The Quasispecies Equation and Classical Population Models

Foreword
Contents
Chapter 1 Introduction
Part I Finite Genotype Space
	Overview of Part I
	Chapter 2 The Quasispecies Equation
		2.1 The Equilibrium Equation
		2.2 The Perron–Frobenius Theorem
		2.3 Solutions
	Chapter 3 Non-Overlapping Generations
		3.1 The Moran–Kingman Model
		3.2 The Galton–Watson Model
		3.3 The Wright–Fisher Model
	Chapter 4 Overlapping Generations
		4.1 The Eigen Model
		4.2 The Continuous Branching Model
		4.3 The Moran Model
	Chapter 5 Probabilistic Representations
		5.1 Stopped RandomWalk
		5.2 Stopped Branching Process
Part II The Sharp Peak Landscape
	Overview of Part II
	Chapter 6 Long Chain Regime
		6.1 Genotypes and Mutations
		6.2 Sharp Peak Fitness
		6.3 Hamming Classes
		6.4 Limit Equation
	Chapter 7 Error Threshold and Quasispecies
		7.1 The Error Threshold
		7.2 The Distribution of the Quasispecies
	Chapter 8 Probabilistic Derivation
		8.1 Asymptotics of c*
		8.2 Limit of the Mutant Walk Representation
		8.3 The Poisson Random Walk
		8.4 Formal Derivation
	Chapter 9 Summation of the Series
		9.1 Stirling Numbers
		9.2 Eulerian Numbers
		9.3 Combinatorial Identities
	Chapter 10 Error Threshold in Infinite Populations
		10.1 The Moran–Kingman Model
		10.2 The Eigen Model
Part III Error Threshold in Finite Populations
	Overview of Part III
	Chapter 11 Phase Transition
		11.1 The Moran Model
		11.2 The Wright–Fisher Model
	Chapter 12 Computer Simulations
	Chapter 13 Heuristics
		13.1 A Simplified Process
		13.2 A Renewal Argument
		13.3 Persistence Time
	Chapter 14 Shape of the Critical Curve
		14.1 Critical Curve for the Moran Model
		14.2 Critical Curve for the Wright–Fisher Model
	Chapter 15 Framework for the Proofs
		15.1 Candidate Limits for Moran
		15.2 Candidate Limits for Wright–Fisher
Part IV Proof for Wright–Fisher
	Overview of Part IV
	Chapter 16 Strategy of the Proof
		16.1 Main Ideas
		16.2 Invariant Probability Measure
		16.3 Upper Bounds
	Chapter 17 The Non-Neutral Phase M
		17.1 Large Deviations Principle
		17.2 Perturbed Dynamical System
		17.3 Time away from the Fixed Points
		17.4 Reaching the Quasispecies
		17.5 Escape from the Quasispecies
	Chapter 18 Mutation Dynamics
		18.1 Binary Process of Differences
		18.2 Hamming Class Dynamics
		18.3 Time away from the Equilibrium
		18.4 Reaching the Equilibrium
		18.5 Escape from the Equilibrium
	Chapter 19 The Neutral Phase N
		19.1 Ancestral Lines
		19.2 Monotonicity and Correlations
		19.3 Time away from the Disorder
		19.4 Reaching the Disorder
		19.5 Escape from the Disorder
	Chapter 20 Synthesis
		20.1 The Quasispecies Regime
		20.2 The Disordered Regime
Part V Class-Dependent Fitness Landscapes
	Overview of Part V
	Chapter 21 Generalized Quasispecies Distributions
		21.1 Class-Dependent Fitness Landscapes
		21.2 Up-Down Coefficients
		21.3 Re-Expansion
	Chapter 22 Error Threshold
		22.1 Eventually Constant Fitness Functions
		22.2 Error Threshold
		22.3 Further Solutions
	Chapter 23 Probabilistic Representation
		23.1 Asymptotics of Perron–Frobenius
		23.2 Mutant Walk Representation
		23.3 Computation of the Limit
		23.4 Rearranging the Sums
	Chapter 24 Probabilistic Interpretations
		24.1 Poisson Random Walk
		24.2 The Branching Poisson Walk
	Chapter 25 Infinite Population Models
		25.1 The Moran–Kingman Model
		25.2 The Eigen Model
Part VI A Glimpse at the Dynamics
	Overview of Part VI
	Chapter 26 Deterministic Level
		26.1 The Moran–Kingman Model
		26.2 The Eigen Model
	Chapter 27 From Finite to Infinite Population
		27.1 From Moran’s to Eigen’s Model
		27.2 From Wright–Fisher’s to Moran–Kingman’s Model
	Chapter 28 Class-Dependent Landscapes
		28.1 Moran Model
		28.2 The Wright–Fisher Model
Appendix A Markov Chains and classical results
	A.1 Monotonicity
	A.2 Construction of Markov Processes
	A.3 Lumping
	A.4 The FKG Inequality
	A.5 Hoeffding’s Inequality
References
Index