Understanding Complex Systems

Information Geometry and Population Genetics

The Mathematical Structure of the Wright-Fisher Model

Authors: Hofrichter, Julian, Jost, J., Tran, Tat Dat

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  • 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.
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  • ISBN 978-3-319-52045-2
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Hardcover $149.99
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Softcover $109.99
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  • ISBN 978-3-319-84805-1
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About this book

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.

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


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)

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-319-52045-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-319-52044-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $109.99
price for USA in USD
  • ISBN 978-3-319-84805-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Information Geometry and Population Genetics
Book Subtitle
The Mathematical Structure of the Wright-Fisher Model
Authors
Series Title
Understanding Complex Systems
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-52045-2
DOI
10.1007/978-3-319-52045-2
Hardcover ISBN
978-3-319-52044-5
Softcover ISBN
978-3-319-84805-1
Series ISSN
1860-0832
Edition Number
1
Number of Pages
XII, 320
Number of Illustrations
1 b/w illustrations, 2 illustrations in colour
Topics