Probabilistic Models of Population Evolution

Scaling Limits, Genealogies and Interactions

  • Étienne Pardoux

Part of the Mathematical Biosciences Institute Lecture Series book series (MBILS, volume 1.6)

Also part of the Stochastics in Biological Systems book sub series (STOCHBS, volume 1.6)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Étienne Pardoux
    Pages 1-3
  3. Étienne Pardoux
    Pages 5-11
  4. Étienne Pardoux
    Pages 23-44
  5. Étienne Pardoux
    Pages 45-61
  6. Étienne Pardoux
    Pages 63-82
  7. Étienne Pardoux
    Pages 83-98
  8. Étienne Pardoux
    Pages 99-108
  9. Back Matter
    Pages 109-125

About this book

Introduction

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.

Keywords

Evolutionary Models Markov Chains Population Models Bienaymé-Galton-Watson Processes Continuous State Branching Processes Populations with Interactions

Authors and affiliations

  • Étienne Pardoux
    • 1
  1. 1.Institut de Math´ematiques de MarseilleAix-Marseille Universit´eMarseillesFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-30328-4
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-30326-0
  • Online ISBN 978-3-319-30328-4
  • About this book
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