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Stochastics in Biological Systems

Stochastic Models for Structured Populations

Scaling Limits and Long Time Behavior

Authors: Méléard, Sylvie, Bansaye, Vincent

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  • 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
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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 of individuals.

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.

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.

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)


Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-319-21711-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Models for Structured Populations
Book Subtitle
Scaling Limits and Long Time Behavior
Authors
Series Title
Stochastics in Biological Systems
Series Volume
1.4
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-21711-6
DOI
10.1007/978-3-319-21711-6
Softcover ISBN
978-3-319-21710-9
Series ISSN
2364-2297
Edition Number
1
Number of Pages
X, 107
Number of Illustrations
4 b/w illustrations
Topics