Adaptive Dynamics

Adaptive dynamics

course at the University of Vienna
5 - 28 June 2007

Stefan Geritz & Eva Kisdi

Adaptive dynamics is a mathematical theory that explicitly links population dynamics to long-term evolution driven by mutation and natural selection. It provides methods of model formulation, methods of model analysis and mathematical theorems that relate phenomena on an evolutionary time scale to processes and structures defined in ecological and population dynamical terms.

Adaptive dynamics is a new but rapidly developing theory that poses various interesting and mathematically challenging problems. From an applications point of view, a great strength of adaptive dynamics is its capability to model evolution driven by complex ecological interactions. Adaptive dynamics is being applied by a growing number of researchers to a wide variety of concrete ecological-evolutionary problems.

This course is an introduction to the mathematical theory of adaptive dynamics and its applications. The aim of the course is twofold: we provide the students with the necessary tools to analyse the dynamics of adaptation in a broad class of ecological systems, and we show where the research frontiers lay in the underlying general theory of adaptive dynamics.

Time and place

Prerequisites

Some familiarity with dynamical systems and differential equations; elements of mathematical ecology (basic models of population growth).

Literature

A collection of papers on adaptive dynamics is listed here.

Course contents

The course consists of 14 lectures and an individual student project. You can choose the project from the list below, subject to the constraint that each student must have a different project. The projects are supervised individually. The results of the project must be written up in a report of 5-10 pages (including figures), which is due by 29 June. As a last step, you will read the report of one other project and prepare a brief (1/2 page) summary of it. The course has no formal exam; the grade is determined by the completion and quality of the project.

Projects

The projects listed below are based on published papers. The references will be distributed among the course participants but only after the completion of the projects; anyone else interested in these projects please contact the lecturers for references. At places, the projects also go beyond the published material. In every case you use material from the projects, please consult the references carefully and cite the original papers appropriately.

The projects proposed here are misleading in one significant aspect: They are all simple. While working with simple models is obviously the only way to get experience in a short time, this bias should not eclipse the fact that adaptive dynamics is applicable to a wide class of possibly very complex ecological models.

When writing the report, talk to someone who knows the course material but no more. Introduce the ecological problem at hand. Link the analysis to the background given in the course. In the Discussion part, summarise the most important findings and mention if you see possible directions of further research. Please submit the report in one pdf file. - It may be tempting to submit a Mathematica or similar interactive notebook you developed where the user can explore various phenomena in the model. Please do not do so. Besides possible software incompatibility problems, it is your job to decide which results are worth mentioning in the report and to make sure the analysis is complete. Just like when writing a research paper, a text file with figures must be sufficient.

Evolution of resource use