Fast Variables in Stochastic Population Dynamics

✍ Scribed by George William Albert Constable (auth.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 172
• Series: Springer Theses
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvii
Introduction....Pages 1-10
Technical Background....Pages 11-44
The Conditioning Method....Pages 45-64
The Projection Matrix Method....Pages 65-82
Analysis of the Reduced Metapopulation Moran Model....Pages 83-101
Further Developments....Pages 103-126
Conclusion....Pages 127-132
Back Matter....Pages 133-163

✦ Subjects

Socio- and Econophysics, Population and Evolutionary Models; Community & Population Ecology; Genetics and Population Dynamics; Biological Networks, Systems Biology