Information Geometry and Population Genetics
The Mathematical Structure of the Wright-Fisher Model
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Beschreibung
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.
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.
Autor*in
Julian Hofrichter
Themen in »Information Geometry and Population Genetics«
35K75 60J25 60F10 92D25 35K20 35J70 60J70 53C99 information geometry population genetics Wright-Fisher model Kolmogorov equations free energy functional multiallele/multilocus model
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“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)
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