TY  - BOOK
AU  - Hofrichter,Julian
AU  - Jost,Jürgen
AU  - Tran,Tat Dat
ED  - SpringerLink (Online service)
TI  - Information Geometry and Population Genetics: The Mathematical Structure of the Wright-Fisher Model 
T2  - Understanding Complex Systems,
SN  - 9783319520452
AV  - QH323.5 
U1  - 570.285 23
PY  - 2017///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematical statistics
KW  - Human genetics
KW  - Global analysis (Mathematics)
KW  - Geometry
KW  - Distribution (Probability theory
KW  - Mathematical and Computational Biology
KW  - Statistical Theory and Methods
KW  - Human Genetics
KW  - Analysis
KW  - Probability Theory and Stochastic Processes
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-52045-2
ER  -