Mathematical Biology and Ecology - 2024 entry

This module will give you the opportunity to learn how mathematics may be applied to the biosciences in order to quantitatively model biological processes, from molecular  processes at work within living cells up to the behaviour of populations and demographic phenomena. The subject matter has been selected so as to give a wide-ranging overview of the role applied mathematics has to play in the biological disciplines. You will build and analyse models (typically as differential equations or iterated maps) using real world examples from nature. Examples that may be studied within the module include: the population dynamics of insects, animals or fish, competitive  exclusion of species, the behaviour of the chemical reactions kinetics that power living cells and mechanisms of biological pattern formation from reaction-diffusion equations.

 

Pre-requisite module: MTH2003 or equivalent

On successful completion of this module, you should be able to:

 

Module Specific Skills and  Knowledge:

1 Appreciate how mathematics can be usefully employed in various aspects of the life sciences;

 

Discipline Specific Skills and Knowledge:

2 Understand the role of mathematical modelling in real-life situations;

3 Recognise how many aspects of applied mathematics learned in earlier modules have practical uses;

4 Develop considerable expertise in using analytical and numerical techniques to explore mathematical models, including the use of appropriate software (e.g. MATLAB, Python, R etc.)

5 Formulate simple models;

6 Study adeptly the resulting equations;

7 Draw conclusions about likely behaviours.

 

Personal and Key Transferable/ Employment Skills and Knowledge:

8 Display enhanced numerical and computational skills via the suite of practical exercises that accompany the formal lecture work; 

9 Show enhanced literature searching and library skills in order to investigate various phenomena discussed;

10 Demonstrate enhanced time management and organisational abilities.

 

- Continuous models for a single species; analysis of models using linear stability theory; Hysteresis effects; harvesting a single natural population; discrete models and cobwebbing; discrete logistic growth and the route to chaos;

- Two-dimensional models; introduction to simple phase plane analysis; realistic models for various cases (e.g. predator-prey interactions) and the principles of competitive exclusion and mutualism;

- Introduction to population projection models; geometric growth, stable stage structures and reproductive value for stage-structured ecological populations; asymptotic analysis and transient bounds;

- Tools for analysing PPMs; sensitivity and elasticity; use of transfer function analysis to achieve exact perturbations; applications to managed conservation strategies; reaction kinetics and the law of mass action;

- Enzyme-substrate kinetics; Michaelis-Menten theory and activation/inhibition phenomena;

- Reaction-diffusion problems and biological waves; the Fisher equation; Turing instabilities and diffusion-driven instabilities in two-component systems; generation of patterning by domain geometry; minimal domains for stable pattern formation

Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped.  

  

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 40%.