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The use of probabilistic methods in the biological sciences has
been so well established by now that mathematical biology is
regarded by many as a distinct dis cipline with its own repertoire
of techniques. The purpose of the Workshop on sto chastic methods
in biology held at Nagoya University during the week of July 8-12,
1985, was to enable biologists and probabilists from Japan and the
U. S. to discuss the latest developments in their respective fields
and to exchange ideas on the ap plicability of the more recent
developments in stochastic process theory to problems in biology.
Eighteen papers were presented at the Workshop and have been
grouped under the following headings: I. Population genetics (five
papers) II. Measure valued diffusion processes related to
population genetics (three papers) III. Neurophysiology (two
papers) IV. Fluctuation in living cells (two papers) V.
Mathematical methods related to other problems in biology,
epidemiology, population dynamics, etc. (six papers) An important
feature of the Workshop and one of the reasons for organizing it
has been the fact that the theory of stochastic differential
equations (SDE's) has found a rich source of new problems in the
fields of population genetics and neuro biology. This is especially
so for the relatively new and growing area of infinite dimensional,
i. e., measure-valued or distribution-valued SDE's. The papers in
II and III and some of the papers in the remaining categories
represent these areas."
To show the importance of stochastic processes in the change of
gene frequencies, the authors discuss topics ranging from molecular
evolution to two-locus problems in terms of diffusion models.
Throughout their discussion, they come to grips with one of the
most challenging problems in population genetics--the ways in which
genetic variability is maintained in Mendelian populations. R.A.
Fisher, J.B.S. Haldane, and Sewall Wright, in pioneering works,
confirmed the usefulness of mathematical theory in population
genetics. The synthesis their work achieved is recognized today as
mathematical genetics, that branch of genetics whose aim is to
investigate the laws governing the genetic structure of natural
populations and, consequently, to clarify the mechanisms of
evolution. For the benefit of population geneticists without
advanced mathematical training, Professors Kimura and Ohta use
verbal description rather than mathematical symbolism wherever
practicable. A mathematical appendix is included.
This textbook, originally published in 1970, is a classic in the
field of Population Genetics. It presents the field of population
genetics, starting with elementary concepts and leading the reader
well into the field. It is concerned mainly with population
genetics in a strict sense and deals primarily with natural
populations and less fully with the rather similar problems that
arise in breading livestock and cultivated plans. The emphasis is
on the behavior of genes and population attributes under natural
selection where the most important measure is Darwinian fitness.
This text is intended for graduate students and advanced
undergraduates in genetics and population biology This book steers
a middle course between completely verbal biological arguments and
the rigor of the mathematician. The first two-thirds of the book do
not require advanced mathematical background. An ordinary knowledge
of calculus will suffice. The latter parts of the book, which deal
with population stochastically, use more advanced methods. Chapter
Titles: 1.Models of population growth. 2.Randomly mating
populations. 3.Inbreeding. 4.Correlation between relatives and
assertive mating. 5.Selection. 6.Populations in approximate
equilibrium. 7.Properties of a finite population. 8.Stochastic
processes in the change of gene frequencies. 9.Distribution of gene
frequencies in populations. Appendix. Some statistical and
mathematical methods frequently used in population genetics.
Bibliography. Glossary. Index.
One of this century's leading evolutionary biologists, Motoo Kimura
revolutionized the field with his random drift theory of molecular
evolution--the neutral theory--and his groundbreaking theoretical
work in population genetics. This volume collects 57 of Kimura's
most important papers and covers forty years of his diverse and
original contributions to our understanding of how genetic
variation affects evolutionary change.
Kimura's neutral theory, first presented in 1968, challenged the
notion that natural selection was the sole directive force in
evolution. Arguing that mutations and random drift account for
variations at the level of DNA and amino acids, Kimura advanced a
theory of evolutionary change that was strongly challenged at first
and that eventually earned the respect and interest of evolutionary
biologists throughout the world. This volume includes the seminal
papers on the neutral theory, as well as many others that cover
such topics as population structure, variable selection intensity,
the genetics of quantitative characters, inbreeding systems, and
reversibility of changes by random drift.
Background essays by Naoyuki Takahata examine Kimura's work in
relation to its effects and recent developments in each area.
Motoo Kimura, as founder of the neutral theory, is uniquely placed
to write this book. He first proposed the theory in 1968 to explain
the unexpectedly high rate of evolutionary change and very large
amount of intraspecific variability at the molecular level that had
been uncovered by new techniques in molecular biology. The theory -
which asserts that the great majority of evolutionary changes at
the molecular level are caused not by Darwinian selection but by
random drift of selectively neutral mutants - has caused
controversy ever since. This book is the first comprehensive
treatment of this subject and the author synthesises a wealth of
material - ranging from a historical perspective, through recent
molecular discoveries, to sophisticated mathematical arguments -
all presented in a most lucid manner.
Motoo Kimura revolutionized evolutionary biology with his random
drift theory of molecular evolution - the neutral theoryand his
groundbreaking theoretical work in population genetics. This volume
collects fifty-seven of Kimura's most important papers and covers
forty years of his diverse and original contributions to our
understanding of how genetic variation affects evolutionary change.
Kimura's neutral theory, first presented in 1968, challenged the
notion that natural selection was the sole directive force in
evolution. Arguing that mutations and random drift account for
variations at the level of DNA and amino acids, Kimura advanced a
theory of evolutionary change that was strongly challenged at first
and that eventually earned the respect and interest of evolutionary
biologists throughout the world. This volume includes the seminal
papers on the neutral theory, as well as many others that cover
such topics as population structure, variable selection intensity,
the genetics of quantitative characters, inbreeding systems, and
reversibility of changes by random drift. Background essays by
Naoyuki Takahata examine Kimura's work in relation to its effects
and recent developments in each area. This book will stand as a
valuable reference for students and professionals in evolutionary
biology for years to come.
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