Dynamic Energy
Budget Theory - I
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with contributions from :
Tânia Sousa
Tjalling Yager & Bas Kooijman
Environmental Applications
 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?
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, …
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
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 ...
Ecotoxicology

 Daphnia reproduction test OECD guideline 211
Reproduction test
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Reproduction test

Reproduction test

wait for 21 days …
Range of Concentrations

Dose-response plot

total offspring
NOEC
EC50
log concentration
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?”
 (almost) nothing!
total offspring
 What does this answer tell me about other
situations?
EC50
log concentration
Organisms are complex…

 Response to stress depends on
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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.
E.g., effect on reproduction

E.g., effect on reproduction

E.g., effect on reproduction

E.g., effect on reproduction

E.g., effect on reproduction

To understand an effect on reproduction …
• need to know how food is used to make offspring
• and how chemicals interfere with this process
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

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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
What is DEB theory?

 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
A widespread biological empirical fact:
Von Bertalanffy growth

 Growth as a function of time
L(t )  L  ( L  Lb ) e  rB t
 Depends on length at birth,
maximum length and
growth rate
 It was proposed in 1938 by
Von Bertalanffy an austrian
biologist
Basic concepts in DEB Theory

 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)
A DEB organism

ME - Reserve
 Metabolism in a DEB
individual.
 The boundary of the
organism
 Rectangles are state
variables
MH - Maturity
MV - Structure
DEB model: the State Variables

 What defines a DEB organism?
 Biomass
 Mv - Mass of Reserve
 ME - Mass of Structure
 Life-Cycle approach: different life stages
 MH - Level of Maturity (it represents neither mass nor
energy)
 What about other possibles state variables such as
age?

Not age, but size
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
Trichopsis vittatus
DEB model: Reserve and Structure
 Strong homeostasis

 Reserve & Structure have constant aggregated
chemical composition
 Weak homeostasis
 At constant food organisms tend to constant
aggregated chemical composition
 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
DEB model: Maturity

 Life Stages (dark blue) and transitions (light blue)
embryo
fertilization
baby
birth
juvenile
adult
infant
weaning
puberty
death
 Essential switch points for metabolic behavior
 Birth (start of feeding)
 Puberty (start of allocation to reproduction)
 Switch points sometimes in reversed order (aphids)
MHb- threshold of maturity at birth
MHp- threshold of maturity at puberty
Notation 1

Notation 2
General
Indices for compounds
Indices for transformations

A DEB organism

Feeding
J XA
J EA
ME - Reserve
Assimilation
MH - Maturity
MV - Structure
 Metabolism in a DEB
individual.
 Rectangles are state
variables
 Arrows are flows of food
JXA, reserve JEA, JEC, JEM, JET ,
JEG, JER, JEJ or structure JVG.
 Circles are processes
Feeding & Assimilation

 Feeding: the uptake of food
 Assimilation: conversion of substrate (food,
nutrients, light) into reserve(s)
 Depends on substrate availability & structural
surface area (e.g. surface area of the gut)
𝐽𝐸𝐴 = 𝑦𝐸𝑋 𝐽𝑋𝐴 = 𝑓(𝑋) 𝐽𝐸𝐴𝑚 𝑉 2/3
𝐽𝐸𝐴𝑚 - surface maximum assimilation rate
𝑦𝐸𝑋 -yield of reserve on food
 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
Intra-taxon predation: efficient conversion
yEX a high yield of reserve on food

Hemiphractus fasciatus
is a frog-eating frog
Beroe sp
is a comb jelly-eating comb jelly
Euspira catena
is a snail-eating snail
Coluber constrictor
is a snake-eating snake
Solaster papposus
is a starfish-eating starfish
Chrysaora hysoscella
is a jelly fish-eating jelly fish
Intra-taxon predation: efficient conversion
yEX a high yield of reserve on food
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Asplanchna girodi
is a rotifer-eating rotifer
Falco peregrinus
is a bird-eating bird
Didinium nasutum
is a ciliate-eating ciliate
Acinonyx jubatus
is a mammal-eating mammal
Esox lucius
is a fish-eating fish
Enallagma carunculatum
is a insect-eating insect