Information Geometry and Population Genetics
Springer International Publishing (Verlag)
978-3-319-84805-1 (ISBN)
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.
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
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.
"Information Geometry and Population Genetics masterfully explores the stochastic dynamics of the progressive distribution of alleles over generations through a geometric perspective on the traditional Wright-Fisher model. ... The present book is a useful piece of literature for applied biologists with a fair understanding of calculus, who are looking toward the exploration of new dimensions in research on genetic evolution." (Ranjita Pandey, Canadian Studies in Population, Vol. 45 (1-2), 2018)
“Information Geometry and Population Genetics masterfully explores the stochastic dynamics of the progressive distribution of alleles over generations through a geometric perspective on the traditional Wright-Fisher model. … The present book is a useful piece of literature for applied biologists with a fair understanding of calculus, who are looking toward the exploration of new dimensions in research on genetic evolution.” (Ranjita Pandey, Canadian Studies in Population, Vol. 45 (1-2), 2018)
| Erscheinungsdatum | 05.03.2022 |
|---|---|
| Reihe/Serie | Understanding Complex Systems |
| Zusatzinfo | XII, 320 p. 3 illus., 2 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 5037 g |
| Themenwelt | Informatik ► Weitere Themen ► Bioinformatik |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | 35K20 35J70 60J70 53C99 • 35K75 60J25 60F10 92D25 • free energy functional • information geometry • Kolmogorov equations • multiallele/multilocus model • Population Genetics • Wright-Fisher Model |
| ISBN-10 | 3-319-84805-4 / 3319848054 |
| ISBN-13 | 978-3-319-84805-1 / 9783319848051 |
| Zustand | Neuware |
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