Details of the programme

Note that we will provide a Reader and a booklet with papers for the Working Groups for all participants, to be handed out on arrival. The Reader will contain copies of the relevant material for all lectures.

Lecture contents per lecturer

Bas Kooijman
Dynamic Energy Budget theory for the metabolic organization of life at the various levels: from molecules to ecosystems
I will concentrate on trophic interrelationships between organisms in a community that do account for all types of exchanges of compounds (nutrients, and organic matter), and include the molecular basis for these couplings; cells as symbiontic communities. The basic theory is discussed in the DEB-book:
  • S. A. L. M. Kooijman: Dynamic Energy and Mass Budgets in Biological Systems. Cambridge University Press.

This substantially reworked and enlarged second edition will appear in Feb 2000 (paperback, approx 40 euro). A postscript preprint is available, without the long inclusions.


  1. The Basic model: 1 substrate, 1 reserve, 1 structure; conceptual backgrounds, relationship with static budgets. Structural homeostasis.
    • Chapter 2 of the DEB-book
    • Chapter 3 of the DEB-book
  2. Mass-energy coupling; indirect calorimetry; Body Size scaling relationships
    • Chapter 4 of the DEB-book
    • Chapter 8 of the DEB-book
  3. Multivariate extensions of the basic DEB model on the basis of Synthesizing Units: several substrates, several reserves, two structures. Photosynthesis, simultaneous limitations, plants.
    • Chapter 2 and 5 of the DEB-book
  4. Syntrophy, symbiosis, mixotrophs in a closed environment, canonical communities. Mass and energy balances, the flux matrix.
    • Chapter 9 of the DEB-book
  5. Applications of the theory in ecotoxicology, biodegradation, tumor biology, sewage treatment, production optimazation, global change.
    • Chapter 6 of the DEB-book
    • S. A. L. M. Kooijman and J. J. M. Bedaux. The analysis of aquatic toxicity data. VU University Press (1996). ISBN 90-5383-477-X, 160 pp. and floppy DEBtox; downloadable from
Rob de Boer
Models of the Immune system
  1. Diversity
    • why is the lymphocyte repertoire so diverse?
    • probabilistic and simulation models
    • J. A. M. Borghans, A. J. Noest, R. J. De Boer: How specific should immunological memory be? J. Immunol. 163 (1999), 569-575.
    • R. J. De Boer, A. S. Perelson: How diverse should the immune system be? Proc. R. Soc. Lond., B, Biol. Sci. 252 (1993), 171-175.
  2. Competition and Repertoires
    • lymphocyte repertoire is ecosystem of competing populations
    • derive appropriate models, see the resource competition, and compare to data
    • R. J. De Boer, A. S. Perelson: Competitive control of the self-renewing T cell repertoire. Int. Immunol. 9 (1997), 779-790.
    • R. J. De Boer, A. S. Perelson: Towards a general function describing T cell proliferation. J. Theor. Biol. 175 (1995), 567-576.
  3. T cell vaccination - regulatory interactions - phase plane methods
    • J. A. M. Borghans, R. J. De Boer: A minimal model for T-cell vaccination. Proc. R. Soc. Lond., B, Biol. Sci. 259 (1995), 173-178.
  4. Telomere shortening and T cell dynamics
    • derive 2-dimensional model for n-dimensional model
    • see how it helps to interpret data
    • R. J. De Boer, A. J. Noest: T cell renewal rates, telomerase, and telomere length shortening. J. Immunol. 160 (1998) 5832-5837.
  5. MHC diversity
    • population based polymorphism of transplatation antigens
    • simulation by means of a genetic algorithm
    • Manuscript in prep. with a deadline of 15 October 1999.
Horst Thieme
Structured population models
  1. The most rudimentary population model with a juvenile and adult stage(e.g., for amphibians). Hopf bifurcation of periodic solutions. A simple population model for the Arizonan tiger salamander.
  2. Population models with more stages. Persistence and invasion theory. The role of cannibalism in Arizonan tiger salamanders.
  3. Discretely structured metapopulation models (with small subpopulations)
  4. Transition to continuous structure variables. The Pease/Inaba influenza model. Measures as state space.
  5. More general continuously structured population models.

If I find that this is too much material, I will skip (3) and spread the other topics out. An permeant mathematical theme for (2) to (5) will be persistence theory (conveniently formulated in terms of semiflows [dynamical systems]).

  • H.R. Thieme: Uniform weak implies uniform strong persistence also for non-autonomous semiflows. Proc. Amer. Math. Soc. 127 (1999), 2395-2403.
  • H.R. Thieme: Uniform persistence and permanence for non-autonomous semiflows in population biology, 41 pages (submitted).
For the influenza model:
  • C.M. Pease: An evolutionary epidemiological mechanism, with applications to type A influenza. Theor. Pop. Biol. 31 (1987), 422-452.
  • H. Inaba: Mathematical analysis for an evolutionary epidemic model. in Mathematical Models in Medical and Health Sciences (M.A. Horn, G. Simonett and G.F. Webb; eds.) Vanderbilt Press 1998, 213-236.
On physiologically structured populations:
  • J.A.J. Metz, O. Diekmann: The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics 68. Springer 1986.
  • O. Diekmann, M. Gyllenberg, J.A.J. Metz, H.R. Thieme: On the formulation and analysis of general deterministic structured population models. I. Linear theory. J. Math. Biol. (1998), 349-388.
On Metapopulations:
  • M. Gyllenberg, I. Hanski, A. Hastings: Structured Metapopulation Models. In Metapopulation Biology. Ecology, Genetics and Evolution (I. A. Hanski, M. E. Gilpin; eds). Academic Press 1996, Chapter 5.
  • A.T. Smith, M.E. Gilpin: Spatially correlated dynamics in a pika metapopulation. In Metapopulation Biology. Ecology, Genetics and Evolution (I. A. Hanski, M. E. Gilpin; eds). Academic Press 1996, 407-428.
  • O. Diekmann: The many facets of evolutionary dynamics. Preprint.
Fred Adler
Ecology and evolution
I will discuss the implications of interactions between neighbors for the evolution of resource use strategies. Models of evolution of cooperation require local interactions of some sort (within groups or families) and some temporal duration of the interaction (as in tit-for-tat models). For sedentary organisms, long-term local interactions with neighbors are unavoidable, and provide a place where "cooperative" strategies for resource use might evolve. My goal is to outline an empirically testable resource-based approach to evolution of cooperation.


  1. Classical group selection models and an extension to include simple resource dynamics.
    • D. S. Wilson: A theory of group selection. Proc. Nat. Acad. Sci. 72 (1975), 143-146.
    • M. Slatkin and D. S. Wilson: Coevolution in structured demes. Proc. Nat. Acad. Sci. 76 (1979), 2084-2087.
  2. Population viscosity and kin selection - how do the details of dispersal affect evolution?
    • D. S. Wilson, G. B. Pollock and L. A. Dugatkin: Can altruism evolve in purely viscous populations? Evolutionary Ecology 6 (1992), 331-341.
    • P. D. Taylor: Altruism in viscous populations: an inclusive fitness model. Evolutionary Ecology 6 (1992), 352-356.
  3. Models of competition for space.
    • M. Slatkin and D. J. Anderson: A model of competition for space. Ecology 65 (1984), 1840-1845.
    • S. W. Pacala and J. Weiner: Effects of competitive asymmetry on local density models of plant interference. Journal of Theoretical Biology 149 (1991), 165-179.
    • F. R. Adler: A model of self-thinning through local competition. Proc. Nat. Acad. Sci. 93 (1996), 9980-9984.
  4. Integrating models of competition for space with foraging and life history theory.
    • F. R. Adler and D. M. Gordon: Integrating models of competition for space with the life history theory of seed-harvester ants. (preprint)
  5. Signalling and information sharing in plants.
    • P. Aphalo and C. Ballare: On the importance of information acquiring systems in plant-plant interactions. Functional Ecology 9 (1995), 5-14.
    • J. Schmitt: Is photomorphogeenic shade avoidance adaptive? Perspectives from population biology. Plant, Cell and Environment 20 (1997), 826-830.
Roger Nisbet
Ecological dynamics
The plan assumes the students have some limited previous exposure to simple (unstructured) population, and to systems of ordinary differential equations (including concepts of equilibrium and local stability). This material is reviewed in lecture 1, but at high speed! Lectures 2,3, and 4 provide an introduction to the formulation and use of structured population models. The preceding lectures mainly use material from the recent book Ecological Dynamics by Bill Gurney and myself.


  1. Review of dynamics of unstructured populations. Population dynamics in an ecological context. Density-independent growth in constant and variable environments. Consumer-resource interactions (discrete and continuous time). Competition.
    • Chapters 5 and 6 of W. S. C. Gurney and R. M. Nisbet: Ecological Dynamics, Oxford University Press 1998.
  2. Formulating structured population models. Parallel introductions to discrete and continuous representations of age-structured populations. Size-structured populations.
    • Chapter 8 of W. S. C. Gurney and R. M. Nisbet: Ecological Dynamics, Oxford University Press 1998.
  3. Biomass-based models. Simplifying assumptions that lead to biomass dynamics in terms of the ordinary-differential equations discussed in lecture 1. Case study (Daphnia population dynamics in lab and field) illustrating the predictive power and limitations of simple population models.
    • Parts of chapters 5 and 6 of W. S. C. Gurney and R. M. Nisbet: Ecological Dynamics, Oxford University Press 1998.
  4. Stage-structured models. An introduction to the use of delay-differential equations to describe structured populations.
    • R. M. Nisbet: Delay differential equations for structured populations. In Structured Population Models in Marine, Terrrestrial, and Freshwater Systems (S. Tuljapurkar and H. Caswell; eds). Chapman and Hall. New York. 1997, 89-118.
  5. Inferring biological mechanism from population data. Combining statistical and mechanistic modeling approaches to determine mechanisms of population regulation from time series.

Working group papers

  1. S. A. L. M. Kooijman: The Synthesizing Unit as model for the stoichiometric fusion and branching of metabolic fluxes. Biophysical Chemistry 73 (1998), 179-188.
  2. S. A. L. M. Kooijman and R. M. Nisbet: How light and nutrients affect life in a closed bottle. In Thermodynamics and ecology (S. E. Jorgensen; ed). CRC-Press, to appear.
  3. J. A. M. Borghans, R. De Boer, L. A. Segel: Extending the quasi-steady state approximation by changing variables. Bulletin of Mathematical Biology 58 (1996), 43-63.
  4. J. P. Cheek, J. P. Collins: Effect of food and density on development of typical and cannibalistic salamander larvae in Ambystoma tigrinum nebulosum. Amer. Zool. 23 (1983), 77-84.
  5. T. J. Maret, J. P. Collins: Individual responses to population size structure: the role of size variation in controlling expression of a trophic polymorphism. Oecologia 100 (1994), 279-285.
  6. T. J. Maret, J. P. Collins: Effect of prey vulnerability on population size structure of a gape-limited predator. Ecology 77 (1996), 320-324.
  7. A. Grafen: Biological signals as handicaps. Journal of Theoretical Biology 144 (1990), 517-546.
    • B. E. Kendall, C. J. Briggs, W. M. Murdoch, P. T. Turchin, S. P. Ellner, E. McCauley, R. M. Nisbet, S. N. Wood: Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches. Ecology 80 (1999), 1789-1805.
    • A. L. Lloyd, R. M. May: Synchronicity, chaos and population cycles: spatial coherence in an uncertain world. TREE 14 (1999), 417-418.
  8. M. Pascual, S. A. Levin: Spatial scaling in a benthic population model with density-depentdent disturbance. Theoretical Population Biology 56 (1999), 106-122.