Information Geometry and Population Genetics
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.
| Autor: | Hofrichter, Julian Jost, Jürgen Tran, Tat Dat |
|---|---|
| ISBN: | 9783319848051 |
| Sprache: | Englisch |
| Seitenzahl: | 320 |
| Produktart: | Kartoniert / Broschiert |
| Verlag: | Springer International Publishing |
| Veröffentlicht: | 18.07.2018 |
| Untertitel: | The Mathematical Structure of the Wright-Fisher Model |
| Schlagworte: | 35K20 35J70 60J70 53C99 35K75 60J25 60F10 92D25 Kolmogorov equations Wright-Fisher model free energy functional information geometry multiallele/multilocus model population genetics |
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