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Fast Variables in Stochastic Population Dynamics

Part of the Springer Theses Book Series

DOI: 10.1007/978-3-319-21218-0

ISBN: 978-3-319-21217-3

Publisher: Springer International Publishing - Springer Journals

Jul 26, 2015

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Chapter 1Introduction

Constable, George William Albert

Pages: 1 –10

[In what follows I am going to explore how concepts and mathematical tools originally developed within physics can be applied to a variety of other fields. These can include, but are not limited to, population genetics, evolution, opinion dynamics, epidemiology and ecology. This thesis will focus...
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Chapter 2Technical Background

Constable, George William Albert

Pages: 11 –44

[In this chapter, I will review some of the fundamental ideas and mathematical tools employed in the analysis of stochastic systems.]
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Chapter 3The Conditioning Method

Constable, George William Albert

Pages: 45 –64

[In this chapter the conditioning method is introduced. The core of the approach is to examine the behaviour of a stochastic system in the SDE framework under the condition that its trajectories are confined to the slow subspace of the deterministic version of the system. A similar procedure has...
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Chapter 4The Projection Matrix Method

Constable, George William Albert

Pages: 65 –82

[In this section, a second method of fast variable elimination in stochastic systems will be introduced. This method aims to remove the problems encountered in the conditioning method when the noise matrix is singular (see Sect. 3.5). The essential idea is to explicitly remove any contribution to...
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Chapter 5Analysis of the Reduced Metapopulation Moran Model

Constable, George William Albert

Pages: 83 –101

[In the last chapter, the projection matrix method was used to simplify the migration model to a one-dimensional SDE with the form of Eq. (4.27).]
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Chapter 6Further Developments

Constable, George William Albert

Pages: 103 –126

[In this chapter further developments of the conditioning and projection matrix method are presented. In the following section, the discussion of the metapopulation Moran model is completed by adding mutation. Following this, a more detailed comparison of the two reduction methods is conducted....
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Chapter 7Conclusion

Constable, George William Albert

Pages: 127 –132

[In the introduction to this thesis, some time was spent discussing the choices one makes in modelling any system. In some sense we are playing a game by which we wish to incorporate enough detail so as to be realistic and informative, but not so much as to render the model resistant to...

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