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Information Geometry and Population Genetics

The Mathematical Structure of the Wright-Fisher Model

  • Julian Hofrichter
  • Jürgen Jost
  • Tat Dat Tran

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 1-15
  3. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 17-43
  4. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 45-76
  5. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 77-101
  6. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 103-122
  7. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 123-167
  8. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 169-194
  9. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 195-218
  10. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 219-267
  11. Julian Hofrichter, Jürgen Jost, Tat Dat Tran
    Pages 269-287
  12. Back Matter
    Pages 289-319

About this book

Introduction

The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amari's and Chentsov's information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools. Altogether, the manuscript provides a solid and broad working basis for graduate students and researchers interested in this field.

Keywords

35K75 60J25 60F10 92D25 35K20 35J70 60J70 53C99 information geometry population genetics Wright-Fisher model Kolmogorov equations free energy functional multiallele/multilocus model

Authors and affiliations

  • Julian Hofrichter
    • 1
  • Jürgen Jost
    • 2
  • Tat Dat Tran
    • 3
  1. 1.Mathematik in den NaturwissenschaftenMax-Planck-InstitutLeipzigGermany
  2. 2.Mathematik in den NaturwissenschaftenMax Planck InstitutLeipzigGermany
  3. 3.Mathematik in den NaturwissenschaftenMax Planck InstitutLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-52045-2
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-52044-5
  • Online ISBN 978-3-319-52045-2
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site
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