Spatial models in ecology and evolution, spring 2015

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 the evolution of altruistic behaviour.

This is a course in applied mathematics. Instead of choosing the problem to suit a method, we emphasise the use of versatile techniques. On the way, 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.

Lecturer

Eva Kisdi

Scope

8 sp.

Type

Advanced studies

Lectures

Weeks 3-9 and 11-18, Monday 10-12 and Friday 10-12 in room B322. Two hours of exercise classes every other week.  

Easter Holiday 2.-8.4. First lecture: Friday 16 January. The lecture of Monday 23 February is replaced with an exercise class, the lecture of Friday 13 March is cancelled. On Monday 13 April, the exercise class is in the morning and the lecture is in the afternoon.

Due to an emergency, the lecture of Friday 10 April is cancelled. On Monday 13 April, exercise class in the morning, no lecture in the afternoon. Replacement lectures: Monday 20 April 14-16 in CK111 and Thursday 23 April 14-16 in B322, in addition to the regular lectures.

Exams

Wednesday 13 May, 10-13, in room C122.

Exercises

Exercises 1.1-1.4 (discussed on 26 January)
Exercises 2.1-2.4 (discussed on 9 February)
Exercises 3.1-3.5 (discussed on 23 February)
Exercises 4.1-4.5 (discussed on 23 March)
Exercises 5.1-5.4 (discussed on 13 April, note that the exercise class is in the morning)
Exercises 6.1-6.4 (discussed on 27 April, last exercise class)
Optional exercise: complete the proof of the next generation theorem.

Exercise classes are in weeks 5,7,9 and 13,16,18 only.

Registration

 
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