Overview
- This book provides an in-depth study of the Eigen's Quasispecies equation in the context of population models.
- The case of the Wright-Fisher model is treated in detail, other classical population models are also discussed.
- Contains a foreword by Michel Benaïm.
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 102)
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Table of contents (28 chapters)
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Front Matter
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Finite Genotype Space
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Front Matter
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The Sharp Peak Landscape
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Front Matter
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Error Threshold in Finite Populations
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Front Matter
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Proof for Wright–Fisher
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Front Matter
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Keywords
- Analysis of Quasispecies equation
- Manfred Eigen quasispecies model
- Population models book
- Mutation-Selection equilibrium analysis
- Markov chains mathematical biology
- Wright-Fisher model
- Long Chain Regime
- Galton-Watson model biology
- Population Genetics
- Moran-Kingman model
- Raphael Cerf math
- Joseba Dalmau
About this book
This monograph studies a series of mathematical models of the evolution of a population under mutation and selection. Its starting point is the quasispecies equation, a general non-linear equation which describes the mutation-selection equilibrium in Manfred Eigen’s famous quasispecies model. A detailed analysis of this equation is given under the assumptions of finite genotype space, sharp peak landscape, and class-dependent fitness landscapes. Different probabilistic representation formulae are derived for its solution, involving classical combinatorial quantities like Stirling and Euler numbers.
It is shown how quasispecies and error threshold phenomena emerge in finite population models, and full mathematical proofs are provided in the case of the Wright–Fisher model. Along the way, exact formulas are obtained for the quasispecies distribution in the long chain regime, on the sharp peak landscape and on class-dependent fitness landscapes.
Finally, several other classical population models are analyzed, with a focus on their dynamical behavior and their links to the quasispecies equation.
This book will be of interest to mathematicians and theoretical ecologists/biologists working with finite population models.
Reviews
“The text is written in an easy-to-read style and is suitable for use in various courses, including probability theory, Markov chains, mathematical ecology and population dynamics. The book can be expected to provide several ideas for further investigation of finite population models.” (Attila Dénes, zbMATH 1507.92072, 2023)
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: The Quasispecies Equation and Classical Population Models
Authors: Raphaël Cerf, Joseba Dalmau
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-031-08663-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-08662-5Published: 31 July 2022
Softcover ISBN: 978-3-031-08665-6Published: 01 August 2023
eBook ISBN: 978-3-031-08663-2Published: 30 July 2022
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: X, 242
Number of Illustrations: 1 b/w illustrations
Topics: Mathematics, general, Life Sciences, general, Probability Theory and Stochastic Processes, Ecology, Community & Population Ecology