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The Quasispecies Equation and Classical Population Models

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Quasispecies Equation and Classical Population Models/ by Raphaël Cerf, Joseba Dalmau.
作者:	Cerf, Raphaël.
其他作者:	Dalmau, Joseba.
面頁冊數:	X, 242 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Applied Probability. -
電子資源:	https://doi.org/10.1007/978-3-031-08663-2
ISBN:	9783031086632

The Quasispecies Equation and Classical Population Models
Cerf, Raphaël.

The Quasispecies Equation and Classical Population Models[electronic resource] /by Raphaël Cerf, Joseba Dalmau. - 1st ed. 2022. - X, 242 p. 1 illus.online resource. - Probability Theory and Stochastic Modelling,1022199-3149 ;. - Probability Theory and Stochastic Modelling,76.

1. Introduction -- Part I.Finite Genotype Space -- 2. The Quasispecies equation -- 3. Non-Overlapping Generations -- 4. Overlapping Generations -- 5. Probabilistic Representations -- Part II. The Sharp Peak Landscape -- 6. Long Chain Regime -- 7. Error Threshold and Quasispecies -- 8. Probabilistic Derivation -- 9. Summation of the Series -- 10. Error Threshold in Infinite Populations -- Part III. Error Threshold in Finite Populations -- 11.Phase Transition -- 12. Computer Simulations -- 13. Heuristics -- 14. Shape of the Critical Curve -- 15. Framework for the Proofs -- Part IV. Proof for Wright-Fisher -- 16. Strategy of the Proof -- 17. The Non-Neutral Phase M -- 18. Mutation Dynamics -- 19. The Neutral Phase N -- 20. Synthesis -- Part V. Class-Dependent Fitness Landscapes -- 21. Generalized Quasispecies Distributions -- 22. Error Threshold -- 23. Probabilistic Representation -- 24. Probabilistic Interpretations -- 25. Infinite Population Models -- Part VI. A Glimpse at the Dynamics -- 26. Deterministic Level -- 27. From Finite to Infinite Population -- 28. Class-Dependent Landscapes -- A. Markov Chains and Classical Results -- References -- Index.

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.

ISBN: 9783031086632

Standard No.: 10.1007/978-3-031-08663-2doiSubjects--Topical Terms:

1390075
Applied Probability.

LC Class. No.: QA1-939

Dewey Class. No.: 510

The Quasispecies Equation and Classical Population Models
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505 0 $a 1. Introduction -- Part I.Finite Genotype Space -- 2. The Quasispecies equation -- 3. Non-Overlapping Generations -- 4. Overlapping Generations -- 5. Probabilistic Representations -- Part II. The Sharp Peak Landscape -- 6. Long Chain Regime -- 7. Error Threshold and Quasispecies -- 8. Probabilistic Derivation -- 9. Summation of the Series -- 10. Error Threshold in Infinite Populations -- Part III. Error Threshold in Finite Populations -- 11.Phase Transition -- 12. Computer Simulations -- 13. Heuristics -- 14. Shape of the Critical Curve -- 15. Framework for the Proofs -- Part IV. Proof for Wright-Fisher -- 16. Strategy of the Proof -- 17. The Non-Neutral Phase M -- 18. Mutation Dynamics -- 19. The Neutral Phase N -- 20. Synthesis -- Part V. Class-Dependent Fitness Landscapes -- 21. Generalized Quasispecies Distributions -- 22. Error Threshold -- 23. Probabilistic Representation -- 24. Probabilistic Interpretations -- 25. Infinite Population Models -- Part VI. A Glimpse at the Dynamics -- 26. Deterministic Level -- 27. From Finite to Infinite Population -- 28. Class-Dependent Landscapes -- A. Markov Chains and Classical Results -- References -- Index.
520 $a 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.
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