Branching Processes in Biology

1. Front Matter

   Pages i-xviii

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2. Motivating Examples and Other Preliminaries

   • Marek Kimmel, David E. Axelrod

   Pages 1-18

3. Biological Background

   • Marek Kimmel, David E. Axelrod

   Pages 19-31

4. The Galton-Watson Process

   • Marek Kimmel, David E. Axelrod

   Pages 33-63

5. The Age-Dependent Process: The Markov Case

   • Marek Kimmel, David E. Axelrod

   Pages 65-86

6. The Bellman-Harris Process

   • Marek Kimmel, David E. Axelrod

   Pages 87-102

7. Multitype Processes

   • Marek Kimmel, David E. Axelrod

   Pages 103-139

8. Branching Processes with Infinitely Many Types

   • Marek Kimmel, David E. Axelrod

   Pages 141-177

9. References

   • Marek Kimmel, David E. Axelrod

   Pages 179-195

10. Back Matter

    Pages 197-230

    PDF

In this book biological examples of Branching Processes are introduced from molecular and cellular biology as well as from the fields of human evolution and medicine and discussed in the context of the relevant mathematics, providing a useful introduction on how the modelling can be done and for what types of problems branching processes can be useful. As an aid to understanding specific examples, two introductory chapters provide background material in mathematics and biology.
This book will interest scientists who work in quantitative modelling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, and cell and molecular biologists and bioinformaticians.
The authors of this monograph are a mathematician and a cell biologist who have collaborated in the field of Branching Processes for more than a decade.

• Branching Processes
• Branching process
• Galton-Watson process
• Mathematical Biology
• biology

From the reviews:

MATHEMATICAL REVIEWS

"The book is clearly written and provides a basic knowledge of branching processes and molecular biology. The scope of the present volume is unique in that it illustrates a paradigm in which theoretical results are simulated by biological applications and biological processes are illuminated by mathematics. It is an excellent source of information to probabilists, mathematical biologists and bioinformaticians."

 

M. Kimmel and D.E. Axelrod

Branching Processes in Biology

"This is a book written jointly by a mathematician and a cell biologist, who have collaborated on research in branching processes for more than a decade. In their own words, their monograph is intended for ‘mathematicians and statisticians who have had an introduction to stochastic processes but have forgotten much of their college biology, and for biologists who wish to collaborate with mathematicians and statisticians.’ They have largely succeeded in achieving their goal. The book can be strongly recommended to all students of branching processes; all libraries should have a copy." —ZENTRALBLATT MATH

"This book treats the theory of several important types of branching processes and demonstrates their usefulness by many interesting and important applications. … Mathematical theory and biological applications are nicely interwoven. This text will be useful both to mathematicians (including graduate students) interested in relevant applications of stochastic processes in biology, as well as to mathematically oriented biologists working on the above mentioned topics." (R. Bürger, Monatshefte für Mathematik, Vol. 143 (1), 2004)

"This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests incellular and molecular biology." (Charles J. Mode, Siam Review, Vol. 45 (2), 2003)

"Branching processes have made important contributions to biology and medicine in the areas of molecular biology, cell biology, developmental biology, immunology, evolution and ecology. … The book is clearly written and provides a basic knowledge of branching processes and molecular biology. The scope of the present volume is unique in that it illustrates a paradigm in which theoretical results are simulated by biological applications and biological processes are illuminated by mathematics. It is an excellent source of information to probabilists, mathematical biologists and bioinformaticians." (P.R. Parthasarathy, Mathematical Reviews, 2003 b)

"The theory of branching processes is an intensively developing area of mathematics, particularly stochastic processes, with many important applications in biology, medicine, physics and other natural sciences. This book contains … many examples of very interesting and successful applications of branching processes to biological and medical problems … . The book will be very interesting and useful for mathematicians, statisticians and biologists as well, and especially for researchers developing mathematical methods in biology, medicine and other natural sciences." (V.V. Anisimov, Short Book Reviews, Vol. 23 (2), 2003)

"Study of branching processes emerged from … mathematical analysis of the problem of extinction of the surnames of the British upper class. This area of stochastic processes continues to evolve and provides useful models of a large variety of far more significant biological processes. … This book is clearly a very useful compendium of work in this area, an area in which the authors have published extensively. Any mathematician contemplating work in this field would benefit from having the book on his or her shelf." (David Kault, The Australian Mathematical Society Gazette, Vol. 30 (2),2003)

"This is a book written jointly by a mathematician and a cell biologist, who have collaborated on research in branching processes for more than a decade. … their monograph is intended for ‘mathematicians and statisticians who have had an introduction to stochastic processes … and for biologists who wish to collaborate with mathematicians and statisticians.’ They have largely succeeded in achieving their goal. … The book can be strongly recommended to all students of branching processes; all libraries should have a copy of it." (Joseph M. Gani, Zentralblatt Math, Vol. 994 (19), 2002)

• Department of Statistics, Rice University, Houston, USA

  Marek Kimmel

• Department of Genetics, Rutgers University Nelson Biolabs, Piscataway, USA

  David E. Axelrod

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