Stochastic Models for Structured Populations: Scaling Limits and Long Time Behavior (Mathematical Biosciences Institute Lecture Series, 1.4) - Softcover

Meleard, Sylvie

Softcover

ISBN 10: 3319217100 ISBN 13: 9783319217109

Publisher: Springer, 2015

Synopsis

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.

About this title

About the Author

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.

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2015
• Language: English
• ISBN 10: 3319217100
• ISBN 13: 9783319217109
• Binding: Paperback
• Edition number: 1
• Number of pages: 117