Study information

# Mathematical Biology and Ecology - 2023 entry

MODULE TITLE CREDIT VALUE Mathematical Biology and Ecology 15 MTH3006 Prof Marc Goodfellow (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
 Number of Students Taking Module (anticipated) 90
DESCRIPTION - summary of the module content
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
AIMS - intentions of the module

This module is designed to illustrate the application of mathematics to the biological science, and emphasises realistic situations throughout. These include: population dynamics and stage-structured population models incorporating complex demographies. They also include harvesting models; competitive exclusion of species; reaction kinetics; biological waves; diffusion-driven instabilities and the effects of geometry on pattern formation in animals. On this module, you will learn how to use core applied mathematics techniques, such as differential equation modelling and matrix algebra. However, no previous biological knowledge will be assumed.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
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.

SYLLABUS PLAN - summary of the structure and academic content of the module
- 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
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 33 117 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled Learning and Teaching Activities 33 Lectures, example classes Guided Independent Study 117 Lecture and assessment preparation; wider reading

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Four Coursework Sheets 5-6 questions per sheet 1-10 Feedback sheet and in-class review of model solutions

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 20 80 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework 1 – based on questions submitted for assessment 10 15 hours  All Annotated script and written/verbal feedback
Coursework 2 - based on questions submitted for assessment 10 15 hours All Annotated script and written/verbal feedback
Written Exam 80 2 hours (Summer) 1-7 Written/Verbal on request, SRS

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
Written Exam* Written Exam (2 hours) (10%) All August Ref/Def Period
Coursework 1 Coursework 1 (10%) All August Ref/Def Period
Coursework 2 Coursework 2 (80%) All August ref/Def Period

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

RE-ASSESSMENT NOTES
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%.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Type Author Title Edition Publisher Year ISBN
Set Murray, J.D. Mathematical Biology 2nd Springer 1993 000-3-540-57204-X
Set Jones, D.S. & Sleeman, B.D. Differential Equations and Mathematical Biology Electronic Allen & Unwin 2003 000-0-045-15001-X
Set Fife, P.C. Mathematical Aspects of Reacting and Diffusing Systems Springer 1979 000-3-540-09117-3
Set May, R.M. Theoretical Ecology. Principles and Applications Electronic Blackwell Scientific Publications 2007 000-0-632-00762-1
Set Alstad, D. Basic Populus Models of Ecology Prentice-Hall 2001 978-0130212894
Set Caswell, H. Matrix Population Models: Construction, Analysis, and Interpretation 2nd Sinauer Associates 2001 9780878930937
Set Britton, N.F. Essential Mathematical Biology Springer 2005 978-1852335366
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES MTH2003
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 6 No Tuesday 10th July 2018 Thursday 26th January 2023
KEY WORDS SEARCH Mathematical Biology; Ecology; Nonlinear Dynamics; Systems Biology; Population Dynamics; Mathematical Modelling; Linear Algebra; Differential Equations