Module Details

Module Specification

The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.

Module Title

POPULATION DYNAMICS

Module Code

MATH332

Year

Session 2023-24

Originating Department

Mathematical Sciences

Faculty

Fac of Science & Engineering

Semester

Second Semester

CATS Level

Level 6 FHEQ

CATS Value

Member of staff with responsibility for the module

Professor KJ Sharkey

Mathematical Sciences

K.J.Sharkey@liverpool.ac.uk

10.

Module Moderator

11.

Other Contributing Departments

12.

Other Staff Teaching on this Module

Professor R Bearon

Mathematical Sciences

R.Bearon@liverpool.ac.uk

13.

Board of Studies

14.

Mode of Delivery

15.

Location

Main Liverpool City Campus

		Lectures	Seminars	Tutorials	Lab Practicals	Fieldwork Placement	Other	TOTAL
16.	Study Hours			12			36	48
17.	Private Study							102
18.	TOTAL HOURS							150

		Lectures	Seminars	Tutorials	Lab Practicals	Fieldwork Placement	Other
19.	Timetable (if known)

20.	Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

21.	Modules for which this module is a pre-requisite:

22.	Co-requisite modules:

23.	Linked Modules:

24.	Programme(s) (including Year of Study) to which this module is available on a mandatory basis:

25.	Programme(s) (including Year of Study) to which this module is available on a required basis:

26.	Programme(s) (including Year of Study) to which this module is available on an optional basis:

27.

Aims

- To provide a theoretical basis for the understanding of population ecology - To explore the classical models of population dynamics - To learn basic techniques of qualitative analysis of mathematical models

28.

Learning Outcomes

(LO1) The ability to relate the predictions of the mathematical models to experimental results obtained in the field.

(LO2) The ability to recognise the limitations of mathematical modelling in understanding the mechanics of complex biological systems.

(LO3) The ability to use analytical and graphical methods to investigate population growth and the stability of equilibrium states for continuous-time and discrete-time models of ecological systems.

(S1) Problem solving skills

(S2) Numeracy

29.

Teaching and Learning Strategies

Material is provided in advance of classes for students to study asynchronously. The contact hours consist of one 2-hour active learning session and one 2-hour supported study/drop-in session.

30.

Syllabus

Single species systems: Fundamental balance equations. Malthus's model. Intraspecific competition. Continuous time logistic model. Discrete time models: Hassell model and logistic map. Relationship between continuous and discrete time models. Equilibria, stability, cycles and a mention of period doubling and chaos in the discrete time models. Explicit time delays, stability triangle. Age structure, use of Leslie matrices for linear problems. Multi-species systems: Coupled balance equations leading to m-species discrete and continuous time models. Linear stability analysis, community matrix for both continuous and discrete time. Lotka-Volterra-Gause models for interspecific competition. Gause's competitive exclusion principle. Lotka-Volterra and other predator-prey models, including a discussion of functional and numerical responses. Nicholson-Bayley host-parasitoid model as a predator-prey system in discrete time. Kermack-McKendrick models of infectious diseases. Methods o f analysis: Linear stability analysis and phase plane analysis. Poincare-Andronov-Hopf theorem. Lyapunov stability theory. Poincare-Bendixson theory.

31.

Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Assessment

32.	EXAM	Duration	Timing (Semester)	% of final mark	Resit/resubmission opportunity	Penalty for late submission	Notes
	Final assessment There is a resit opportunity.	90		70

33.	CONTINUOUS	Duration	Timing (Semester)	% of final mark	Resit/resubmission opportunity	Penalty for late submission	Notes
	Class Test	60		30