Fast Variables in Stochastic Population Dynamics

Beschreibung

 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. 
 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.
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

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George William Albert Constable

Themen in »Fast Variables in Stochastic Population Dynamics«

Demographic stochasticity Fast Variable Elimination Method Moran model Stochastic Population Dynamics Stochastic Theory of Biological Systems Stochastic Theory of Ecological Systems Timescale Separation data-driven science, modeling and theory building systems biology

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