Branching Processes and Neutral Evolution

  • Ziad Taïb

Part of the Lecture Notes in Biomathematics book series (LNBM, volume 93)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Ziad Taïb
    Pages 1-13
  3. Ziad Taïb
    Pages 14-19
  4. Ziad Taïb
    Pages 20-22
  5. Ziad Taïb
    Pages 23-31
  6. Ziad Taïb
    Pages 32-45
  7. Ziad Taïb
    Pages 46-51
  8. Ziad Taïb
    Pages 52-59
  9. Ziad Taïb
    Pages 60-70
  10. Ziad Taïb
    Pages 71-80
  11. Ziad Taïb
    Pages 81-84
  12. Ziad Taïb
    Pages 85-93
  13. Ziad Taïb
    Pages 94-99
  14. Back Matter
    Pages 100-112

About this book

Introduction

The Galton-Watson branching process has its roots in the problem of extinction of family names which was given a precise formulation by F. Galton as problem 4001 in the Educational Times (17, 1873). In 1875, an attempt to solve this problem was made by H. W. Watson but as it turned out, his conclusion was incorrect. Half a century later, R. A. Fisher made use of the Galton-Watson process to determine the extinction probability of the progeny of a mutant gene. However, it was J. B. S. Haldane who finally gave the first sketch of the correct conclusion. J. B. S. Haldane also predicted that mathematical genetics might some day develop into a "respectable branch of applied mathematics" (quoted in M. Kimura & T. Ohta, Theoretical Aspects of Population Genetics. Princeton, 1971). Since the time of Fisher and Haldane, the two fields of branching processes and mathematical genetics have attained a high degree of sophistication but in different directions. This monograph is a first attempt to apply the current state of knowledge concerning single-type branching processes to a particular area of mathematical genetics: neutral evolution. The reader is assumed to be familiar with some of the concepts of probability theory, but no particular knowledge of branching processes is required. Following the advice of an anonymous referee, I have enlarged my original version of the introduction (Chapter Zero) in order to make it accessible to a larger audience. G6teborg, Sweden, November 1991.

Keywords

Branching process Evolution Theory Mathematical Genetics Neural Mutation Probability theory Seen

Authors and affiliations

  • Ziad Taïb
    • 1
    • 2
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden
  2. 2.The University of GöteborgGöteborgSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-51536-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55529-2
  • Online ISBN 978-3-642-51536-1
  • Series Print ISSN 0341-633X
  • About this book