Raphael Cerf,Joseba Dalmau
The Quasispecies Equation and Classical Population Models
The Quasispecies Equation and Classical Population Models
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- More about The Quasispecies Equation and Classical Population Models
This book explores the mathematical models of population evolution, focusing on the quasispecies equation and its application to finite population models. It discusses the emergence of quasispecies and error threshold phenomena, provides exact formulas for the quasispecies distribution, and analyzes other classical population models.
Format: Hardback
Length: 242 pages
Publication date: 31 July 2022
Publisher: Springer International Publishing AG
This comprehensive monograph delves into a series of mathematical models that explore the dynamics of a population evolving through the processes of mutation and selection. It begins with the quasispecies equation, a fundamental non-linear equation that captures the equilibrium between mutation and selection in Manfred Eigens renowned quasispecies model. Through a detailed analysis, the equation is examined under specific assumptions, including finite genotype space, sharp peak landscapes, and class-dependent fitness landscapes. Various probabilistic representation formulae are derived to solve the equation, involving classical combinatorial quantities such as Stirling and Euler numbers.
The book demonstrates how quasispecies and error threshold phenomena arise in finite population models, providing mathematical proofs for the Wright–Fisher model. Additionally, exact formulas are obtained for the quasispecies distribution in different scenarios, including the long chain regime, sharp peak landscape, and class-dependent fitness landscapes. Furthermore, the book analyzes several other classical population models, focusing on their dynamical behavior and their connections to the quasispecies equation.
This book holds significant appeal to mathematicians and theoretical ecologists/biologists engaged in the study of finite population models. Its detailed analysis and mathematical proofs provide valuable insights into the complex dynamics of population evolution, offering valuable tools for researchers in these fields.
Weight: 547g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031086625
Edition number: 1st ed. 2022
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