Information Geometry and Population Genetics: The Mathematical Structure of the Wright-Fisher Model

Front Cover
Springer, Feb 23, 2017 - Mathematics - 320 pages

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.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

1 Introduction
1
2 The WrightFisher Model
16
3 Geometric Structures and Information Geometry
45
4 Continuous Approximations
77
5 Recombination
102
6 Moment Generating and Free Energy Functionals
123
7 Large Deviation Theory
169
8 The Forward Equation
195
9 The Backward Equation
219
10 Applications
268
A Hypergeometric Functions and Their Generalizations
289
Bibliography
306
Index of Notation
313
Index
316
Copyright

Other editions - View all

Common terms and phrases

About the author (2017)

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


Bibliographic information