Kaisa_2012_3_photo by Veikko Somerpuro

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

The ecological time scale concerns the question which mutant types that are not yet present in a population of given resident types could invade if they were produced by a mutation, and what would be the outcome of such an invasion in terms of which types will remain in the population and which will be eliminated. These questions concern dynamics in a space of population densities of different types. In the course we focus on the population dynamics given by (systems of) ordinary differential equations.

The evolutionary time scale is about the long-term consequences of many successive ecological invasion-elimination events in terms of changes in the composition of the population. The evolutionary time scale thus concerns dynamics in the space of all possible types. This dynamics is essentially non-deterministic due to the random nature of mutations.

EXAMPLES
Examples are largely taken from publications in the scientific literature.

PERSPECTIVE
Adaptive dynamics is a relatively new and still 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 in systems with complicated ecological interactions. Adaptive dynamics is being applied by a growing number of researchers both within mathematics and biology to a wide variety of concrete ecological-evolutionary problems.

REFERENCES
Adaptive dynamics is new, and there does not exist a comprehensive textbook on adaptive dynamics. For an extensive list of references to both theory and applications of adaptive dynamics in the scientific literature, see the website http://www.mv.helsinki.fi/home/kisdi/ad.htm

LECTURE NOTES
Lecture notes will be anded out on the go as the course advances.

EXAMINATION
There will be no exam -- instead there will be project assignments. In the second half of the course, the project assignments take the place of the homework exercises. The lecturer or the assistant will be available for advise during the normal time and place of the exercise classes. A written report and a 15 minute in-class presentation of the report take the place of the exam, i.e., the grade is based on the report and the presentation. The presentations take place during the last two weeks of the course.

PREREQUISITES
Basic knowledge of differential equations, probability theory and some basic skills in programming (preferably Mathematica or Maple).

Enrol

Messages

Stefan Geritz

Published, 17.3.2020 at 15:36

The sudden switch from normal lectures to online teaching and supervision takes us all by surprise. At least I need some days to adjust. Here are some things I can already say now:
- There will be no deadline for when you hand in the final report of your project, i.e., the report that I will grade. During the summer months (June, July and August), however, I may be slow in responding to your questions.
- I will continue with my reporting on my own project (the cannibalism time budget model) as an example and a means of introducing several methods and techniques that were not covered by the lectures. At the same time it also provides you with code to implement those methods in Mathematica.
- In the meanwhile you can already start working on the project of your choice.
- If you don't know how to start, please ask me by email, and I will help you out.
- Keep an eye on the messages on the course website (so that is here, this place) for new info.

Finally, Eva Kisdi (eva.kisdi@helsinki.fi) volunteered to be my backup, i.e., she will take over supervision in the case I get ill.

Stefan Geritz

Published, 16.3.2020 at 16:21

The zip-files with the projects have now been restored in the Materials section.

Stefan Geritz

Published, 16.3.2020 at 15:51

I lost the file with the project during the process of updating the Mathematica primer for AD. No panic. I will find them and upload them in a separate file.

Stefan Geritz

Published, 15.3.2020 at 17:58

Dear all,

As a precaution due to the coronavirus, Tuomas Hytönen, Head of Department of
Mathematics and Statistics, has decided that all contact teaching at the Department
of Mathematics and Statistics will be terminated on Friday 20 March 2020 at the
latest, and thereafter replaced by web-based teaching methods chosen by each
teacher. Teachers are encouraged to replace their contact teaching by web-based
teaching already earlier.

So, for us there will be no more lectures of adaptive dynamics in the classroom,
starting tomorrow, Monday 16 March.

The good thing is that we have already gone through most of the general material.
Additional theory I will publish on the course website. What remains are the
projects, and those are quite suitable for supervision via email.

I propose that you start working on your project in Mathematicxa, effectively
following the example of the cannibalism time-budget model (see Materials) or
the Mathematica primer for ADS (see Materials). Both files have been updated,
by the way.

If you have questions, anything, please send me an email with "question AD" in
the subject line.

Mathematica and corresponding licence for home use (i.e., on your own computer)
can be downloaded from the University.

Stefan Geritz

Published, 15.3.2020 at 17:57

Dear all,

As a precaution due to the coronavirus, Tuomas Hytönen, Head of Department of
Mathematics and Statistics, has decided that all contact teaching at the Department
of Mathematics and Statistics will be terminated on Friday 20 March 2020 at the
latest, and thereafter replaced by web-based teaching methods chosen by each
teacher. Teachers are encouraged to replace their contact teaching by web-based
teaching already earlier.

So, for us there will be no more lectures of adaptive dynamics in the classroom,
starting tomorrow, Monday 16 March.

The good thing is that we have already gone through most of the general material.
Additional theory I will publish on the course website. What remains are the
projects, and those are quite suitable for supervision via email.

I propose that you start working on your project in Mathematicxa, effectively
following the example of the cannibalism time-budget model (see Materials) or
the Mathematica primer for ADS (see Materials). Both files have been updated,
by the way.

If you have questions, anything, please send me an email with "question AD" in
the subject line.

Mathematica and corresponding licence for home use (i.e., on your own computer)
can be downloaded from the University.

Stefan Geritz

Published, 12.1.2020 at 20:57

Beginning of course delayed by one week
because the teacher go the flue.

The first lecture will be on Monday 20 January
from 12:15-14:00 in room BK114 (Exactum).

Material

Description

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Ordinary differential equations

Modelling evolution by natural selection as derived from possibly complex ecological interactions. Familiarity with the mathematical theory of adaptive dynamics and practice in its application to various biological problems.

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

Adaptive dynamics is a modern mathematical framework to model evolution by natural selection, where selection derives from (possibly complex) ecological interactions between the individuals. The course contains the methods and theorems of adaptive dynamics as well as a number of applications to concrete biological problems.

Lectures and exercise classes; individual project with written report and oral presentation of the results

Individual project (written report and presentation), Course will be graded with grades 1-5

Individual project