# Mathematics (Penryn)

## ECM3905 - Mathematics Biology and Ecology (2018)

MODULE TITLE CREDIT VALUE Mathematics Biology and Ecology 15 ECM3905 Unknown
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 bio-diversity. 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. This may include the development of models for turtles, geese, grasshoppers and bacterial swarms. Modelling techniques will draw on projection matrices, differential equations and reaction diffusion systems.

Prerequisite modules: “Calculus and Geometry” (ECM1901) and “Vectors and Matrices” (ECM1902) or equivalent

AIMS - intentions of the module

This module is designed to illustrate how mathematics may be used in ecology and more widely in the bio-sciences in general. Throughout, emphasis will be placed on realistic situations and include: population dynamics, stage-structured population models incorporating complex demography; harvesting models; competitive exclusion of species; simple analysis of reaction kinetics; biological waves and diffusion driven instabilities; effects of geometry and pattern formation on animals. The module is self contained and only assumes knowledge of Calculus and Numbers and Vectors and Matrices.

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 considerable expertise in using analytical and numerical techniques to explore mathematical models;
5 formulate simple models;
6 study adeptly 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 enhance time management and organisational abilities.

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

- Continuous models for a single species, the Malthus model and analysis of models using linear stability theory; Applications to the spruce budworm insect model, hysteresis effects; Harvesting a single natural population [3 hours];
- Discrete models and cobwebbing; Discrete logistic growth and the route to chaos [3 hours];
- Introduction to simple phase plane analysis and its use in investigating continuous population models; Competitive exclusion and mutualism [6 hours];
- Introduction to stage-structured population projection models [3 hours];
- Geometric growth, stable stage structures and reproductive value for stage-structured populations [3 hours];
- Reaction kinetics and the law of mass action; Enzyme-substrate kinetics; Examples of more complex chemical kinetics; Michaelis-Menten theory and activation/inhibition phenomena [3 hours];
- Reaction-diffusion systems; The Fisher equation; Turing instabilities and diffusion driven instabilities; Generation of patterning by geometry [3 hours];
- Transient and reactive dynamics in stage-structured populations; Applications to invasion by mutant species [6 hours];
- Evolutionary dynamics: Adaptive dynamics; Population dynamics and games [3 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 Computer classes Scheduled learning and teaching activities 22 Formal lectures and example classes of new material 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
2 exercise sheets 2 x 3 hours 1-11 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 Sheet 1 10 3 hours 1-11 Written and oral
Coursework Sheet 2 10 3 hours 1-11 Written and oral
Written Exam - closed book 80 2 hours 1-8, 10,11 Annotated scripts

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 Written Exam (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.

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

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 Murray J.D. Mathematical Biology 2nd Springer 1993 000-3-540-57204-X [Library]
Set Jones D.S. & Sleeman B.D. Differential Equations and Mathematical Biology Electronic Allen & Unwin 2003 000-0-045-15001-X [Library]
Set Fife P.C. Mathematical aspects of reacting and diffusing systems Springer 1979 000-3-540-09117-3 [Library]
Set May R.M. Theoretical Ecology. Principles and Applications Electronic Blackwell Scientific Publications 2007 000-0-632-00762-1 [Library]
Set Alstad, D Basic Populus Models of Ecology Prentice-Hall 2001 978-0130212894 [Library]
Set Britton, Nicholas F Essential Mathematical Biology Springer 2005 978-1852335366 [Library]
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES ECM1901, ECM1902
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 6 No Thursday 23 January 2014 Friday 09 March 2018
KEY WORDS SEARCH Mathematical biology; Ecology; Nonlinear dynamics; Systems biology; Population dynamics; Evolutionary dynamics.