DEB Research Program



Twin origin of DEB research

DEB research, as done at the Dept. of Theoretical Biology VUA, started in the spring of 1979, when Bas Kooijman, then working at the Laboratory of Applied Technological Research TNO-Delft, was asked to solve to problem of quantifying how toxicants affect reproduction of waterfleas, and how this affects population and ecosystem dynamics. The ecological literature was of little help at that time for translating effects on individuals into that on populations; existing models for the uptake and use of substrates by organisms were scarce and primitive or problematic.

Bas seeked advice from his former room-mate Hans Metz at the Institute of Theoretical Biology Leiden, who was closely collaborating with Odo Diekmann, then working at the Centre for Mathematics and Computer Science CWI-Amsterdam. Hans was interested in the problem because it is basic to population dynamics, and Odo saw possibilities of application and further development of semi-group theory, on which he was working. This collaboration was the start of two twin research lines, which later involved an increasing number of workers: the DEB theory for structuring individuals and the theory of Physiologically Structured Population Dynamics (PSPD) for the translation of properties of individuals into that of populations.

A first paper on the translation of effects on individuals to that on populations was written in 1982 (Kooijman, S.A.L.M. and Metz, J.A.J. 1983 On the dynamics of chemically stressed populations; The deduction of population consequences from effects on individuals. Ecotoxicol. Environ. Saf., 8: 254-274) for immediate needs, but both authors felt that science was in need of a much more fundamental approach.

PSPD theory

Three events accelerated the early development of PSPD theory. The group of persons that became interested in PSPD theory rapidly grew, and new areas of related interest were explored. Odo developed a research line with Hans Heesterbeek in epidemiology, which can be considered as an application of PSPD theory. This recently resulted in the book Heesterbeek, H. and Diekmann, O. 2000 Mathematical Epidemiology of Infectious Diseases; Model building, analysis and interpretation, Wiley, Chichester. Hans Metz became interested in effects of parameter values on the asymptotic behaviour of PSPD, and developed theory for Adaptive Dynamics for processes at an evolutionary time scale.

DEB theory

Because waterfleas were popular in ecotoxicological research, DEB theory was initially developed and tested on these creatures. An intensively interacting group of workers started modelling DEB for Daphnia.

Physicist Roger Nisbet, then at Strathclyde University Scotland, worked on delay differential equations for analysing stage-structured (insect) population dynamics with Bill Gurney. He tried to generalize his results to more general physiologically structured individuals. He met experimental biologist Ed McCauley (Calgary University, Canada, where he still works) in 1983, and, as a result, became involved in modelling DEB for waterfleas. Hans Metz spent a short sabbatical leave in Strathclyde, and brought Roger into contact with Bas. A stimulating workshop on modelling waterflea eco-physiology was organized in 1985 at TNO-Delft. The Scots-Canadian waterflea-work culminated in the paper Nisbet, R. M., Murdoch, W. W. and McCauley, E. and Gurney, W. S. C. 1988 The physiological ecology of Daphnia II: A new model of growth and reproduction, Ecology. Continued research revealed, however, that the model was too complex for useful PSPD analysis.

Tom Hallam identified modelling effects of pollutants in the environment as the main field of interest for his group at Tennessee University in Knoxville, and visited Bas in Delft in 1983. This initiated a long-lasting collaboration. Tom invested a lot of effort in developing parallel computational methods for integrating partial differential equations for PSPD.

When Bas moved to Amsterdam in 1985, his ecotoxicological motivation changed into a more fundamental and general biological one, and waterfleas where no longer the primary focus of interest. DEB's implications for body size scaling relationships were already known in 1983 (and published in 1986), which convinced Bas that the DEB theory had a much wider applicability. Research on the application to micro-organisms was initiated in 1985. A full integration of the animal and microbial model formulations occurred in 1992, with the notion of changing shapes. Contacts with Ad Stouthamer and his microbiological group at the Vrije Universiteit in Amsterdam fired the interest for simultaneous energy and mass budgets. The aging module was created in 1992; the full multivariate approach, which is required to model simultaneous nutrient limitation in algal and plant eco-physiology, was developed after the invention of Synthesizing Units in nov 1995 (and published in 1996). This multivariate formulation eventually allowed to replace the last empirical assumption of the DEB theory (the one on reserve kinetics) by a more fundamental one. The progam since 2002 strongly developed into the directions of ecosystem (direct and indirect syntrophy) as well as in sub-organismal organisation.

DEB Research Program

The Dynamic Energy Budget (DEB) theory has been chosen as focus for the department of Theoretical Biology because of its relevance for a wide variety of biological specialisms: the availability of nutrients and energy is frequently the most important limiting factor in the development and functioning of living systems. The aim of the program is to develop a quantitative and coherent theory for energy and mass transduction that links theories concerning all levels of organization, from membrane physiology to ecosystem dynamics. `Quantitative' means: formulated in terms of mathematical models. `Coherence' implies that changes in some details of the theory can have repercussions for the theory at other levels of organization. This improves the possibilities for testing and prediction. Apart from quantitative formulation and coherence other criteria are considered important in the program: consistency, simplicity, mechanistic design and realism. Adequate simplification gets special attention in the program since attempts to cover various levels of organization easily lead to unusable complex theories.

Model formulation, testing models against experimental data and analysis of properties of models all get serious attention in the program. Bifurcation analysis of complex systems is an important tool in analysizing the asymptotic behaviour of models. Due attention is given to the further development of methods like these.

The program is executed through projects with limited aims and durations. In almost all projects, there is intensive project-specific collaboration with researchers in experimental biology, other sciences, mathematics and computer science, frequently within the framework of large multidisciplinary research programs.

Applications of the results of the program comprise global change, ecotoxicology and biotechnology. These applications are developed in national and international research projects in which the department participates, in collaboration with research groups that are specialized in these applications.

Overview of results

The program started with the development of the Dynamic Energy Budget (DEB) theory for heterotrophs, i.e. organisms that use organic material as source for energy and nutrients. This theory gives simple, mechanistic, rules for the processes of resource uptake and use by individuals. The basic processes are feeding, digestion, storage, maintenance, growth, development, propagation (reproduction or division) and aging. `Dynamic' refers to the quantitative changes of energy fluxes during the embryonic, the juvenile and the adult stages (or during the cell cycle of unicellular organisms). The basic state variables are amounts of reserve and structure. The parameters are individual-specific with small differences among individuals of the same species and large differences between species. Although the theory only concerns basic mechanisms for energy transduction, its structure implies rules for the co-variation of parameter values across species, which allows the prediction of how particular physiological traits, such as respiration, reproduction, juvenile periods and life spans, vary among species with different body sizes. We have been able to develop a consistent thermodynamic framework for the DEB theory, and provide a theoretical basis for indirect calorimetric methods. An explanation has been found for the heat increment of feeding, also known as the specific dynamic action.

Population dynamics is studied, in which the uptake and use of resources for individual animals is governed by DEB theory. Techniques used are computer simulation and mathematical analysis on simplified versions of the full model, with special attention for the bifurcation behaviour of complex systems. The development of efficient algorithms is part of the research aims, as well as the development of the mathematical theory, that is required for the interpretation of the simulation and bifurcation results. This includes local and global stability analysis. Theory is derived for the dynamics of food chains and food webs, which represent modules of the dynamics of (generalized) ecosystems. A full analysis of chemical transformations and energy dissipation in a simple and closed community of producers, consumers and decomposers is presently undertaken.

Extensions of the DEB theory have been developed to include autotrophs, i.e. organisms that use light and mineral compounds. Energy and nutrient limitations interact in a more complex way, compared to heterotrophs, and require more nutritional state variables for the individual. To integrate the uptake of nutrients and light under stoichiometric constraints, we created the concept ` Synthesizing Unit', a simple multi-substrate generalization of the Michaelis Menten enzyme kinetics. This construct allows a natural extension of the DEB theory to include more reserves and structural mass (roots and shoots), which is essential to include algae and plants. Modules have been formulated to include photo-adaptation and photo-inhibition, and more general stoichiometric constraints on population dynamics. Microbial population dynamics is studied on the basis of these extensions, serving as modules of the dynamics of (generalized) ecosystems. These results are part of large programs on global change, which aim to analyse processes at global scale and to evaluate human impacts.

Explored applications

The purification of sewage is usually accompanied by a substantial production of microbial biomass that has to be processed at high costs, both financial and in terms of environmental impact. The DEB theory has been used to design setups for sewage treatment that reduce this biomass production, and process it biologically in food chains. These results are presently applied in technical projects that aim to built improved reactors.

The various effects of toxic compounds on mass and energy transformations (growth, reproduction), and survival, have been worked out on the basis of a three-step approach: a toxico-kinetic module that relates external concentrations to internal ones; an effect module that relates internal concentrations of changes in one or more parameters of the DEB; and an output module that relate these changes to quantities that can readily be measured. Realistic models for toxico-kinetics have been developed for compounds with a variety of properties, that have close links with the DEB theory (changes in reserves, so in lipid-content, affect the kinetics of lipophilic compounds, dilution by growth, etc). These models allow to relate the effects of toxicants to their physico-chemical properties on the basis of first principles. Software package DEBtox has been developed, together with a book that gives the theoretical backgrounds. It is now widely used to analyse the results of a set of standardized toxicity experiments and has been accepted by the ISO and OECD as a method to analyse routine toxicity data in 2004.

We used the DEB theory to quantify the biodegradation of (xenobiotic) compounds. This theory twins the earlier development of theory to quantify the effect of toxicants on organisms, which resulted in the software package DEBtox. We presently work on further theory to link effects on individuals to that one populations, as well as for theory to deal with (complex) mixutres of toxicants. Models have be formulated for the interaction between tumours and their host, in relation to the aging process (DEBtum project).

DEB theory has been used to model primary production and calcification processes by phytoplankton (Emiliania huxleyi). This work is now continuated to quantify the rate at which the carbon-pump is working (that binds carbon dioxide from the atmosphere and transport is to the deep ocean by the action of phytoplankton). We also initiated research into the self-organisation of ecosystems, using the reasoning of adative dynamics, as a priliminary study to evaluate the role of biota in the climate and the geochemistry of system earth.

Program development

With the inclusion of autotrophs, the DEB theory now applies to all types of organisms, although a lot of testing and evaluation still needs to be done, particularly with respect to plants. The books about the DEB theory ( 1993, 2000) aim to integrate and stimulate research in this field.

The analysis of interactions between organisms (predator/prey, (endo)symbiosis, parasitism) in an evolutionary context will be an important issue in the next five years. The dynamics of foodwebs and simple communities will be evaluated. Collaborations with groups working in geochemistry and oceanography will be continued within the framework of the Global Emiliania Modelling initiative, in order to contribute to the international global change program, and, eventually, to theory for processes in the biosphere, at global level.

We plan to extend the theory into the direction of the molecular level, in collaboration with groups working in the field of mathematical biochemistry. This extension is quite natural, because the theory has many roots at the molecular level, and makes use of the relationships between membrane (surface area) and cytosol (volume) bound processes. The aim is to uncover the hierarchy in metabolic control and regulation, and model the integration of loosely coupled biochemical processes, such that a consistent energetic behaviour of the individual emerges.


Being fundamental to the processes of substrate uptake and use by organisms, the DEB theory has many potential applications.
Examples are:

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