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Lecture Notes in Mathematics

Spatial Fleming-Viot Models with Selection and Mutation

Authors: Dawson, Donald, Greven, Andreas

  • Develops a class of spatial models of a population undergoing mutation, selection and migration
  • Develops new duality methods for multitype population models
  • Develops the McKean-Vlasov limit of exchangeable population models and their entrance laws
  • Identifies mutation-selection equilibria
  • Offers valuable insights into the role of migration in the emergence of rare mutants in spatial Fleming-Viot models
  • Sheds new light on the role of migration in sustaining biodiversity in evolution
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  • ISBN 978-3-319-02153-9
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About this book

This book constructs a rigorous framework for analysing selected phenomena in evolutionary theory of populations arising due to the combined effects of migration, selection and mutation in a spatial stochastic population model, namely the evolution towards fitter and fitter types through punctuated equilibria. The discussion is based on a number of new methods, in particular multiple scale analysis, nonlinear Markov processes and their entrance laws, atomic measure-valued evolutions and new forms of duality (for state-dependent mutation and multitype selection) which are used to prove ergodic theorems in this context and are applicable for many other questions and renormalization analysis for a variety of phenomena (stasis, punctuated equilibrium, failure of naive branching approximations, biodiversity) which occur due to the combination of rare mutation, mutation, resampling, migration and selection and make it necessary to mathematically bridge the gap (in the limit) between time and space scales.

Table of contents (15 chapters)

  • Introduction

    Dawson, Donald A. (et al.)

    Pages 1-10

  • Mean-Field Emergence and Fixation of Rare Mutants in the Fisher–Wright Model with Two Types

    Dawson, Donald A. (et al.)

    Pages 11-38

  • Formulation of the Multitype and Multiscale Model

    Dawson, Donald A. (et al.)

    Pages 39-53

  • Formulation of the Main Results in the General Case

    Dawson, Donald A. (et al.)

    Pages 55-104

  • A Basic Tool: Dual Representations

    Dawson, Donald A. (et al.)

    Pages 105-145

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-319-02153-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $119.00
price for USA
  • ISBN 978-3-319-02152-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Spatial Fleming-Viot Models with Selection and Mutation
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2092
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-02153-9
DOI
10.1007/978-3-319-02153-9
Softcover ISBN
978-3-319-02152-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVII, 856
Number of Illustrations and Tables
1 b/w illustrations
Topics