Spatial models in ecology and evolution, spring 2013

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 cu.

Type

Advanced studies

Prerequisites

Lectures

Weeks 3-9 and 11-18, Monday 10-12 and Friday 10-12 in room B322.
First lecture on Friday 18 January. The lecture of 1 March is cancelled.

Easter holiday 28.3.-3.4.

Exams

Written exam where notes, books, etc. can be used. Computers are not necessary but can be used if so desired, only the Internet must be switched off.

Time and place: Monday 13 May 10.15 - 13.00, in room B322

Bibliography

Registration

Did you forget to register? What to do.

Exercise groups

Exercises only in weeks 5, 7, 9, 13, 16, 18 (first exercise class on Tuesday 29 January)

Exercises

Exercises 1.1-1.4 discussed on 29 January
Exercises 2.1-2.4 discussed on 12 February
Exercises 3.1-3.4 discussed on 26 February
Exercises 4.1-4.4 discussed on 8 April
Exercises 5.1-5.4 discussed on 16 April
Exercises 6.1-6.4 discussed on 30 April

Downloads

Introduction to discrete-space models
Conway's Game of Life by Carl Fredrik Abelson
Contact process (snapshots)

Feedback

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