The Influence of Demographic Stochasticity on Population Dynamics

A Mathematical Study of Noise-Induced Bistable States and Stochastic Patterns

  • Tommaso┬áBiancalani
Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Tommaso Biancalani
    Pages 1-17
  3. Tommaso Biancalani
    Pages 19-30
  4. Tommaso Biancalani
    Pages 31-61
  5. Tommaso Biancalani
    Pages 63-82
  6. Tommaso Biancalani
    Pages 83-98
  7. Tommaso Biancalani
    Pages 99-105
  8. Back Matter
    Pages 107-113

About this book

Introduction

The dynamics of population systems cannot be understood within the framework of ordinary differential equations, which assume that the number of interacting agents is infinite. With recent advances in ecology, biochemistry and genetics it is becoming increasingly clear that real systems are in fact subject to a great deal of noise. Relevant examples include social insects competing for resources, molecules undergoing chemical reactions in a cell and a pool of genomes subject to evolution. When the population size is small, novel macroscopic phenomena can arise, which can be analyzed using the theory of stochastic processes. This thesis is centered on two unsolved problems in population dynamics: the symmetry breaking observed in foraging populations, and the robustness of spatial patterns. We argue that these problems can be resolved with the help of two novel concepts: noise-induced bistable states and stochastic patterns.

Keywords

Fluctuation in Small Populations Fokker-Planck Equation Gillespie Algorithm Noise-induced Bistability Population Dynamics and Noise Robustness of Spatial Patterns Stochastic Patterns Symmetry Breaking in Foraging Populations Van Kampen Expansion

Authors and affiliations

  • Tommaso┬áBiancalani
    • 1
  1. 1.Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-07728-4
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-07727-7
  • Online ISBN 978-3-319-07728-4
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • About this book