Hofrichter, Julian. Information Geometry and Population Genetics : The Mathematical Structure of the Wright-Fisher Model / [electronic resource] : / by Julian Hofrichter, Jürgen Jost, Tat Dat Tran.. — 1st ed. 2017.. — XII, 320 p. 3 illus., 2 illus. in color. : online resource. — (Understanding Complex Systems,) 1860-0832. - Understanding Complex Systems, .
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.
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Анотація: 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.
9783319520452
10.1007/978-3-319-52045-2 doi
Biomathematics. Statistics . Human genetics. Mathematical analysis. Analysis (Mathematics). Geometry. Probabilities. Mathematical and Computational Biology. Statistical Theory and Methods. Human Genetics. Analysis. Geometry. Probability Theory and Stochastic Processes.