具體描述
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.
著者簡介
圖書目錄
Introduction....Pages 1-15
The Wright–Fisher Model....Pages 17-43
Geometric Structures and Information Geometry....Pages 45-76
Continuous Approximations....Pages 77-101
Recombination....Pages 103-122
Moment Generating and Free Energy Functionals....Pages 123-167
Large Deviation Theory....Pages 169-194
The Forward Equation....Pages 195-218
The Backward Equation....Pages 219-267
Applications....Pages 269-287
Back Matter....Pages 289-319
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