Branching Processes: Variation, Growth, and Extinction of Populations (Cambridge Studies in Adaptive Dynamics, Series Number 5)

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. 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 A Basic Command Of Calculus, Matrix Algebra, And Probability Theory. More Advanced Results From Basic Probability Theory Are Treated In A Special Appendix.--jacket. Generalities -- Discrete-time Branching Processes -- Branching In Continuous Time -- Large Populations -- Extinction -- Development Of Populations -- Specific Models. Patsy Haccou, Peter Jagers, Vladimir A. Vatutin. Includes Bibliographical References (p. 295-305) And Index. "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 a basic command of calculus, matrix algebra, and probability theory. More advanced results from basic probability theory are treated in a special appendix."--Back cover. Branching processes assist predictions about extinction risks, and the development of population composition, and also uncovers aspects of a population's history from current genetic composition. Branching processes play an important role in models of genetics, molecular biology, microbiology, ecology and evolutionary theory. This book presents these mathematical ideas for biologists.

This book covers the mathematical idea of branching processes, and tailors it for a biological audience.