Mathematics

ECM3905 - Mathematical Biology and Ecology (2015)

MODULE TITLE CREDIT VALUE Mathematical Biology and Ecology 15 ECM3905 Dr Colin Torney (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
 Number of Students Taking Module (anticipated) 20
DESCRIPTION - summary of the module content

We are surrounded by the natural living world in which populations boom or go extinct. So what drives this amazing spectrum of dynamically varying biodiversity? In this module you will learn how mathematics can be used to quantify and model population and demographic phenomena. You will draw on real data sets from ecology-based research.

Pre requisites: ECM1903, ECM1904

AIMS - intentions of the module

This module is designed to illustrate how mathematics and computational tools may be used in ecology and more widely in the bio-sciences in general. Throughout, emphasis will be placed on realistic situations and include: disease dynamics and SIR models; population management and conservation; collective behaviour and animal movement; evolution and games. The module is self-contained and only assumes knowledge of A-level mathematics.

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 and computing can be usefully employed in various aspects of life and environmental sciences;
2 understand the role of mathematical modelling for natural systems.
Discipline Specific Skills and Knowledge:
3 appreciate how matrix techniques and calculus have diverse practical uses;
4 demonstrate expertise in using analytical and numerical techniques to explore mathematical models;
5 formulate simple models;
6 analyse the resulting equations;
7 draw conclusions about likely behaviours.
Personal and Key Transferable/ Employment Skills and  Knowledge:
9 demonstrate enhanced numerical and computational skills via the suite of practical exercises that accompany the formal lecture work;
10 demonstrate enhanced literature searching and library skills in order to investigate various phenomena discussed;
11 demonstrate enhanced time management and organisational abilities.

SYLLABUS PLAN - summary of the structure and academic content of the module

A refresher of key mathematical tools and supporting computer programming [9 hours]

SIR models and disease [6 hours]

Adaptive management as a conservation tool [6 hours]

Collective behavior, animal movement and agent-based modelling [6 hours]

Evolution and game theory [6 hours]

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 11 Lectures Scheduled learning and teaching activities 22 Computer classes, 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
4 exercise sheets 4 x 2 hours 1-10 In-class review of model solutions

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 100 0 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework Sheet 1 25 5 hours 1-7 Written and oral
Coursework Sheet 2 25 5 hours 1-7 Written and oral
Group Report 20 4 hours 1-10 Written and oral
Individual Report 30 6 hours 1-10 Written and Oral

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-assessment
All above Coursework (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

The reassessment will take the form of an extended coursework sheet. The first part will be short questions in the format of the assessed coursework sheets (50%). Then there will be a more open-ended question whose solution is preparation for a controlled computation/simulation assessment (50%).

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

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

Basic reading:

ELE: ELE: http://vle.exeter.ac.

Web based and Electronic Resources:

Other Resources:

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Caswell, Hal Matrix population models : construction, analysis, and interpretation 2nd Sinauer Associates 2001 9780878930937 [Library]
Set Sarah P. Otto & Troy Day A Biologist's Guide to Mathematical Modeling in Ecology and Evolution 1st Princeton University Press 2007 978-0691123448 [Library]
Set Steven H. Strogatz Nonlinear Dynamics and Chaos 2nd Sinauer Associates 2014 978-0813349107 [Library]
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES ECM1903, ECM1904
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 6 No Thursday 23 January 2014 Friday 13 March 2015
KEY WORDS SEARCH Mathematical biology; ecology; nonlinear dynamics; systems biology; population dynamics; evolutionary dynamics.