Information Geometry and Population Genetics

The Mathematical Structure of the Wright-Fisher Model

Nonfiction, Science & Nature, Mathematics, Applied, Statistics, Science
Cover of the book Information Geometry and Population Genetics by Julian Hofrichter, Jürgen Jost, Tat Dat Tran, Springer International Publishing
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Author: Julian Hofrichter, Jürgen Jost, Tat Dat Tran ISBN: 9783319520452
Publisher: Springer International Publishing Publication: February 23, 2017
Imprint: Springer Language: English
Author: Julian Hofrichter, Jürgen Jost, Tat Dat Tran
ISBN: 9783319520452
Publisher: Springer International Publishing
Publication: February 23, 2017
Imprint: Springer
Language: English

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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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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