Evolution and Ecology Program

EEP Books
Cambridge Studies in Adaptive Dynamics

Branching Processes by Patsy Haccou, Peter Jagers, and Vladimir Vatutin Cambridge University Press (2005). From the Back Cover As biology takes s special place among the other natural sciences because biological units, be the pieces of DNA, cells, or organisms, reproduce more or less faithfully. Like any other biological process, 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 determine extinction risks and predict the development of population composition, and also uncover 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, if only for its rich stock of realistic biological examples. It can be read by anyone with basic command of calculus, matrix algebra, and probability theory. More advanced results from basic probability theory are treated in a special appendix.


Introduction "Why should a biologist read a book about branching processes in biology, and why should a mathematician? This book is aimed primarily at biologists, so let us start with the mathematicians. You should read this book because it places a beautiful mathematical theory in proper context. This is not to say that branching processes cannot be viewed in contexts other than those of population biology. On the contrary, branching processes occur in particle physics, in chemistry, and in computer science. However, mathematics can lose its direction in the jungle of problems that are syntactically well formed and mathematically intriguing, but that have no clear bearing on the outside world. Too many mathematicians, in our view, work on intellectual riddles, while important scientific problems escape their attention. You should read this book to see that branching processes are not only a fascinating mathematical structure, but also can help us to understand fundamental questions of the nature."

Table of Contents 1 Generalities 2 Discrete-Time Branching Processes 3 Branching in Continuous Time 4 Large Populations 5 Extinction 6 Development of Populations 7 Specific Models

Book Review of the International Statistical Institute "The authors opine that much of mathematical biology should be treated probabilistically rather than deterministically. They also advocate stochastic modelling at the individual level rather than deterministic modelling at the population level. As they say, the former can be scaled up and approximated transparently whereas the latter may contain hidden unrealistic features. Such thoughts, and much more wide-ranging wisdom, are presented in Chapter 1, a good read for any statistician."

Book Review in Folia Geobotanica "In its seven chapters, the reviewed book brings theoretical insight into the background of population dynamics[...]." "The book can be used by many researchers and graduate students working on population dynamics [...]."

Book Review in Biometrics "[...] the book will serve well for an advanced course in mathematical biology. It would also be possible to use it for a course of statistics and probability students at a rather early stage of their studies. "

Book Review in Ecoscience "Overall, this book gives a modern point of view on branching processes and their applications, and is of great help for modelling purposes. It reviews a wide spectrum of models, which are expressed in a way that is quite well adapted to biologists' viewpoint. It is a good demonstration of the fact that randomness has an important role to play in contemporary population biology. Hopefully, it will contribute to thelp researchers in this challenge."

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