Probabilistic Models of Population Evolution
Scaling Limits, Genealogies and Interactions
Authors: Pardoux, Étienne
Free Preview- Includes deep mathematical notions in connection with motivating applications
- Suitable for graduate students and researchers in mathematical biology
- Co-published jointly with Mathematical Biosciences Institute
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- About this Textbook
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This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the size of the population tends to infinity. The size of the population is described as a random function of time and of the initial population (the ancestors at time 0). The genealogical tree of such a population is given. Most models imply that the population is bound to go extinct in finite time. It is explained when the interaction is strong enough so that the extinction time remains finite, when the ancestral population at time 0 goes to infinity. The material could be used for teaching stochastic processes, together with their applications.
Étienne Pardoux is Professor at Aix-Marseille University, working in the field of Stochastic Analysis, stochastic partial differential equations, and probabilistic models in evolutionary biology and population genetics. He obtained his PhD in 1975 at University of Paris-Sud. - About the authors
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Étienne Pardoux is Professor at Aix-Marseille University, working in the field of Stochastic Analysis, in particular Stochastic partial differential equations. He obtained his PhD in 1975 at University of Paris-Sud.
- Reviews
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“This book presents the mathematical description of evolutionary models of populations subject to interactions within the population. … For readers’ convenience, the book contains an appendix summarizing the necessary backgrounds and technical results on stochastic calculus. The materials are presented with clarity, brevity and styles. … The book provides nice supplementary material for courses in stochastic processes and stochastic calculus.” (Chao Zhu, Mathematical Reviews, April, 2017)
“The main originality of the book is the fact that it describes the evolution of a population where the birth or death rates of the various individuals are affected by the size of the population. … The book is mainly intended to readers with some basic knowledge of stochastic processes and stochastic calculus. All in all, this is a serious piece of work.” (Marius Iosifescu, zbMATH 1351.92003, 2017)
- Table of contents (8 chapters)
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Introduction
Pages 1-3
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Branching Processes
Pages 5-11
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Convergence to a Continuous State Branching Process
Pages 13-21
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Continuous State Branching Process (CSBP)
Pages 23-44
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Genealogies
Pages 45-61
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Table of contents (8 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Probabilistic Models of Population Evolution
- Book Subtitle
- Scaling Limits, Genealogies and Interactions
- Authors
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- Étienne Pardoux
- Series Title
- Stochastics in Biological Systems
- Series Volume
- 1.6
- Copyright
- 2016
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-30328-4
- DOI
- 10.1007/978-3-319-30328-4
- Softcover ISBN
- 978-3-319-30326-0
- Series ISSN
- 2364-2297
- Edition Number
- 1
- Number of Pages
- VIII, 125
- Number of Illustrations
- 4 b/w illustrations, 2 illustrations in colour
- Additional Information
- Copublished with the Mathematical Biosciences Institute, Columbus, OH, USA
- Topics
