S.A.L.M. Kooijman

Dynamic energy budget theory for metabolic organisation

Preface 1. Basic concepts 2. Standard DEB model in time, length and energy 3. Energy, compounds and metabolism 4. Univariate DEB models 5. Multivariate DEB models 6. Effects of compounds on budgets 7. Extensions of DEB models 8. Co-variation of DEB parameter values 9. Living together 10. Evolution 11. Evaluation Bibliography Glossary Notation and symbols Taxonomic index Subject index.

Energy budgets can explain body size relations

The size-dependence of some 20 physiological variables has been derived from a rather simple model for energy budgets. This nine parameter model is based on detailed observations on the growth and reproduction at varying food densities, and has the state variables size and storage. The size-dependence of some variables works out to be different for animals of the same species as opposed to animals of different species. The reproductive rate, for instance, tends to increase with size for animals of the same species, but to decrease with size for animals of different species. This is because the parameter values are constants within a species, but vary in a size dependent manner for animals of different species. Although growth at constant food density is assumed to be of the von Bertalanffy type, and routine metabolism to be proportional to size, respiration turns out to be about proportional to size to the power 3/4, both within and between species. The value of about 3/4 has frequently been found, but it has always been thought to be incompatible with von Bertalanffy growth.

Fundamental connections among organism c:n:p stoichiometry, macromolecular composition and growth.

Whereas it is acknowledged that the C:N:P stoichiometry of consumers and their resources affects both the structure and the function of food webs, and eventually influences broad-scale processes su ...

From empirical patterns to theory: a formal metabolic theory of life

The diversity of life on Earth raises the question of whether it is possible to have a single theoretical description of the quantitative aspects of the organization of metabolism for all organisms. However, similarities between organisms, such as von Bertalanffys growth curve and Kleibers law on metabolic rate, suggest that mechanisms that control the uptake and use of metabolites are common to all organisms. These and other widespread empirical patterns in biology should be the ultimate test for any metabolic theory that hopes for generality. The present study (i) collects empirical evidence on growth, stoichiometry, feeding, respiration and energy dissipation and exhibits it as stylized biological facts; (ii) formalizes assumptions and propositions in a metabolic theory that is fully consistent with the Dynamic Energy Budget theory; and (iii) proves that these assumptions and propositions are consistent with the stylized facts.

Dynamic energy budget theory restores coherence in biology

We present the state of the art of the development of dynamic energy budget theory, and its expected developments in the near future within the molecular, physiological and ecological domains. The degree of formalization in the set-up of the theory, with its roots in chemistry, physics, thermodynamics, evolution and the consistent application of Occams razor, is discussed. We place the various contributions in the theme issue within this theoretical setting, and sketch the scope of actual and potential applications.

Analysis of toxicity tests on Daphnia survival and reproduction

We present a statistical analysis of bioassays for Daphnia survival and reproduction, such as the routine toxicity test that is described in the OECD guideline 202. The analysis is based on the Dynamic Energy Budget theory and a one-compartment kinetics for the toxic compound. It is fully process oriented. We compare a formulation in terms of effects on survival during oogenesis to various direct and indirect effects on the energetics of reproduction. All formulations characterize the effects by a no-effect concentration, a tolerance concentration and the elimination rate. We conclude that all options lead to similar no-effect levels. We compare the analysis to the standard NOEC/EC50 analysis and conclude that our analysis is both simpler and more effective.

Application of a dynamic energy budget model to Mytilus edulis (L.)

Abstract Filtering, ingestion, assimilation respiration, growth and reproduction of the blue mussel Mytilus edulis were successfully described in terms of a dynamic energy budget (DEB) model, which previously had been applied successfully to a variety of other species. The relation between oxygen consumption rate and ingestion rate could be derived from elementary model assumptions. Parameters of the DEB model, estimated for laboratory situations, were applied to field data. The varying growth rates in the field could be described by taking account of changes in food density and quality, and temperature, on the basis of the Arrhenius relation. A methodology is given to reconstruct ambient food densities from observed growth curves. This can be used to assess the nutritive value of measured substances such as POM or chlorophyll. The concept Scope For Growth is discussed and interpreted in terms of the DEB model. The energy conductance is found to be 0.36 mm·d −1 at 20°C, which is close to the mean of many species: 0.43 mm·d −1 .

From food-dependent statistics to metabolic parameters, a practical guide to the use of dynamic energy budget theory.

The standard model of the dynamic energy budget theory for metabolic organisation has variables and parameters that can be quantified using indirect methods only. We present new methods (and software) to extract food‐independent parameter values of the energy budget from food‐dependent quantities that are easy to observe, and so facilitate the practical application of the theory to enhance predictability and extrapolation. A natural sequence of 10 steps is discussed to obtain some compound parameters first, then the primary parameters, then the composition parameters and finally the thermodynamic parameters; this sequence matches a sequence of required data of increasing complexity which is discussed in detail. Many applications do not require knowledge of all parameters, and we discuss methods to extrapolate parameters from one species to another. The conversion of mass, volume and energy measures of biomass is discussed; these conversions are not trivial because biomass can change in chemical composition in particular ways thanks to different forms of homeostasis. We solve problems like “What would be the ultimate reproduction rate and the von Bertalanffy growth rate at a specific food level, given that we have measured these statistics at abundant food?” and “What would be the maximum incubation time, given the parameters of the von Bertalanffy growth curve?”. We propose a new non‐destructive method for quantifying the chemical potential and entropy of living reserve and structure, that can potentially change our ideas on the thermodynamic properties of life. We illustrate the methods using data on daphnids and molluscs.

Statistical analysis of bioassays, based on hazard modelling

A stochastic model is proposed to describe time-dependent lethal effects of toxic compounds. It is based on simple mechanistic assumptions and provides a measure for the toxicity of a chemical compound, the so-called killing rate. The killing rate seems a promising alternative for the LC50. The model also provides the no-effect level and the LC50, both as a function of exposure time. The model is applied to real data and to simulated data.

A biology-based approach for mixture toxicity of multiple endpoints over the life cycle.

Typical approaches for analyzing mixture ecotoxicity data only provide a description of the data; they cannot explain observed interactions, nor explain why mixture effects can change in time and differ between endpoints. To improve our understanding of mixture toxicity we need to explore biology-based models. In this paper, we present an integrated approach to deal with the toxic effects of mixtures on growth, reproduction and survival, over the life cycle. Toxicokinetics is addressed with a one-compartment model, accounting for effects of growth. Each component of the mixture has its own toxicokinetics model, but all compounds share the effect of body size on uptake kinetics. The toxicodynamic component of the method is formed by an implementation of dynamic energy budget theory; a set of simple rules for metabolic organization that ensures conservation of mass and energy. Toxicant effects are treated as a disruption of regular metabolic processes such as an increase in maintenance costs. The various metabolic processes interact, which means that mixtures of compounds with certain mechanisms of action have to produce a response surface that deviates from standard models (such as ‘concentration addition’). Only by separating these physiological interactions from the chemical interactions between mixture components can we hope to achieve generality and a better understanding of mixture effects. For example, a biology-based approach allows for educated extrapolations to other mixtures, other species, and other exposure situations. We illustrate our method with the interpretation of partial life-cycle data for two polycyclic aromatic hydrocarbons in Daphnia magna.