Overview
- 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.
Part of the book series: Understanding Complex Systems (UCS)
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Table of contents (10 chapters)
Keywords
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.
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Authors and Affiliations
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
Book Title: Information Geometry and Population Genetics
Book Subtitle: The Mathematical Structure of the Wright-Fisher Model
Authors: Julian Hofrichter, Jürgen Jost, Tat Dat Tran
Series Title: Understanding Complex Systems
DOI: https://doi.org/10.1007/978-3-319-52045-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-52044-5Published: 06 March 2017
Softcover ISBN: 978-3-319-84805-1Published: 18 July 2018
eBook ISBN: 978-3-319-52045-2Published: 23 February 2017
Series ISSN: 1860-0832
Series E-ISSN: 1860-0840
Edition Number: 1
Number of Pages: XII, 320
Number of Illustrations: 1 b/w illustrations, 2 illustrations in colour
Topics: Mathematical and Computational Biology, Statistical Theory and Methods, Human Genetics, Analysis, Geometry, Probability Theory and Stochastic Processes