Module Details |
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. |
Title | POPULATION DYNAMICS | ||
Code | MATH332 | ||
Coordinator |
Dr KJ Sharkey Mathematical Sciences K.J.Sharkey@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2020-21 | Level 6 FHEQ | Second Semester | 15 |
Aims |
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- 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 |
Learning Outcomes |
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(LO1) The ability to relate the predictions of the mathematical models to experimental results obtained in the field. |
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(LO2) The ability to recognise the limitations of mathematical modelling in understanding the mechanics of complex biological systems. |
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(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. |
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(S1) Problem solving skills |
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(S2) Numeracy |
Syllabus |
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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. |
Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
final assessment open book and remote There is a resit opportunity. Assessment Schedule (When) :second semester | 1 hour time on task | 50 | ||||
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Class Test 1 open book and remote | around 60-90 minutes | 50 |