Overview
- Illustrates the tools of modelling in ecology and evolution for students and researchers in the field
- Co-published jointly with mathematical biosciences institute
- Top international authors in area of stochastic processes in biology series of lectures suitable for graduate students and researchers in mathematical biology
- Based on works with biologists from ecology and evolution
Part of the book series: Mathematical Biosciences Institute Lecture Series (MBILS, volume 1.4)
Part of the book sub series: Stochastics in Biological Systems (STOCHBS)
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Table of contents (9 chapters)
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Front Matter
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Discrete Monotype Population Models and One-dimensional Stochastic Differential Equations
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Front Matter
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Structured Populations and Measure-valued Stochastic Differential Equations
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Front Matter
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Back Matter
Keywords
About this book
In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes.
Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample ofindividuals.
These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France).
Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.
Reviews
“It deals mainly with the study of the limiting behavior under different scaling limits of several types of continuous-time individual based models of population dynamics subjected to demographic stochasticity … . The reader interested in the subject finds in this book very interesting results and a very well organized account on the state of the art, which integrates the main contributions of the authors and many other researchers in the (mostly recent) literature.” (Carlos A. Braumann, zbMATH 1333.92004, 2016)
Authors and Affiliations
About the authors
Vincent Bansaye is Associate Professor at Ecole Polytechnique in France and is a specialist of branching processes, particularly branching processes in random environments.
Sylvie Méléard is Full Professor at Ecole Polytechnique in France and is a specialist of random particle systems and their large number approximations models for physics and biology.
Bibliographic Information
Book Title: Stochastic Models for Structured Populations
Book Subtitle: Scaling Limits and Long Time Behavior
Authors: Sylvie Meleard, Vincent Bansaye
Series Title: Mathematical Biosciences Institute Lecture Series
DOI: https://doi.org/10.1007/978-3-319-21711-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2015
Softcover ISBN: 978-3-319-21710-9Published: 15 September 2015
eBook ISBN: 978-3-319-21711-6Published: 03 September 2015
Edition Number: 1
Number of Pages: X, 107
Number of Illustrations: 4 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Genetics and Population Dynamics, Theoretical Ecology/Statistics