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Information Geometry and Population Genetics

  • Livre Relié
  • 320 Nombre de pages
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The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetic... Lire la suite
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Description

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.



Provides a new systematic and geometric approach to the Wright--Fisher model of population genetics

Introduces new tools from information geometry and statistical mechanics that lead to a deeper understanding

Includes precise formulas and a detailed analysis of the boundary behavior (loss of allele events)

Provides a solid and broad working basis for graduate students and researchers interested in this field.



Auteur

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




Contenu

1. Introduction.- 2. The WrightFisher 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.

Informations sur le produit

Titre: Information Geometry and Population Genetics
Auteur:
Code EAN: 9783319520445
ISBN: 978-3-319-52044-5
Format: Livre Relié
Editeur: Springer, Berlin
Genre: Mathématique
nombre de pages: 320
Poids: 647g
Taille: H25mm x B240mm x T159mm
Année: 2017
Auflage: 1st ed. 2017

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