The quasispecies equation and classical population models / / Raphaël Cerf, Joseba Dalmau

• Record Nr.: UNISA996483153803316
• Autore: Cerf Raphaël
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 3-031-08663-5
• Descrizione fisica: 1 online resource (236 pages)
• Collana: Probability theory and stochastic modelling ; ; Volume 102
• Disciplina: 519.2
• Soggetti: Probabilities; Quasisymmetric groups; Probabilitats; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- 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.