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Fast Variables in Stochastic Population Dynamics

  • Book
  • © 2015

Overview

Authors:
  1. George William Albert Constable

    1. Department of Ecology and Evolutionary B, Princeton University, Princeton, USA

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  • Nominated as an outstanding Ph.D. thesis by the University of Manchester, UK
  • Features a clear introduction to stochastic population dynamics, making the thesis easily accessible to non-experts
  • Develops techniques of broad interest for researchers working in theoretical population dynamics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Introduction

    • George William Albert Constable
    Pages 1-10

  3. Technical Background

    • George William Albert Constable
    Pages 11-44

  4. The Conditioning Method

    • George William Albert Constable
    Pages 45-64

  5. The Projection Matrix Method

    • George William Albert Constable
    Pages 65-82

  6. Analysis of the Reduced Metapopulation Moran Model

    • George William Albert Constable
    Pages 83-101

  7. Further Developments

    • George William Albert Constable
    Pages 103-126

  8. Conclusion

    • George William Albert Constable
    Pages 127-132

  9. Back Matter

    Pages 133-163
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Keywords

About this book

 In this thesis two variants of the fast variable elimination method are developed. They are intuitive, simple to implement and give results which are in very good agreement with those found from numerical simulations. The relative simplicity of the techniques makes them ideal for applying to problems featuring demographic stochasticity, for experts and non-experts alike.
Within the context of mathematical modelling, fast variable elimination is one of the central tools with which one can simplify a multivariate problem. When used in the context of of deterministic systems, the theory is quite standard, but when stochastic effects are present, it becomes less straightforward to apply.
While the introductory and background chapters form an excellent primer to the theory of stochastic population dynamics, the techniques developed can be applied to systems exhibiting a separation of timescales in a variety of fields including population genetics, ecology and epidemiology.

Authors and Affiliations

  • Department of Ecology and Evolutionary B, Princeton University, Princeton, USA

    George William Albert Constable

About the author

George Constable has a background in non-equilibrium statistical physics, and is especially interested in applying the ideas and techniques of stochastic theory to ecological and biological systems. His first degree was from the University of Glasgow and his Ph.D was obtained from the University of Manchester. While there, his work was primarily concerned with the derivation of effective theories for microscopically defined individual based models. Currently, he is a postdoctoral researcher looking at the effects of spatial structure on population level dynamics in the Ecology and Evolutionary Biology Department at Princeton University.

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