Motoo Kimura

Takeyuki Hida

Gopinath Kallianpur

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.

Proceedings of a Workshop held in Nagoya, Japan July 8–12 1985

Stochastic Methods in Biology

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.

Selected Papers

Population Genetics, Molecular Evolution, and the Neutral Theory

Tomoko Ohta

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.

Theoretical Aspects of Population Genetics

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

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