The DEB-theory and its applications in Ecotoxicology Modélisation en écotoxicologie Modelleren in de ecotoxicologie Modeling in ecotoxicology The DEB-theory and its applications in Ecotoxicology Jacques J.M. Bedaux Dept Theoretical Biology Vrije Universiteit Amsterdam

Overview DEB-theory DEBtox modeling frame work Some examples Extensions to standard DEBtox New developments (demo of DEBtox)

DEB theory Dynamic Energy Budget theory History: It started as a statistical methodology for the study of toxic effects on Dapnnia reproduction. DEB theory presents simple mechanistic rules that describe the uptake and use of energy and nutrients (substrates, food, light) and the consequences for physiological organisation throughout an organism's life cycle History of the DEB theory: as Bas Kooijman writes in the preface of his first book it started in 1978 as a statistical methodology for the study of toxic effects on daphnid reproduction! Large daphnids tend to have bigger litters (i.e. they produce more offspring) than small ones, so modelling reproduction is impossible without looking at growth, feeding etc. So it started as a model for Daphnia, but evolved into a non-species-specific theory. It is impossible too say much about DEB-theory in half an hour. I’ll give some information about it, and

DEB model (simple form) food reserve structure maturation maint. somatic maint. reproduction k 1-k DEB model for a reproducing heterotroph (such as many animals); Structural body mass and reserves are the state variables of the individual; The kappa-rule: a fixed fraction of the energy, used from the reserves, is spent on somatic maintenance plus growth. Maintenance is proportional to structural body volume. Feeding rate is proportional to the surface area of the body. Under starvation conditions, individuals always give priority to somatic maintenance. Feeding starts at the transition from embryo to juvenile, and the transition to adult initiates reproduction

The DEB model The model is tested on a large amount of empirical data. Daphids dataset: Ingestion rate : proportional with f.L^2 Oxygen-consumption rate: proportional with vL^2 + km.L^3 Growth: Von Bertalanffy

framework of toxicological model external concentration of chemical compound Standard way of toxicological modeling: The toxicological endpoint, like reproduction, is taken as a function of environmental concentration, without incorporating time of exposure. This way of static modeling is easy to apply, but not very realistic and without biological motivation. toxicological endpoint (growth, reproduction, survival)

static toxicological model Log-logistic model Standard way of toxicological modeling: The toxicological endpoint, like reproduction, is taken as a function of environmental concentration, without incorporating time of exposure. This way of static modeling is easy to apply, but not very realistic and without biological motivation.

dynamic toxicological model external concentration toxicokinetics internal concentration effects (toxicodynamics) physiological parameter blanc physiology toxicological endpoint

framework standard DEBtox model external concentration toxicokinetics first-order internal concentration effects linear physiological parameter blanc physiology DEB model toxicological endpoint

Example: acute test, survival external concentration C’(t) = kuc – keC(t) internal concentration Hazard rate proportional to internal concentration minus threshold h(t)  (C(t) – threshold)+ The most simple example is an acute survival test. Short term test, so we can neglect growth of the animals. We relate the fraction of survivors (the survivor function) directly to the internal concentration by stating that the hazard rate is proportional tot the internal concentration, as far as it exceeds an internal threshold. We believe that an animal can handle some amount of toxicants without any damage. By the way, this threshold might be equal to zero for some species/toxicant combination. In this example DEB theory is not really present, only the DEB philosophy! S(t) = exp(-0th(u)du) fraction of survivors

internal concentration c > NEC internal threshold c = NEC c < NEC time hazard rate survivor function time time

time-dose response surface dose response curve time-dose response surface time concentration concentration 4 parameters NEC elimination rate killing rate background mortality

Example: chronic test, reproduction food assimilation reserve The most complex test we have worked out is the chronic test on effects on reproduction. Here the DEB model is indispensable. DEB theory describes reproduction rate as a function of length (by constant feeding). We assume that the structure of the DEB model is not affected by a toxicant, only some parameters values are changed. For instance growth maintenance reproduction structure work eggs

Effects on reproduction costs external concentration First order, dilution by growth internal concentration Energy costs per egg proportional to internal concentration minus threshold Here we look at one of the five modes of action: effects on reproduction costs. DEB is involved in all levels. It leads to a system of three coupled differential equations, describing length, concentration en total reproductive output. In standard experiments we only have data on reproductive output. Four parameters have to be estimated. energy costs per egg reproduction rate

Chronic tests: reproduction DEBtox specifies length, internal concentration and reproduction rate data only on reproductive output! 4 parameters to be estimated: - NEC, tolerance concentration, - elim. rate, max. reproduction rate numerically heavy

Free software: DEBtox Four types of toxicity tests - Survival - (Fish) Body length growth - (Daphnia) Reproduction - (Algae) Population growth Parameter estimation, confidence intervals, likelihood profiles, statistical tests, graphical output Windows, Unix - User friendly (Windows) - For experts (Unix) downloadable on http://www.bio.vu.nl/thb/deb

Extensions to standard DEBtox From effects on individuals to effects on population level Time-inhomogeneous concentrations (Alexandre Péry) More-samples analysis

From individual to population Euler-Lotka equation mc/m0 c EC10

References References on DEB: Kooijman, S.A.L.M. (2000) Dynamic Energy and Mass Budgets in Biological Systems (2nd ed) Cambrige UP. Kooijman, S.A.L.M. (2000) Quantitative aspects of metabolic organization: a discussion of concepts, Phil Trans R Soc LondB 356 Nisbet, R.M. et al (2000) From molecules tot ecosystems through dynamic energy budget models, Journal of Animal Ecology 69 References on DEBtox: Kooijman, S.A.L.M. and Bedaux, J.J.M. (1996) The analysis of aquatic toxicity data, VU UP. http://www.bio.vu.nl/thb/deb

Related projects Biodegradation (DEBdeg) Tumor incidence (DEBtum) Food-webs