Stochastic Problems in Population Genetics

✍ Scribed by Dr. Takeo Maruyama (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1977
• Tongue: English
• Leaves: 253
• Series: Lecture Notes in Biomathematics 17
• Edition: 1
• Category: Library

✦ Synopsis

These are" notes based on courses in Theoretical Population Genetics given at the University of Texas at Houston during the winter quarter, 1974, and at the University of Wisconsin during the fall semester, 1976. These notes explore problems of population genetics and evolution involving stochastic processes. Biological models and various mathematical techniques are discussed. Special emphasis is given to the diffusion method and an attempt is made to emphasize the underlying unity of various problems based on the Kolmogorov backward equation. A particular effort was made to make the subject accessible to biology students who are not familiar with stochastic processes. The references are not exhaustive but were chosen to provide a starting point for the reader interested in pursuing the subject further. Acknowledgement I would like to use this opportunity to express my thanks to Drs. J. F. Crow, M. Nei and W. J. Schull for their hospitality during my stays at their universities. I am indebted to Dr. M. Kimura for his continuous encouragement. My thanks also go to the small but resolute groups of.students, visitors and colleagues whose enthusiasm was a great source of encouragement. I am especially obliged to Dr. Martin Curie-Cohen and Dr. Crow for reading a large part eX the manuscript and making many valuable comments. Special gratitude is expressed to Miss Sumiko Imamiya for her patience and endurance and for her efficient preparation of the manuscript.

✦ Table of Contents

Front Matter....Pages I-VIII
Orientation....Pages 1-23
Population Genetics Models....Pages 24-35
Classification of Boundaries....Pages 36-42
Expectation of Integration Along Sample Paths....Pages 43-73
Modification of Processes....Pages 74-94
Numerical Integration of the Kolmogorov Backward Equation....Pages 95-101
Eigenvalues and Eigenvectors of the KBE....Pages 102-120
Approximation Methods....Pages 121-129
Geographical Structure of Populations....Pages 130-155
Geographically Invariant Properties....Pages 156-186
Gene Frequency Distributions and Random Drift in Geographically Structured Populations....Pages 187-200
Some Special Problems....Pages 201-217
Back Matter....Pages 218-247

✦ Subjects

Probability Theory and Stochastic Processes; Mathematics, general