# Mathematics

## ECM3706 - Mathematical Biology and Ecology (2015)

MODULE TITLE CREDIT VALUE Mathematical Biology and Ecology 15 ECM3706 Dr Ozgur Akman (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
 Number of Students Taking Module (anticipated) 41
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 quantify population 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. Some use of software will enable you to build and analyse models using real world examples from nature. As an example, you may study the population dynamics of insects, animals or fish, or the competitive exclusion of species, and be able to draw conclusions about likely behaviours.

Prerequisite module: ECM2702 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 (spruce budworms, whales) 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;
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 display enhanced numerical and computational skills via the suite of practical exercises that accompany the formal lecture work;
10 show 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

- continuous models for a single species; analysis of models using linear stability theory; applications to the spruce budworm insect model, Hysteresis effects; harvesting a single natural population; discrete models and cobwebbing; discrete logistic growth and the route to chaos.

- two-species 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;

- reactivity and transient amplification in stage-structured populations; structured perturbations and ecological robustness.

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
2 exercise sheets 6-7 questions per sheet 1-11 In-class review of model solutions

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 20 80
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 80 2 hours 1-4, 6-9 None
Coursework – two assessed coursework sheets 20 4-5 questions per sheet 1-11 Feedback sheet and in-class review of model solutions

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
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:

http://vle.exeter.ac.uk