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Spatial models in ecology and evolution, spring 2017


Teacher: Eva Kisdi 

Scope: 10 cr

Type: Advanced studies


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.


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).


  • 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.


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: pdf

Stability analysis in a nonlinear reaction-diffusion model with absorbing boundaries: pdf (optional)

Lemma used for deriving the Fourier transform of a derivative: pdf (optional)

Introduction to discrete-space models: pdf


Did you forget to register? What to do?



A competition to solve this problem - 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 pdf 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

1.Monday 14-16 C129 Eva Kisdi 

Course feedback

Course feedback can be given at any point during the course. Click here.

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