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Stochastic Problems in Population Genetics

  • Book
  • © 1977

Overview

Authors:
  1. Takeo Maruyama

    1. National Institute of Genetics, Sizuoka-Ken 411, Japan

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Part of the book series: Lecture Notes in Biomathematics (LNBM, volume 17)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Orientation

    • Takeo Maruyama
    Pages 1-23

  3. Population Genetics Models

    • Takeo Maruyama
    Pages 24-35

  4. Classification of Boundaries

    • Takeo Maruyama
    Pages 36-42

  5. Expectation of Integration Along Sample Paths

    • Takeo Maruyama
    Pages 43-73

  6. Modification of Processes

    • Takeo Maruyama
    Pages 74-94

  7. Numerical Integration of the Kolmogorov Backward Equation

    • Takeo Maruyama
    Pages 95-101

  8. Eigenvalues and Eigenvectors of the KBE

    • Takeo Maruyama
    Pages 102-120

  9. Approximation Methods

    • Takeo Maruyama
    Pages 121-129

  10. Geographical Structure of Populations

    • Takeo Maruyama
    Pages 130-155

  11. Geographically Invariant Properties

    • Takeo Maruyama
    Pages 156-186

  12. Gene Frequency Distributions and Random Drift in Geographically Structured Populations

    • Takeo Maruyama
    Pages 187-200

  13. Some Special Problems

    • Takeo Maruyama
    Pages 201-217

  14. Back Matter

    Pages 218-247
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Keywords

About this book

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.

Authors and Affiliations

  • National Institute of Genetics, Sizuoka-Ken 411, Japan

    Takeo Maruyama

Bibliographic Information

  • Book Title: Stochastic Problems in Population Genetics

  • Authors: Takeo Maruyama

  • Series Title: Lecture Notes in Biomathematics

  • DOI: https://doi.org/10.1007/978-3-642-93065-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1977

  • Softcover ISBN: 978-3-540-08349-8Published: 01 August 1977

  • eBook ISBN: 978-3-642-93065-2Published: 13 March 2013

  • Series ISSN: 0341-633X

  • Series E-ISSN: 2196-9981

  • Edition Number: 1

  • Number of Pages: VIII, 248

  • Topics: Probability Theory and Stochastic Processes, Mathematics, general

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