Adaptive dynamics

a course at the Fourth Winter School on Population Dynamics Woudschoten, The Netherlands, January 3 - 7, 2002

Hans (J. A. J.) Metz & Eva Kisdi




1. Introduction: Evolution of resource utilisation as a simple example for frequency-dependent selection. Long-term evolution by trait substitution. Simulation of evolutionary trees

2. Evolutionary singularities and their stability properties. Evolutionary branching

3. Coevolution of several coexisting strategies. The canonical equation of directional evolution

4. Adaptive dynamics with multilocus genetics and the quantitative genetic approach

5. Fitness with more complex population dynamics

6. When does evolution optimise?

7. On the evolution of multidimensional traits and on bifurcations in adaptive dynamics


The introductory lectures of the course were developed on the blackboard and are not available here. Almost all essential points of these lectures, however, are contained in a rather accessible form in only two papers, Geritz et al. (1998 Evol. Ecol.; the second paper in the Reader) and Dieckmann and Law (1996 J. Math. Biol.; the third paper in the Reader). The overheads used in lectures 4-7 can be downloaded as PDF documents.

Adaptive dynamics and multilocus/quantitative genetics (582 KB)

How should we define fitness for general ecological scenarios? (127 KB)

When does evolution optimise? (156 KB)

Bifurcations of evolutionarily singular strategies & multivariate adaptive dynamics (197 KB)




Click here for a list of references (formerly on this page)


Papers in the Reader

Metz, J. A. J., R. M. Nisbet, S. A. H. Geritz. 1992. How should we define 'fitness' for general ecological scenarios? TREE 7:198-202.

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.

Dieckmann U. & R. Law. 1996. The dynamical theory of coevolution: A derivation from stochastic ecological processes. J. Math. Biol. 34:579-612. 

Abrams P.A., Y. Harada & H. Matsuda. 1993. On the relationship between quantitative genetic and ESS models. Evolution 47: 982-985.

Dieckmann U. & M. Doebeli. 1999. On the origin of species by sympatric speciation. Nature 400:354-357.

Metz J.A.J., Mylius S.D. & Diekmann O. 1996. When Does Evolution Optimize? On the Relation Between Types of Density Dependence and Evolutionarily Stable Life History Parameters. IIASA Working Paper WP-96-004

Metz J.A.J. A set of models from evolutionary epidemiology demonstrating the essential differentiating characteristics of the various types of simple environmental feedback loops (unpublished notes)

G. Meszéna, É. Kisdi, U. Dieckmann, S.A.H. Geritz & J.A.J. Metz (2001): Evolutionary optimisation models and matrix games in the unified perspective of adaptive dynamics. Selection, in press; also available as IIASA Interim Report IR-00-039

Discussion papers

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.

Day T. 2000. Competition and the effect of spatial resource heterogeneity on evolutionary diversification. Am. Nat. 155:790-803.

Abrams P. A. 2001. Modelling the adaptive dynamics of traits involved in inter- and intraspecific interactions: An assessment of three methods. Ecology Letters 4:166-175.

Leimar O. 2001. Evolutionary change and Darwinian demons. Selection 2, in press