Branching Processes: Variation, Growth, and Extinction of Populations

ISBN-13: 9780521832205 / Angielski / Twarda / 2005 / 332 str.

Patsy Haccou; Peter Jagers; Vladimir A. Vatutin

Opis

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.

Recenzje

'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

Spis treści

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.