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Stochastic Models for Structured Populations

Scaling Limits and Long Time Behavior

  • Sylvie Meleard
  • Vincent Bansaye
Book

Part of the Mathematical Biosciences Institute Lecture Series book series (MBILS, volume 1.4)

Also part of the Stochastics in Biological Systems book sub series (STOCHBS, volume 1.4)

Table of contents

  1. Front Matter
    Pages i-x
  2. Vincent Bansaye, Sylvie Méléard
    Pages 1-3
  3. Discrete Monotype Population Models and One-dimensional Stochastic Differential Equations

    1. Front Matter
      Pages 5-5
    2. Vincent Bansaye, Sylvie Méléard
      Pages 7-17
    3. Vincent Bansaye, Sylvie Méléard
      Pages 19-27
    4. Vincent Bansaye, Sylvie Méléard
      Pages 29-38
    5. Vincent Bansaye, Sylvie Méléard
      Pages 39-46
  4. Structured Populations and Measure-valued Stochastic Differential Equations

    1. Front Matter
      Pages 47-47
    2. Vincent Bansaye, Sylvie Méléard
      Pages 49-60
    3. Vincent Bansaye, Sylvie Méléard
      Pages 61-77
    4. Vincent Bansaye, Sylvie Méléard
      Pages 79-87
    5. Vincent Bansaye, Sylvie Méléard
      Pages 89-98
  5. Back Matter
    Pages 99-107

About this book

Introduction

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.

Keywords

Birth and death processes Branching processes in random environment Cell division dynamics Continuous state branching processes Large population approximations Martingale properties Measure-valued Markov processes Population models Two-level models

Authors and affiliations

  • Sylvie Meleard
    • 1
  • Vincent Bansaye
    • 2
  1. 1.CMAP UMR 7641École Polytechnique CNRSPalaiseau CedexFrance
  2. 2.École Polytechnique CNRSPalaiseau CedexFrance

Bibliographic information