Information Geometry and Population Genetics : The Mathematical Structure of the Wright-Fisher Model. 1st ed. 2017

種類:

電子ブック

責任表示:

by Julian Hofrichter, Jürgen Jost, Tat Dat Tran

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Hofrichter, Julian.
• Jost, Jürgen.
• Tran, Tat Dat.
• SpringerLink (Online service)

シリーズ名:

Understanding Complex Systems ;

ISBN:

9783319520452 [3319520458]    

注記:

1. Introduction -- 2. The Wright–Fisher model -- 3. Geometric structures and information geometry -- 4. Continuous approximations -- 5. Recombination -- 6. Moment generating and free energy functionals -- 7. Large deviation theory -- 8. The forward equation -- 9. The backward equation -- 10.Applications -- Appendix -- A. Hypergeometric functions and their generalizations -- Bibliography.
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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