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2010/1 Module Catalogue
Module Provider: Mathematics Short Name: MATM026
Level: M Module Co-ordinator: EZARD TH Dr (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability
Assessment Pattern


Unit(s) of Assessment


Weighting Towards Module Mark( %)










Qualifying Condition(s) 


An overall aggregate mark of 50% for the module is required to pass the module.



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?



MAT2007: Ordinary Differential Equations


MAT3030: Chaotic Dynamics
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.
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.
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;
Methods of Teaching/Learning
Lectures/tutorials/computer labs/research projects including background reading.
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.
Last Updated
November 11th 2010