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＜電子ブック＞
Information Geometry and Population Genetics : The Mathematical Structure of the Wright-Fisher Model / by Julian Hofrichter, Jürgen Jost, Tat Dat Tran
(Understanding Complex Systems. ISSN:18600840)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
本文言語	英語
大きさ	XII, 320 p. 3 illus., 2 illus. in color : online resource
著者標目	*Hofrichter, Julian author Jost, Jürgen author Tran, Tat Dat author SpringerLink (Online service)
件　名	LCSH:Biomathematics LCSH:Statistics  LCSH:Medical genetics LCSH:Mathematical analysis LCSH:Geometry LCSH:Probabilities FREE:Mathematical and Computational Biology FREE:Statistical Theory and Methods FREE:Medical Genetics FREE:Analysis FREE:Geometry FREE:Probability Theory
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-52045-2

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