Information Geometry and Population Genetics

The Mathematical Structure of the Wright-Fisher Model
Buch | Hardcover
XII, 320 Seiten
2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-52044-5 (ISBN)

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Information Geometry and Population Genetics - Julian Hofrichter, Jürgen Jost, Tat Dat Tran
139,09 inkl. MwSt

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 InstituteJ. 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
Reihe/Serie Understanding Complex Systems
Zusatzinfo XII, 320 p. 3 illus., 2 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Informatik Weitere Themen Bioinformatik
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Geometrie / Topologie
Studium 2. Studienabschnitt (Klinik) Humangenetik
Schlagworte 35K20 35J70 60J70 53C99 • 35K75 60J25 60F10 92D25 • Analysis • Calculus and mathematical analysis • free energy functional • Geometry • Human genetics • information geometry • Kolmogorov equations • Mathematical and Computational Biology • Mathematics • mathematics and statistics • Maths for scientists • medical genetics • multiallele/multilocus model • Population Genetics • probability and statistics • Probability theory and stochastic processes • Statistical Theory and Methods • stochastics • Wright-Fisher Model
ISBN-10 3-319-52044-X / 331952044X
ISBN-13 978-3-319-52044-5 / 9783319520445
Zustand Neuware
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