Branching Processes: Variation, Growth, and Extinction of Populations

by Patsy Haccou, Peter Jagers, Vladimir A. Vatutin

Overview

Biology takes a special place among the other natural sciences because biological units, be they pieces of DNA, cells or organisms, reproduce more or less faithfully. As for any other biological processes, reproduction has a large random component. The theory of branching processes was developed especially as a mathematical counterpart to this most fundamental of biological processes. This active and rich research area allows us to make predictions about both extinction risks and the development of population composition, and also uncovers aspects of a population's history from its current genetic composition. Branching processes play an increasingly important role in models of genetics, molecular biology, microbiology, ecology and evolutionary theory. This book presents this body of mathematical ideas for a biological audience, but should also be enjoyable to mathematicians.

Product Details

ISBN-13:	9780521832205
Publisher:	Cambridge University Press
Publication date:	05/19/2005
Series:	Cambridge Studies in Adaptive Dynamics , #5
Pages:	332
Product dimensions:	6.22(w) x 9.29(h) x 0.91(d)

About the Author

PATSY HACCOU is Associate Professor of Mathematical Biology at the Institute of Biology, Leiden University. She is co-author of Statistical Analysis of Behavioural Data.

PETER JAGERS is Professor of Mathematical Statistics at the Chalmers University of Technology and Gothenburg University. He is a member of the Swedish Academy of Sciences. He is author of Branching Processes with Biological Applications and co-editor of Classical and Modern Branching Processes.

VLADIMIR VATUTIN is leading Researcher at the Steklov Mathematical Institute, Moscow, Russia. He is co-author of Probabilistic Methods in Physical Research.

Table of Contents

Authors; Acknowledgements; Notational standards; 1. Generalities; 2. Discrete-time branching processes; 3. Branching in continuous time; 4. Large populations; 5. Extinction; 6. Development of populations; 7. Specific models; Appendix; References; Index.

Editorial Reviews

"Biologists should find this book to be of interest because of its forceful arguments for insights to be gained by expressing biological theories in mathematical terms. It should also be attractive to mathematicians because of the numerous biological examples that can lead to interesting mathematics."
The Quarterly Review of Biology, Edward Pollak, Iowa State University

"An exposition of biological applications combined with a leisurely exposition of the mathematical background. The intended audience is mainly biologists, but the abundance and diversity of biological examples should make the text highly enjoyable also for probabilists and statisticians."
Soren Asmussen, Biometrics

"Overall, this book gives a modern point of view on branching processes and their applications, and is of great help for modeling purposes. It reviews a wide spectrum of models, which are expressed in a way that is quite well adapted to biologists' viewpoints. It is a good demonstration of the fact that randomness has an important role to play in contemporary population biology."
Amaury Lambert, Ecoscience

"... this book nicely complements the existing books with interesting and important modern applications and has brought together contiburions from other scientist concerning related materials. For the first time, some of these materials are available in the book form. I am confident thais book will soon become a standard reference in the subject. I highly recommend this book to anyone who is interested in branching process models in biological sciences."
Anand Vidyasankar, Journal of the American Statistical Association

From the Publisher