Information Geometry and Population Genetics

The Mathematical Structure of the Wright-Fisher Model

AvJulian Hofrichter,Jürgen Jost

Inbunden, Engelska, 2017

Del i serien Understanding Complex Systems

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Häftad

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2017-03-06
Mått:155 x 235 x 24 mm
Vikt:664 g
Format:Inbunden
Språk:Engelska
Serie:Understanding Complex Systems
Antal sidor:320
Upplaga:17001
Förlag:Springer International Publishing AG
ISBN:9783319520445

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Medicinsk genetik inom Medicin

Mer om författaren

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, LeipzigT. 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

Recensioner i media

“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)

Innehållsförteckning

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.