Advertisement

© 2017

Information Geometry and Population Genetics

The Mathematical Structure of the Wright-Fisher Model

  • Provides a new systematic and geometric approach to the Wright--Fisher model of population genetics

  • Introduces new tools from information geometry and statistical mechanics that lead to a deeper understanding

  • Includes precise formulas and a detailed analysis of the boundary behavior (loss of allele events)

  • Provides a solid and broad working basis for graduate students and researchers interested in this field.

Book

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

  1. 1.Mathematik in den NaturwissenschaftenMax-Planck-InstitutLeipzigGermany
  2. 2.Mathematik in den NaturwissenschaftenMax Planck InstitutLeipzigGermany
  3. 3.Mathematik in den NaturwissenschaftenMax Planck InstitutLeipzigGermany

About the authors

J. Jost: Studies of mathematics, physics, economics and philosophy; PhD and habilitation in mathematics (University of Bonn); professor for mathematics at Ruhr-University Bonn; since 1996 director at the MPI for Mathematics in the Sciences, Leipzig, and honorary professor at the University of Leipzig; external faculty member of the Santa Fe Institute

J. Hofrichter: Studies of mathematics and physics in Heidelberg, Granada and Muenster/Westph., diploma in mathematics; graduate studies in mathematics in Leipzig, PhD 2014; postdoctoral researcher at the MPI for Mathematics in the Sciences, Leipzig

T. D. Tran: Studies of mathematics in Hanoi (Vietnam), bachelor and master degree in mathematics; graduate studies in mathematics in Leipzig, PhD 2012; postdoctoral researcher at the MPI for Mathematics in the Sciences, Leipzig


Bibliographic information

Reviews

“Information Geometry and Population Genetics masterfully explores the stochastic dynamics of the progressive distribution of alleles over generations through a geometric perspective on the traditional Wright-Fisher model. … The present book is a useful piece of literature for applied biologists with a fair understanding of calculus, who are looking toward the exploration of new dimensions in research on genetic evolution.” (Ranjita Pandey, Canadian Studies in Population, Vol. 45 (1-2), 2018)