Read The Quasispecies Equation and Classical Population Models

The Quasispecies Equation and Classical Population Models

Raphaël Cerf

4.9/5 (29543 ratings)

Description: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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with The Quasispecies Equation and Classical Population Models. To get started finding The Quasispecies Equation and Classical Population Models, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Pages: 236

Format: PDF, EPUB & Kindle Edition

Publisher: Springer Nature

Release: 2022

ISBN: 9789814520829

Description: 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with The Quasispecies Equation and Classical Population Models. To get started finding The Quasispecies Equation and Classical Population Models, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Special Offer | $0.00

Special Offer! | $0.00

The Quasispecies Equation and Classical Population Models

The Quasispecies Equation and Classical Population Models

More Books

The Wulff Crystal in Ising and Percolation Models: Ecole d'Ete de Probabilites de Saint-Flour XXXIV - 2004: v. 34 (Lecture Notes in Mathematics) by Raphael Cerf (2010-06-02)

The Wulff Crystal in Ising and Percolation Models: Ecole d'Ete de Probabilites de Saint-Flour XXXIV - 2004: v. 34 (Lecture Notes in Mathematics) by Raphael Cerf (2010-06-02)

Large Deviations of Three Dimensional Supercritical Percolation (Asterisque 267)

Large Deviations of Three Dimensional Supercritical Percolation (Asterisque 267)

On Cramers Theory in Infinite Dimensions

On Cramers Theory in Infinite Dimensions

The Wulff Crystal in Ising and Percolation Models: Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 (Lecture Notes in Mathematics, 1878)

The Wulff Crystal in Ising and Percolation Models: Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004 (Lecture Notes in Mathematics, 1878)

The Wulff Crystal in Ising and Percolation Models

The Wulff Crystal in Ising and Percolation Models

The Quasispecies Equation and Classical Population Models (Probability Theory and Stochastic Modelling, 102)

The Quasispecies Equation and Classical Population Models (Probability Theory and Stochastic Modelling, 102)

Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model (Memoirs of the American Mathematical Society)

Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model (Memoirs of the American Mathematical Society)

The Quasispecies Equation and Classical Population Models (Probability Theory and Stochastic Modelling Book 102)

The Quasispecies Equation and Classical Population Models (Probability Theory and Stochastic Modelling Book 102)

Naissance a Vilnius: Romain Gary, Moshe Shalit, Moshe Lewin, Jascha Heifetz, Cesar Cui, Antoni Henryk Radziwi , Dalia Grybauskait, Marija Gimbutas, Raphael Kalinowski, Bohdan Paczy Ski, Gaon de Vilna, Cecile Cerf

Naissance a Vilnius: Romain Gary, Moshe Shalit, Moshe Lewin, Jascha Heifetz, Cesar Cui, Antoni Henryk Radziwi , Dalia Grybauskait, Marija Gimbutas, Raphael Kalinowski, Bohdan Paczy Ski, Gaon de Vilna, Cecile Cerf