1.  Dynamic Energy Budget Theory - I Tânia Sousa with contributions from :Tjalling Yager & Bas Kooijman

2.   Toxicology  Which is the toxicity of the environmental concentration of a compound?  Which are the toxic effects of a compound?  Climate Change  Will an increase in 1ºC have a drastic impact on the distribution range of a species?  Waste water treatment plant  What are the necessary conditions to mantain an healthy microbian comunity in the biological reactors? Environmental Applications

3.  Human-made toxicants  Wide variety of uses  paints, detergents, solvents, pesticides, pharmaceuticals, polymers, …  probably some 100.000 compounds  Chemical industry is BIG business!  production value 2009: 3.4 trillion dollar (3.400.000.000.000 $)  equals the GDP of Germany  All are toxic, some are intended to kill  fungicides, insecticides, herbicides, nematicides, molluscicides, …

4.  Human-made & natural toxicant Dioxins  e.g., 2,3,7,8-TCDD  human: paper and fiber bleaching, incineration of waste, metal smelting, cigarette smoke  natural: incomplete combustion of chlorine-containing things

5.  Human-made vs. natural What is the difference?  Time scale  major increase after second world war  rapid development of new types of molecules  Spatial scale  amounts emitted  landscape and even global instead of local  Since 1970’s, most countries have programmes for environmental protection...

6.   Daphnia reproduction test OECD guideline 211 Ecotoxicology

7.  Reproduction test

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9.  wait for 21 days …

10.  Range of Concentrations

11.  Dose-response plot EC50 total offspring log concentration NOEC

12.  If EC50 is the answer … … what was the question? “What is the concentration of chemical X that leads to 50% effect on the total number of offspring of Daphnia magna (Straus) after 21-day constant exposure under standardised laboratory conditions?”  What does this answer tell me about other situations?  (almost) nothing!

13.  Organisms are complex…  Response to stress depends on  organism (species, life stage, sex, …)  endpoint (size, reproduction, development, …)  type of stressor (toxicant, radiation, parasites, …)  exposure scenario (pulsed, multiple stress, …)  environmental conditions (temperature, food, …)  etc., etc.

14.  E.g., effect on reproduction

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18.  To understand an effect on reproduction … need to know how food is used to make offspring and how chemicals interfere with this process

19.  Why is DEB important for toxicity?  The use of DEB theory allows extrapolation of toxicity test results to other situations and other species  To study the effects of toxicity on life-history traits, DEB follows naturally  food is used to fuel all traits over the life cycle  toxicants affect DEB parameters  should allow extrapolation to untested conditions  it is valuable for environmental risk assessment

20.   It captures the quantitative aspects of metabolism at the individual level for all species  Why the hope for generality?  universality of physics and evolution  Entropy production is >=0  widespread biological empirical patterns What is DEB theory?

21.  A widespread biological empirical fact: Von Bertalanffy growth  Growth as a function of time  Depends on length at birth, maximum length and growth rate  It was proposed in 1938 by Von Bertalanffy an austrian biologist

22.   Consistency with other scientific knowledge (thermodynamics, evolution, etc)  Consistency with empirical data  Life-cycle approach: embryo, juvenile and adult  Occam’s razor: the general model should be as simple as possible (and not more) Basic concepts in DEB Theory

23.   Metabolism in a DEB individual.  The boundary of the organism  Rectangles are state variables A DEB organism ME - Reserve MV - Structure MH - Maturity

24.   What defines a DEB organism?  Biomass  M v - Mass of Reserve  M E - Mass of Structure  Life-Cycle approach: different life stages  M H - Level of Maturity (it represents neither mass nor energy)  What about other possibles state variables such as age? DEB model: the State Variables

25.  These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake Not age, but size Trichopsis vittatus

26.   Strong homeostasis  Reserve & Structure have constant aggregated chemical composition  Weak homeostasis  At constant food organisms tend to constant aggregated chemical composition DEB model: Reserve and Structure  Why more than 1 state variable to define the biomass?  The aggregated chemical composition of organisms is not constant – it changes with the growth rate  Why not use thousands of chemical species to define the organism?  Two are sufficient (in animals and bacteria) to capture the change in aggregated chemical composition with the growth rate  Strong & Weak homeostasis -> higher control over metabolism

27.   Life Stages (dark blue) and transitions (light blue)  Essential switch points for metabolic behavior  Birth (start of feeding)  Puberty (start of allocation to reproduction)  Switch points sometimes in reversed order (aphids) DEB model: Maturity embryojuvenileadult fertilizationbirth puberty death weaning babyinfant M H b - threshold of maturity at birth M H p - threshold of maturity at puberty

28.  Notation 1

29.  Indices for compounds Indices for transformations General Notation 2

30.   Metabolism in a DEB individual.  Rectangles are state variables  Arrows are flows of food J XA, reserve J EA, J EC, J EM, J ET, J EG, J ER, J EJ or structure J VG.  Circles are processes A DEB organism ME - Reserve MV - Structure Feeding MH - Maturity Assimilation

31.  Feeding & Assimilation  Empirical pattern: the heat increment of feeding suggests that there are processes only associated with food processing  Strong homeostasis imposes a fixed conversion efficiency  Consistency with other fields: mass transfer is proportional to area

32.  Intra-taxon predation: efficient conversion y EX a high yield of reserve on food Hemiphractus fasciatus is a frog-eating frog Beroe sp is a comb jelly-eating comb jelly Solaster papposus is a starfish-eating starfish Chrysaora hysoscella is a jelly fish-eating jelly fish Euspira catena is a snail-eating snail Coluber constrictor is a snake-eating snake

33.  Asplanchna girodi is a rotifer-eating rotifer Didinium nasutum is a ciliate-eating ciliate Esox lucius is a fish-eating fish Enallagma carunculatum is a insect-eating insect Falco peregrinus is a bird-eating bird Acinonyx jubatus is a mammal-eating mammal Intra-taxon predation: efficient conversion y EX a high yield of reserve on food