Dynamic Energy Budget Theory - I

Tânia Sousa with contributions from : Tjalling Yager & Bas Kooijman

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

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 ...

Daphnia reproduction test OECD guideline 211

Ecotoxicology

Reproduction test

Reproduction test

Reproduction test

wait for 21 days …

Range of Concentrations

Dose-response plot

EC50

tota

l off

sp

rin

g

log concentration

NOEC

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! EC50EC50

tota

loff

spri

ng

log concentration

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.

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 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

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?

A widespread biological empirical

fact: Von Bertalanffy growth

trb

BeLLLtL )()(

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

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

Metabolism in a DEB

individual. The boundary of the

organism Rectangles are state

variables

A DEB organism

ME - Reserve

MV - StructureMH - Maturity

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?

DEB model: the State Variables

These gouramis are from the same nest, they have the same age and lived in the same tankSocial interaction during feeding caused the huge size differenceAge-based models for growth are bound to fail; growth depends on food intake

Not age, but sizeTrichopsis vittatus

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

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

embryo juvenile adult

fertilization birth puberty deathweaning

baby infant

MHb- threshold of maturity at birth

MHp- threshold of maturity at puberty

Notation 1

Indices for compounds

Indices for transformations

General

Notation 2

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

A DEB organism

ME - Reserve

MV - Structure

Feeding

MH - Maturity

XAJ EAJ

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)

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

- surface maximum assimilation rate -yield of reserve on food

Intra-taxon predation: efficient conversion

yEX a high yield of reserve on food

Hemiphractus fasciatusis a frog-eating frog

Beroe spis 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

Asplanchna girodiis a rotifer-eating rotifer

Didinium nasutumis 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 conversionyEX a high yield of reserve on food