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Mathematical Ecology, Epidemiology, & Evolution - MAT00090H

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  • Department: Mathematics
  • Module co-ordinator: Dr. Gustav Delius
  • Credit value: 20 credits
  • Credit level: H
  • Academic year of delivery: 2024-25
    • See module specification for other years: 2023-24

Module summary

This module aims to introduce students to the enormous diversity and complexity of problems in ecology, epidemiology and evolutionary theory. Students will learn how these problems are abstracted to arrive at well-defined mathematical models, particularly those that can be addressed via dynamical systems techniques.

Throughout the module mathematics students will be given the opportunity to gain familiarity with the vocabulary of biology.

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations


Additional information

This module is taught at both H- and M-level. You can only take the module once.

M-level students will have independent seminar content that will include critical analysis of contemporary research papers. M-level students will synthesise the understanding developed through these seminars, together with the theoretical content taught during the module, to produce a report that leverages computational methods.

Pre-requisite for H-level: Classical Dynamics (I-level)

Prohibited combinations: Mathematical Ecology, Epidemiology, and Evolution (H-level) may not be taken in combination with Mathematical Ecology, Epidemiology, and Evolution (M-level)

Recommended module: (H-level): Mathematical modelling: nonlinearity, uncertainty, and computational methods (H-level, semester 1)

MSc students should have taken a first course in Dynamical Systems.

 

 

Module will run

Occurrence Teaching period
A Semester 2 2024-25

Module aims

This module aims to introduce students to the enormous diversity and complexity of problems in ecology, epidemiology and evolutionary theory. Students will learn how these problems are abstracted to arrive at well-defined mathematical models, particularly those that can be addressed via dynamical systems techniques.

Throughout the module mathematics students will be given the opportunity to gain familiarity with the vocabulary of biology.

Module learning outcomes

By the end of this module students will be expected to be able to:

1. Formulate key processes in ecology, epidemiology, and evolution, as dynamic mathematical models (e.g. models of age and sex structure, species interaction models, SIR models, game theoretic models, trait evolution models, and models from theoretical population genetics).

2. Extend such models in ecology and epidemiology to account for space (e.g. diffusion, directed motion, and emergent travelling waves)

3. Analyse these models mathematically to make predictions about their dynamical and long-term behaviour (e.g. identifying stable states, inferring potential trajectories, and identifying emergent pattern formation)

4.Understand the interplay between ecological and evolutionary processes using adaptive dynamics

5. Understand how stochasticity can affect eco-evolutionary and epidemiological models

6. Articulate these mathematical results as biologically relevant insights (e.g. limits to harvesting, determinants of ecosystem stability, strategies for tackling disease outbreaks, predicting evolutionary trajectories, and explaining genetic patterns)

Module content

This module will cover:

  • Population dynamics of a single species in discrete and continuous time, with and without additional structure (such as age-structure and male-female interactions).

  • Limits to population growth and harvesting.

  • Interactions of two or more species (including predator-prey, competition and symbiosis).

  • Dynamics in space and time (including diffusion and directed motion).

  • Epidemics and travelling waves (including SIR models and vector-borne diseases).

  • Modelling strategies for tackling outbreaks.

  • Evolutionary Game Theory

  • The evolutionary dynamics of ecological systems (Adaptive Dynamics)

  • Stochastic modelling of biological populations

  • Population Genetics; evolution and neutral theory

Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Mathematical Ecology, Epidemiology, & Evolution		 3 hours 70
Essay/coursework
Coursework : Mathematical Ecology, Epidemiology, & Evolution		 N/A 30

Special assessment rules

None

Additional assessment information

The regular formative coursework - handed in for seminars - remains as in typical modules. The continuous summative assessment consists of 5 STACK quizzes, administered via Moodle, which test how well the student is able to apply the material from a previous coursework assignment and the associated feedback.

The student will be required to do all 5 quizzes, but extensions will be possible.

If a student has a failing module mark, only failed components need be reassessed. If a student fails the module and fails the continuous assessment component, then they should retake all 5 quizzes

Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Mathematical Ecology, Epidemiology, & Evolution		 3 hours 70
Essay/coursework
Coursework : Mathematical Ecology, Epidemiology, & Evolution		 N/A 30

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy

Indicative reading

J. D. Murray. Mathematical Biology I. An Introduction. Springer.

J. D. Murray. Mathematical Biology II. Spatial Models and Biomedical Applications. Springer.

W Gurney and R Nisbet, Ecological Dynamics, Oxford University Press (1998)


The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.