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Spatial Fleming-Viot Models with Selection and Mutation

  • Donald A. Dawson
  • Andreas Greven

Part of the Lecture Notes in Mathematics book series (LNM, volume 2092)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Donald A. Dawson, Andreas Greven
    Pages 1-10
  3. Donald A. Dawson, Andreas Greven
    Pages 39-53
  4. Donald A. Dawson, Andreas Greven
    Pages 55-104
  5. Donald A. Dawson, Andreas Greven
    Pages 105-145
  6. Donald A. Dawson, Andreas Greven
    Pages 147-159
  7. Donald A. Dawson, Andreas Greven
    Pages 167-375
  8. Donald A. Dawson, Andreas Greven
    Pages 377-714
  9. Donald A. Dawson, Andreas Greven
    Pages 781-786
  10. Donald A. Dawson, Andreas Greven
    Pages 787-810
  11. Donald A. Dawson, Andreas Greven
    Pages 811-828
  12. Donald A. Dawson, Andreas Greven
    Pages 829-837
  13. Donald A. Dawson, Andreas Greven
    Pages 839-839
  14. Back Matter
    Pages 841-858

About this book

Introduction

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.

Keywords

60J70,92D15,92D25,60J80,60J85. Dual processes Emergence of rare mutants Fleming-Viot processes Mutation-selection Spatial migration

Authors and affiliations

  • Donald A. Dawson
    • 1
  • Andreas Greven
    • 2
  1. 1.Carleton University, School of Mathematics & StatisticsOttawaCanada
  2. 2.Department MathematikUniversität Erlangen-Nürnberg, Mathematisches InstitutErlangenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-02153-9
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-02152-2
  • Online ISBN 978-3-319-02153-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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