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 phenotypes that are not yet present in a population of given resident phenotypes could invade if they were produced by a mutation, and what would be the outcome of such an invasion in terms of which phenotypes will remain in the population and which will be eliminated. These questions concern dynamics in a space of population densities of different phenotypes. 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 phenotypic composition of the population. The evolutionary time scale thus concerns dynamics in the space of all possible phenotypes. This dynamics is essentially non-deterministic (e.g., due to the random nature of the effect of a mutation on the phenotype) and is studied using difference inclusions, and in limiting case of infinitesimally small mutation steps, the Focker-Planck equation or the transport equation.

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

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 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.

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 will be produced on the go as the course advances. Older lecture notes are available here https://wiki.helsinki.fi/display/mathstatKurssit/Adaptive+dynamics,+fall...
For older exercises and solutions see past AD courses on my home page https://wiki.helsinki.fi/display/mathstatHenkilokunta/Geritz,+Stefan

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 week of the course.

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

11.12.2017 klo 09:00 - 1.5.2018 klo 23:59


Stefan A H Geritz

Julkaistu, 8.3.2018 klo 13:02

I have selected a collection of papers for the projects, but because of copyright issues I cannot just dump them in the section MATERIALS below -- still have to figure out how we do that ...

Stefan A H Geritz

Julkaistu, 23.2.2018 klo 13:33

Exercises for Tuesday 27-02-2018 now available under MATERIAL

Stefan A H Geritz

Julkaistu, 1.2.2018 klo 9:58

Exercises 4--6 for Tuesday 6 February now available under MATERIAL

Stefan A H Geritz

Julkaistu, 24.1.2018 klo 13:52

Exercises 1--3 for Tuesday 30 January now available under MATERIAL

Stefan A H Geritz

Julkaistu, 18.1.2018 klo 9:04

For the exercise class on Tuesday 23 January from 14:15-16:00 room B121, we will look at the example model in the paper "Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree" by Geritz et al. in Evolutionary Ecology 1998, Vol. 12, pp. 35-57.

Stefan A H Geritz

Julkaistu, 15.1.2018 klo 14:30

I have moved the exercises classes from Mondays 12-14 to Tuesdays 14-16.
I hope this is consistent with the schedules of at east most of you.

N.B., the change required the "old" classes to be cancelled before the "new" classes could be installed. If you find that your enrollment has been cancelled in this process, just enroll again.)


Tästä osiosta löydät kurssin opetusaikataulun. Tarkista mahdolliset muut aikataulut kuvauksesta.

Ma 15.1.2018
10:15 - 12:00
Ti 16.1.2018
10:15 - 12:00
Ma 22.1.2018
10:15 - 12:00
Ti 23.1.2018
10:15 - 12:00
Ma 29.1.2018
10:15 - 12:00
Ti 30.1.2018
10:15 - 12:00
Ma 5.2.2018
10:15 - 12:00
Ti 6.2.2018
10:15 - 12:00
Ma 12.2.2018
10:15 - 12:00
Ti 13.2.2018
10:15 - 12:00
Ma 19.2.2018
10:15 - 12:00
Ti 20.2.2018
10:15 - 12:00
Ma 26.2.2018
10:15 - 12:00
Ti 27.2.2018
10:15 - 12:00
Ma 12.3.2018
10:15 - 12:00
Ti 13.3.2018
10:15 - 12:00
Ma 19.3.2018
10:15 - 12:00
Ti 20.3.2018
10:15 - 12:00
Ma 26.3.2018
10:15 - 12:00
Ti 27.3.2018
10:15 - 12:00
Ma 9.4.2018
10:15 - 12:00
Ti 10.4.2018
10:15 - 12:00
Ma 16.4.2018
10:15 - 12:00
Ti 17.4.2018
10:15 - 12:00
Ma 23.4.2018
10:15 - 12:00
Ti 24.4.2018
10:15 - 12:00
Ma 30.4.2018
10:15 - 12:00

Muu opetus

15.01.2018 Ma 12.15-14.00
23.01. - 27.02.2018 Ti 14.15-16.00
13.03. - 27.03.2018 Ti 14.15-16.00
10.04. - 24.04.2018 Ti 14.15-16.00
Stefanus Geritz
Opetuskieli: englanti



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