Spatial models in ecology and evolution, spring 2017
Spatial models in ecology and evolution, spring 2017
Teacher: Eva Kisdi
Scope: 10 cr
Type: Advanced studies
Teaching:
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.
Topics:
Prerequisites: linear algebra, differential equations. The course includes two computational projects, where you'll need computer programming (e.g. Matlab or C++ or any language you can use).
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News
- First lecture: 20 January (Friday of the first week of teaching).
- No lecture on 30 January
- 13 March: two lectures (the second in the time slot of the exercise class). We shall have an exercise class on 20 March 14-16 in C129
- No lecture on 7 April
- 24 April: two lectures (the second in the time slot of the exercise class). Last exercise class on 28 April (Friday, in place of the lecture).
Teaching schedule
Weeks 3-9 and 11-18, Monday and Friday 10-12 in room B322. Two hours of exercise classes every other week (see dates below), plus two computational projects carried out independently.
Easter holiday 13.-19.4.
Exams
The exam lasts 2,5 hours. You can use notes, books etc in the exam. Computers are not needed, but may be used with the internet switched off (download necessary files in advance).
The final grade is 80% exam + 20 % computational projects. Course activity (exercise classes and quick tests) decides marginal grades.
Exams: 5 May (Fri) 9.15-12 in B322; 22 May (Mon) 15.15-18 in B119
Course material
Sturm-Liouville theory:
Stability analysis in a nonlinear reaction-diffusion model with absorbing boundaries: (optional)
Lemma used for deriving the Fourier transform of a derivative: (optional)
Introduction to discrete-space models:
Registration
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Exercises
Assignments
- (discussed on 6 February)
- (discussed on 13 February)
- (discussed on 27 February) Solution of 3.3:
- (discussed on 20 March)
- (discussed on 27 March)
- (discussed on 10 April)
- (discussed on 28 April)
A competition to solve - the winner has been announced
A new competition to solve exercise 4.4(a) together with this: prove or disprove that mutual exclusion is also possible in this model.
Computer projects
This contains the computer projects you can choose from; everyone must have two projects from different sections. Email your choice to me. You can choose the same project as someone else in the course, but then your second choice must be different from that student.
#1 - Iwona, Anna
#2 - Sami, Jyri,
#4 - Anna
#5 - Iwona
#11 - Jyri
Exercise classes
Exercise classes are held on the following Mondays: 6, 13, 27 February, 20, 27 March, 10, 24 April
Group | Day | Time | Room | Instructor |
|---|---|---|---|---|
1. | Monday | 14-16 | C129 | Eva Kisdi |
Course feedback
Course feedback can be given at any point during the course. Click here.