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| Module Availability |
| Spring |
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| Assessment Pattern |
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Project
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25
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Exam
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75
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Qualifying Condition(s)
An overall aggregate mark of 50% for the module is required to pass the module.
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| Module Overview |
The module focuses on application of mathematical models to biological dynamics, with a particular interest in population dynamics. It is distinct in attention on application of the mathematical models to biological questions such as: Is herbivore density dependent upon vegetation? Do modern anthropogenic habits facilitate disease transmission? Can harvesting increase abundance?
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| Prerequisites/Co-requisites |
MAT2007: Ordinary Differential Equations
MAT3030: Chaotic Dynamics |
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| Module Aims |
1) to demonstrate the application of mathematical techniques to applied biological questions with real world relevance;
2) to develop ability to use the freely available R environment to construct and analyze different types of mathematical models;
3) to enable students to report their models in a context that is accessible to mathematicians, biologists and members of the public. |
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| Learning Outcomes |
| After completion, students should be able to (1) apply a range of linear and non-linear, single- and multispecies population models distributed unevenly in space; (2) obtain equilibria, asymptotic and transient behavior; and (3) communicate the model results and conclusions in everyday language, i.e. for members of public. |
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| Module Content |
Content will include:
1) introduction; what are models, what use are they and do assumptions matter?
2) single-state population dynamics; coupled dynamics; equilibria and asymptotic behaviour;
3) distributions in space; metapopulation dynamics; immigration and emigration;
4) multi-state population dynamics; age- and stage structured populations; asymptotic and transient dynamics
5) stochastic dynamics; Markov chains; temporal autocorrelation; |
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| Methods of Teaching/Learning |
| Lectures/tutorials/computer labs/research projects including background reading. |
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| Selected Texts/Journals |
Ellner & Guckenheimer 2006 “Dynamic Models in Biology”, Princeton University Press.
Otto & Day 2007 "A Biologist's Guide to Mathematical Modeling in Ecology and Evolution", Princeton University Press.
Journal articles supplied as required. |
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| Last Updated |
| November 11th 2010 |
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