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Branching Processes and Neutral Evolution (Paperback, 1992 ed.)
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Branching Processes and Neutral Evolution (Paperback, 1992 ed.)
Series: Lecture Notes in Biomathematics, 93
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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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