Kaisa_2012_3_photo by Veikko Somerpuro

This course will explore how to model the dynamics and evolution of populations with spatial movement, spatial constraints and spatial interactions between organisms. We start with a brief introduction to mathematical ecology. In spatial ecology, we study diffusion, travelling waves, pattern formation and Turing instability, stochastic patch occupancy models, structured metapopulation models, probabilistic cellular automata and coupled map lattices. We also discuss topical issues of evolutionary biology where spatial structure plays a crucial role, e.g. the evolution of mobility (dispersal), specialisation to different environments, and why space matters for the evolution of altruistic behaviour.

This is a course in applied mathematics. Instead of choosing the problem to suit a method, we emphasize the use of versatile techniques. We introduce/review methods for ordinary differential equations and difference equations, partial differential equations, Fourier analysis, stochastic processes, pair approximation methods, game theory and adaptive dynamics. When necessary, we turn to numerical analysis.

SCHEDULE: The course starts on Wednesday 16 January with a lecture. Afterwards, until the teaching break, lecture on each Monday and Friday except that Friday 1 February is cancelled. Exercise classes on the following Wednesdays: 30 January, 13 and 27 February. After the teaching break, the preliminary schedule is as follows: lecture on each Monday and Friday plus 3 April and 17 April (Wednesdays) except that an exercise class replaces the lecture on 12 April and 3 May. Exercise classes on 13 March (Wed), 27 March (Wed, 12 April (Fri), and 3 May (Fri).

!!! NEW: I must swap the lecture of 15 February (Fri) and the exercise class of 13 February (Wed)

QUICK TESTS: 25 January (Friday), 13 February (Wednesday)

Enrol
10.12.2018 at 09:00 - 3.5.2019 at 23:59

Messages

Add new message

Eva Kisdi's picture

Eva Kisdi

Published, 21.12.2018 at 13:43

The course starts on Wednesday 16 January.

Timetable

Here is the course’s teaching schedule. Check the description for possible other schedules.

DateTimeLocation
Mon 14.1.2019
14:15 - 16:00
Wed 16.1.2019
14:15 - 16:00
Fri 18.1.2019
10:15 - 12:00
Mon 21.1.2019
14:15 - 16:00
Wed 23.1.2019
14:15 - 16:00
Fri 25.1.2019
10:15 - 12:00
Mon 28.1.2019
14:15 - 16:00
Wed 30.1.2019
14:15 - 16:00
Fri 1.2.2019
10:15 - 12:00
Mon 4.2.2019
14:15 - 16:00
Wed 6.2.2019
14:15 - 16:00
Fri 8.2.2019
10:15 - 12:00
Mon 11.2.2019
14:15 - 16:00
Wed 13.2.2019
14:15 - 16:00
Fri 15.2.2019
10:15 - 12:00
Mon 18.2.2019
14:15 - 16:00
Wed 20.2.2019
14:15 - 16:00
Fri 22.2.2019
10:15 - 12:00
Mon 25.2.2019
14:15 - 16:00
Wed 27.2.2019
14:15 - 16:00
Fri 1.3.2019
10:15 - 12:00
Mon 11.3.2019
14:15 - 16:00
Wed 13.3.2019
14:15 - 16:00
Fri 15.3.2019
10:15 - 12:00
Mon 18.3.2019
14:15 - 16:00
Wed 20.3.2019
14:15 - 16:00
Fri 22.3.2019
10:15 - 12:00
Mon 25.3.2019
14:15 - 16:00
Wed 27.3.2019
14:15 - 16:00
Fri 29.3.2019
10:15 - 12:00
Mon 1.4.2019
14:15 - 16:00
Wed 3.4.2019
14:15 - 16:00
Fri 5.4.2019
10:15 - 12:00
Mon 8.4.2019
14:15 - 16:00
Wed 10.4.2019
14:15 - 16:00
Fri 12.4.2019
10:15 - 12:00
Mon 15.4.2019
14:15 - 16:00
Wed 17.4.2019
14:15 - 16:00
Fri 26.4.2019
10:15 - 12:00
Mon 29.4.2019
14:15 - 16:00
Fri 3.5.2019
10:15 - 12:00

Material

Tasks

Conduct of the course

The course has only half the usual number of exercise classes. In addition to the homework problems discussed in these classes, each participant chooses two computational projects to be solved by independent work and written up in a report. Any software (e.g. MatLab, Maple, Mathematica, C++, Python, etc) can be used, but no technical help is provided with the chosen software.

The course has one open-book exam at the end (notes, books etc can be used). During the semester, progress is monitored via closed-book quick test, which focus on the basics and take only 5-10 min during lectures. For the dates of the quick tests, see the end of the introductory text above.

The final grade is from the exam (80%) and the two projects (20%). The quick tests and the homework exercises are meant primarily for self-evaluation, but good quick tests and good exercise class activity will improve marginal grades.

Description

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

BSc courses on differential equations, linear algebra, probability theory; basic computer programming for project work

Mathematical modelling or Introduction to mathematical biology

Familiarity with a range of different models applicable to spatially structured systems, including partial differential equations, probabilistic cellular automata, coupled map lattices and structured metapopulation models.

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

This course will explore how to model the dynamics and evolution of populations with spatial movement, spatial constraints and spatial interactions between organisms. We study diffusion, travelling waves, pattern formation and Turing instability, stochastic patch occupancy models, structured metapopulation models, probabilistic cellular automata and coupled map lattices. We also discuss topical issues of evolutionary biology where spatial structure plays a crucial role, e.g. the evolution of mobility (dispersal), specialisation to different environments, and the evolution of altruistic behaviour. This is a course in applied mathematics. Instead of choosing the problem to suit a method, we emphasize the use of versatile techniques. We introduce/review methods for ordinary differential equations and difference equations, partial differential equations, Fourier analysis, stochastic processes, pair approximation methods, game theory and adaptive dynamics. When necessary, we turn to numerical analysis.

Lectures, exercise classes, project with numerical analysis / simulations

Exam and exercises + project work, Course will be graded with grades 1-5

Exam, other methods will be described later