Ebook: Branching Processes and Neutral Evolution

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.

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This monograph sets out to apply the current knowledge of single-type branching processes to a particular area of mathematical genetics: neutral evolution. It can also serve as an introductory text to branching processes seen as a methodology that can be used in various problems in populationdynamics. The work will be of interest to applied probabilists, researchers in branching processes, researchers in evolution theory and population geneticists. The reader is assumed to befamiliar with some of the concepts of probability theory, but no particular background in branching processes or evolution theory is required. The introduction of the book is accessible to a large audience.

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This monograph sets out to apply the current knowledge of single-type branching processes to a particular area of mathematical genetics: neutral evolution. It can also serve as an introductory text to branching processes seen as a methodology that can be used in various problems in populationdynamics. The work will be of interest to applied probabilists, researchers in branching processes, researchers in evolution theory and population geneticists. The reader is assumed to befamiliar with some of the concepts of probability theory, but no particular background in branching processes or evolution theory is required. The introduction of the book is accessible to a large audience.
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-13
The Construction of the Process....Pages 14-19
Labelled Branching Processes....Pages 20-22
The Number of Distinct Labels....Pages 23-31
The Label Process....Pages 32-45
The Limiting Stable Case....Pages 46-51
The Process of Mutant Ancestors....Pages 52-59
A Measure of Relatedness....Pages 60-70
Infinite Sites Labels....Pages 71-80
Related Individuals....Pages 81-84
Embeddings in Branching Processes....Pages 85-93
Extensions....Pages 94-99
Back Matter....Pages 100-112

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This monograph sets out to apply the current knowledge of single-type branching processes to a particular area of mathematical genetics: neutral evolution. It can also serve as an introductory text to branching processes seen as a methodology that can be used in various problems in populationdynamics. The work will be of interest to applied probabilists, researchers in branching processes, researchers in evolution theory and population geneticists. The reader is assumed to befamiliar with some of the concepts of probability theory, but no particular background in branching processes or evolution theory is required. The introduction of the book is accessible to a large audience.
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-13
The Construction of the Process....Pages 14-19
Labelled Branching Processes....Pages 20-22
The Number of Distinct Labels....Pages 23-31
The Label Process....Pages 32-45
The Limiting Stable Case....Pages 46-51
The Process of Mutant Ancestors....Pages 52-59
A Measure of Relatedness....Pages 60-70
Infinite Sites Labels....Pages 71-80
Related Individuals....Pages 81-84
Embeddings in Branching Processes....Pages 85-93
Extensions....Pages 94-99
Back Matter....Pages 100-112
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