Adaptive dynamics course

University of Oslo, spring 2008

Adaptive dynamics is a theoretical framework to study frequency- and density-dependent evolution with a high degree of ecological realism. This framework integrates and extends concepts and techniques from evolutionary game theory, with special emphasis on dynamical phenomena such as the origin and divergence of new lineages by evolutionary branching. A great strength of adaptive dynamics is its capability to incorporate ecological complexity and to model long-term evolution as driven by ecological interactions. The theory of the ESS has been enormously successful in analysing evolution in complex ecological and behavioural interactions. Adaptive dynamics is an extension of the ESS-theory that preserves its wide applicability to diverse ecological systems. It is being applied by a growing number of researchers to a wide variety of concrete ecological-evolutionary problems.

The lectures will focus on the fundamental theory of adaptive dynamics, but also look more briefly at the links between adaptive dynamics and other modeling frameworks and at the current research challenges within the field. The lectures given in the first week will enable the participants to solve a practical student project, which constitutes the main bulk of the course. This includes the concepts and techniques of adaptive dynamics, but also some widely applicable numerical methods and general principles of model analysis. The lectures of the last week will round off the course by discussing current developments, open challenges, and place the material in wider context for example by linking adaptive dynamics to speciation theory.


Recommended papers:

  • Adaptive dynamics basics: Geritz, S. A. H., É. Kisdi, G. Meszéna, and J. A. J. Metz. 1998. Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12:35-57.
    Note misprint: Inequality (16) should be the reverse (">" instead of "<")
  • A detailed worked example with bifurcation analysis: Geritz S. A. H., E. van der Meijden & J. A. J. Metz. 1999. Evolutionary dynamics of seed size and seedling competitive ability. Theor. Pop. Biol. 55:324-343.
  • Canonical equation: Dieckmann U. & R. Law. 1996. The dynamical theory of coevolution: A derivation from stochastic ecological processes. J. Math. Biol. 34:579-612.

Some further references on topics covered in the first ten lectures (see also more)

  • Optimization: Mylius S.D. & O. Diekmann. 1995. On evolutionarily stable life histories, optimization and the need to be specific about density dependence. Oikos 74: 218-224.
  • Tube Theorem: Geritz S. A. H., M. Gyllenberg, F. J. A. Jacobs & K. Parvinen. 2002. Invasion dynamics and attractor inheritance. J. Math. Biol. 44:548-560. (demanding)
  • Bending Theorem: Geritz S. A. H. 2005. Resident-invader dynamics and the coexistence of similar strategies. J. Math. Biol. 50:67-82. (demanding)
  • Evolutionary suicide: Gyllenberg M. & K. Parvinen. 2001. Necessary and sufficient conditions for evolutionary suicide. Bull. Math. Biol. 63:981-993.
  • Absolute convergence stability (no pleiotropy): Matessi C. & Di Pasquale. 1996. Long-term evolution of multilocus traits. J. Math. Biol. 34:613-653. (only part of the paper is relevant)
  • Isocline connections: Geritz S. A. H., E. van der Meijden & J. A. J. Metz. 1999. Evolutionary dynamics of seed size and seedling competitive ability. Theor. Pop. Biol. 55:324-343. (see Appendix)
  • Strong convergence stability (with pleiotropy): Leimar O. Multidimensional convergence stability and the canonical adaptive dynamics. In: U. Dieckmann & J.A.J. Metz (eds): Elements of adaptive dynamics. Cambridge University Press, in press (pdf available from author´s website)
  • Absolute convergence stability (with pleiotropy): Leimar O. 2001. Evolutionary change and Darwinian demons. Selection 2:65-72 (pdf available from author´s website)

Last three lectures

1. Critical function analysis

  • É. Kisdi. 2006. Trade-off geometries and the adaptive dynamics of two co-evolving species. Evol. Ecol. Res. 8: 959-973. Note misprint: The right hand side of eq. (3) should have phi(x) instead of f(x) at every place.
  • de Mazancourt C. & U. Dieckmann. 2004. Trade-off geometries and frequency-dependent selection. Am. Nat. 164:765-778.
  • Bowers R. G., A. Hoyle, A. White & M. Boots. 2005. The geometric theory of adaptive evolution: Trade-off and invasion plots. J. theor. Biol. 233:363-377.
2. Evolutionary branching without speciation
  • Leimar O. 2005. The evolution of phenotypic polymorphism: Randomized strategies versus evolutionary branching. Am. Nat. 165:669-681.
  • Van Dooren T. J. M., M. Durinx & I. Demon. 2004. Sexual dimorphism or evolutionary branching? Evol. Ecol. Res. 6:857-871.
3. Evolutionary branching with diploid genetics and sympatric speciation: Insights from few-locus models
  • Kisdi E. & S. A. H. Geritz. 1999. Adaptive dynamics in allele space: Evolution of genetic polymorphism by small mutations in a heterogeneous environment. Evolution 53:993-1008.
  • Geritz S. A. H. & E. Kisdi. 2000. Adaptive dynamics in diploid, sexual populations and the evolution of reproductive isolation. Proc. R. Soc. Lond. B 267:1671-1678.
  • Pennings P. S., M. Kopp, G. Meszéna, U. Dieckmann & J. Hermisson. 2008. An analytically tractable model for competitive speciation. Am. Nat. 171: E44-E71.
  • Dieckmann U. & M. Doebeli. 1999. On the origin of species by sympatric speciation. Nature 400:354-357.

A collection of papers on adaptive dynamics is listed here.

Official course page

The course is announced by the University of Oslo, Department of Biology (course code: BIO9910, 10 credits). Please read the official website carefully about admission, credits, prerequisites, etc. Time and place of the lectures is also announced on the official website.


Lecturer Eva Kisdi can be contacted by email (eva.kisdi[funny character]
For local information, contact Ĝistein Haugsten Holen (o.h.holen[funny character]

Course contents

The course consists of 13 lectures, an individual student project, a weekly discussion group supervised by Ĝistein Haugsten Holen during project work, and involvement with peer evaluation of the projects.

Time schedule

7-11 JanuaryLecture week, two double lectures each day
14 Jan - 4 FebrProject work with discussions each Friday
4 FebruaryDeadline for project submission (STRICT)
4-12 FebruaryReview of a peer project
13-15 FebruaryClosing lectures (one double lecture per day)
discussion and evaluation of projects


Figures used during the lectures can be downloaded as pdf files:


As the goal of this course is to give working knowledge in adaptive dynamics, the projects constitute the main part of the course. You can choose a project from the list below, subject to the constraint that each participant must have a different project. The projects are developed individually. The results of the project must be written up in a report of 5-10 pages (including figures), which is due by 4 February (the deadline is strict). Then each participant will read the report of one other project and prepare a brief (1/2 page) summary of it. Between 13 and 15 February, each project will be discussed briefly with the author and with the reviewing participant, and graded on a pass-fail scale. The course has no formal exam; the grade is determined by the completion and quality of the project.

Working on the projects

The projects assume some familiarity with modelling and an attitude of research: the task is to understand the evolutionary dynamics in a given ecological system rather than to answer some pre-defined questions as in an exam (some hints will be given to help getting started). Weekly discussions will monitor progress, give an opportunity to discuss difficulties, and compare methods and results with others. The projects, while simple relative to the level of complexity that can be handled in adaptive dynamics, constitute valid research problems of the past decade.

Most projects are based on published papers. Please do not try to trace down the paper while working on the project. The intention is that you do independent work. Also, the published paper may differ from the project in some aspects, and the projects often go beyond the published material. The references will be distributed among the course participants after the completion of the projects (anyone else interested in these projects please contact the lecturer for references). In every case you use material from the projects later on, please consult the references carefully and cite the original papers appropriately.

When writing the report, assume that the reader 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 or ways to improve the ecological model given in the project.

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.


Participants must have access to a computer and a software package suitable for mathematical modelling which they are familiar with. Typical tasks during numerical analyses of adaptive dynamic models include the following: iterating population dynamics in discrete time; solving differential equations (using the simplest numerical algorithm); finding roots of functions numerically; numerical differentiation; plotting functions (including very complicated functions obtained numerically); contourplots of functions of two variables. All of these must be done easily with the software, since these are commonly applied to complicated equations/functions and repeated many times automatically.

The lectures will explain the basics of the necessary numerical algorithms. Ordinary programming languages such as C, Pascal, etc. are suitable for the implementation of these algorithms. Mathematical packages such as Mathematica, Maple, Matlab can do the same and also provide shortcuts in form of pre-programmed algorithms. Participants are free to choose the software they use, but we may be unable to provide technical assistance with software problems if the chosen software is not familiar to us.

Of related interest

Participants may be interested in a Summer School on Mathematical Ecology and Evolution in August 2008, in Finland.