4.1 Confidence Intervals of Divergence Times
	4.2 Uncertainty in Divergence Time Estimates
		4.2.1 Sources of Uncertainty in Divergence Time Estimates
			4.2.1.1 Uncertainty About Phylogenetic Trees
			4.2.1.2 Uncertainty About Fluctuations in the Substitution Rate
			4.2.1.3 Uncertainty About the Dates and Relations of Fossils
			4.2.1.4 Uncertainty in Statistical Error
			4.2.1.5 Uncertainty About Prior Distributions
		4.2.2 Quantified Uncertainty in Divergence Time Estimates
		4.2.3 Correcting Unquantified Uncertainty in Divergence Time Estimates
	4.3 Excursus: Why Multiply Probabilities by the Proportion of Quantified Certainty?
	4.4 Exercises
5 Estimating Common Ancestors
	5.1 Notation for Conditional Probability
	5.2 Estimating Ancestors in Substituter
		5.2.1 Estimating an Ancestral DNA Sequence
		5.2.2 Estimating an Ancestral Protein Sequence
	5.3 Probabilities for the First Site of the Ancestral DNA Sequence
	5.4 Maximum Likelihood for the First Site of the Ancestral DNA Sequence
	5.5 Uncertainty in Ancestral Sequence Estimates
		5.5.1 Sources of Uncertainty in Ancestral Sequence Estimates
			5.5.1.1 Uncertainty About the Statistical Method and About Prior Probabilities
			5.5.1.2 Uncertainty About the Model Assumptions
		5.5.2 Correcting for Unquantified Uncertainty in Ancestral Sequence Estimates
	5.6 Exercises
6 Testing Hypotheses of Molecular Evolution
	6.1 Maximum Genetic Diversity Hypothesis
	6.2 Genetic Equidistance Phenomenon
	6.3 Slow Clock Method
	6.4 Questions Raised by Distinguishing Macroevolution from Microevolution
	6.5 Exercises
7 Recommendations for Further Reading
	7.1 Molecular Phylogenetics Books
		7.1.1 Phylogenetics Books with Less Mathematics
			7.1.1.1 Phylogenetic Trees Made Easy: A How-To Manual Hall2018main
			7.1.1.2 An Introduction to Molecular Evolution and Phylogenetics bromham2016book
		7.1.2 Phylogenetics Books with More Mathematics
	7.2 Bioinformatics and Genomics Books
	7.3 Imprecise Probability Books
	7.4 Power Law Books
A Probability Interpretation: Support by Data and Model Evidence
	A.1 An Evidential Generalization of Frequentist and Bayesian Probability
	A.2 Evidential Models and Evidential Support Distributions
	A.3 Imprecision Due to Uncertainty
	A.4 Evidential Sufficiency Distributions
	A.5 Special Case: Unquantified Uncertainty Corrected
B Intermittent Point Processes
	B.1 Basics of Intermittency
	B.2 Hurst Exponent
	B.3 Fractal Renewal Processes
C Poisson Processes with Lévy-Stable Substitution Rates
	C.1 Lévy-Stable Processes for Substitution Rates
	C.2 Point Process Models for Molecular Evolution
		C.2.1 Poisson-Stable Processes
		C.2.2 Poisson-Fractal Processes
References
Index