Stochastic Methods in Biology

1. Front Matter

   Pages I-VI

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2. Population Genetics

   1. Front Matter

      Pages 1-1

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   2. A Stochastic Model of Compensatory Neutral Evolution

      • Motoo Kimura

      Pages 2-18

   3. Some Models for Treating Evolution of Multigene Families and Other Repetitive DNA Sequences

      • Tomoko Ohta

      Pages 19-26

   4. A Genealogical Description of the Infinitely-Many Neutral Alleles Model

      • P. J. Donnelly, S. Tavaré

      Pages 27-35

   5. Equilibrium Measures of the Stepping Stone Model with Selection in Population Genetics

      • S. Itatsu

      Pages 36-52

   6. Asymptotic Properties for Kimura’s Diffusion Model with Altruistic Allele

      • Yukio Ogura, Norio Shimakura

      Pages 53-70

3. Measure-Valued Diffusion Processes Related to Population Genetics

   1. Front Matter

      Pages 71-71

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   2. The Infinitely-Many-Alleles Model with Selection as a Measure-Valued Diffusion

      • S. N. Ethier, T. G. Kurtz

      Pages 72-86

   3. Multi-Allelic Gillespie-Sato Diffusion Models and their Extension to Infinite Allelic Ones

      • Tokuzo Shiga

      Pages 87-99

   4. Stationary Distribution of a Diffusion Process Taking Values in Probability Distributions on the Partitions

      • Akinobu Shimizu

      Pages 100-114

4. Neurophysiology

   1. Front Matter

      Pages 115-115

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   2. Weak Convergence of Stochastic Neuronal Models

      • G. Kallianpur, Robert L. Wolpert

      Pages 116-145

   3. Note on the Ornstein-Uhlenbeck Process Model for Stochastic Activity of a Single Neuron

      • Shunsuke Sato

      Pages 146-156

5. Fluctuation in Living Cells

   1. Front Matter

      Pages 157-157

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   2. Fluctuation in Living Cells: Effect of Field Fluctuation and Asymmetry of Fluctuation

      • Fumio Oosawa, Masateru Tsuchiya, Tomoko Kubori

      Pages 158-170

   3. Some Aspects of Oosawa’s Equation

      • Hisao Watanabe

      Pages 171-173

6. Mathematical Methods Related to Other Problems in Biology, Epidemiology, Population Dynamics, etc.

   1. Front Matter

      Pages 175-175

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   2. Problems of Epidemic Modelling

      • J. Gani

      Pages 176-184

   3. Markov Semigroups Associated with One-Dimensional Lévy Operators — Regularity and Convergence —

      • Akira Negoro, Masaaki Tsuchiya

      Pages 185-193

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.

• dynamics
• epidemiology
• genetics
• population dynamics
• probability distribution

• National Institute of Genetics, Shizuoka-ken, 411, Japan

  Motoo Kimura

• Center for Stochastic Processes, Department of Statistics, University of North Carolina, Chapel Hill, USA

  Gopinath Kallianpur

• Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya, 464, Japan

  Takeyuki Hida

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