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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. Branching Processes presents this body of mathematical ideas for a biological audience, but should also be enjoyable to mathematicians.
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
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 (1975) 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.
"[...] the book should serve well, among other things, as an excellent introduction to applied probabilists looking for interesting and worthwhile applications."
- Publication of the International Statistical Institute
"In summary, this is an excellent book with a plethora of real biological examples and lucid writing style that is accessible to most students and scientists with a good command over calculus and basic probability. The book can serve well for a two-semester course in stochastic processes in biology with one semester devoted to branching processes in biology. I am confident this 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."
- Journal of the American Statistical Association
