What is DEB theory?Bas Kooijman

Dept theoretical biologyVrije Universiteit Amsterdam

Bas@bio.vu.nlhttp://www.bio.vu.nl/thb

Melbourne 2012/08/06

What is DEB theory?Bas Kooijman

Dept theoretical biologyVrije Universiteit Amsterdam

Bas@bio.vu.nlhttp://www.bio.vu.nl/thb

Melbourne 2012/08/06

Contents

• What is DEB theory? • Stylised facts• Supply/demand systems• How was it invented?• Selection of concepts• DEBs vs SEBs

Empirical cycle 1.1

Criteria for general energy models• Quantitative Based on explicit assumptions that together specify all quantitative aspects

to allow for mass and energy balancing

• Consistency Assumptions should be consistent in terms of internal logic, with physics

and chemistry, as well as with empirical patterns

• Simplicity Implied model(s) should be simple (numbers of variables and parameters)

enough to allow testing against data

• Generality The conditions species should fulfill to be captured by the model(s) must be

explicit and make evolutionary sense

• Explanatory The more empirical patterns are explained, the better the model

From Sousa et al 2010Phil. Trans. R. Soc. Lond. B 365: 3413-3428

Empirical patterns: stylised facts

Feeding During starvation, organisms are able to reproduce, grow and survive for some time At abundant food, the feeding rate is at some maximum, independent of food density

Growth Many species continue to grow after reproduction has started Growth of isomorphic organisms at abundant food is well described by the von Bertalanffy For different constant food levels the inverse von Bertalanffy growth rate increases linearly with ultimate length The von Bertalanffy growth rate of different species decreases almost linearly with the maximum body length Fetuses increase in weight approximately proportional to cubed time

Reproduction Reproduction increases with size intra-specifically, but decreases with size inter-specifically

Respiration Animal eggs and plant seeds initially hardly use O2

The use of O2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O2 scales approximately with body weight raised to a power close to 0.75 Animals show a transient increase in metabolic rate after ingesting food (heat increment of feeding)

Stoichiometry The chemical composition of organisms depends on the nutritional status (starved vs well-fed) The chemical composition of organisms growing at constant food density becomes constant

Energy Dissipating heat is a weighted sum of 3 mass flows: CO2, O2 and N-waste

Supply-demand spectrum 1.2.5

Historical roots Aug 1979

Two questions:

• How should we quantify effects of chemical compounds on reproduction of daphnids? reproduction energy budget

• How bad is it for the environment if daphnid reproduction is a bit reduced due to toxic stress? individual population ecosystem prediction outside observed range: first principles

Isomorphic growth 2.6c

diam

eter

, m

Wei

ght1/

3 , g

1/3

leng

th, m

m

time, h time, h

time, dtime, d

Amoeba proteusPrescott 1957

Saccharomyces carlsbergensisBerg & Ljunggren 1922

Pleurobrachia pileusGreve 1971

Toxostoma recurvirostreRicklefs 1968

Wei

ght1/

3 , g

1/3

DEB – ontogeny - IBM1980

1990

2000

Daphnia

ISO/OECD

von Foerster

molecularorganisation

DEB 1

DEB 2

DEBtoxNECs

embryosbody size

scaling

morphdynamics indirect

calorimetry

food chains

SynthesizingUnits

multivarplants

adaptationtumour

induction

epidemiolapplications

bifurcationanalysis

Globalbif-analysis

integralformulations

adaptive dynamics

ecosystem self-orginazation

numericalmethods

symbioses

ecosystemdynamicsorgan

function

aging

micro’s

DEB 32010

ecotoxapplication

mixtures

QSARs evolutionecosystem

effects

timedependence

par estimationentropy

production

molecule

cell

individual

population

ecosystem

system earth

time

spac

e

Space-time scales

When changing the space-time scale, new processes will become important other will become less importantThis can be used to simplify models, by coupling space-time scalesComplex models are required for small time and big space scales and vvModels with many variables & parameters hardly contribute to insight

Each process has its characteristic domain of space-time scales

Homeostasisstrong constant composition of pools (reserves/structures) generalized compounds, stoichiometric constraints on synthesis

weak constant composition of biomass during growth in constant environments determines reserve dynamics (in combination with strong homeostasis)

structural

constant relative proportions during growth in constant environments isomorphy .work load allocation

thermal ectothermy homeothermy endothermy

acquisition supply demand systems; development of sensors, behavioural adaptations

Biomass: reserve(s) + structure(s)Reserve(s), structure(s): generalized compounds, mixtures of proteins, lipids, carbohydrates: fixed composition

Reasons to delineate reserve, distinct from structure• metabolic memory• biomass composition depends on growth rate• explanation of respiration patterns (freshly laid eggs don’t respire) method of indirect calorimetry fluxes are linear sums of assimilation, dissipation and growth fate of metabolites (e.g. conversion into energy vs buiding blocks) inter-species body size scaling relationships

Reserve vs structure 2.3

Differences between reserve & structure

• Life span of compounds in reserve: limited due to turnover of reserve all reserve compounds have the same mean life span

structure: controlled by somatic maintenance structure compounds can differ in mean life span

• no maintenance costs for reserve freshly laid eggs consist of reserve and do not respire

Reserve does not mean:• “set apart for later use’: compounds in reserve can have active functions• lipids: the rest would be structure and lipids cannot convert to protein• `material that does not require maintenance’: can also apply to compounds in structure• `material that is synthesize from assimilates’: indirectly applies to all compounds

Reserve residence time 2.3.1b

Surface area/volume interactions• biosphere: thin skin wrapping the earth light from outside, nutrient exchange from inside is across surfaces production (nutrient concentration) volume of environment

• food availability for cows: amount of grass per surface area environment food availability for daphnids: amount of algae per volume environment

• feeding rate surface area; maintenance rate volume (Wallace, 1865)

• many enzymes are only active if linked to membranes (surfaces) substrate and product concentrations linked to volumes change in their concentrations gives local info about cell size ratio of volume and surface area gives a length

Change in body shapeIsomorph: surface area volume2/3

volumetric length = volume1/3

V0-morph: surface area volume0

V1-morph: surface area volume1

Ceratium

Mucor

Merismopedia

Shape correction functionShape correction function

at volume Vactual surface area at volume V

isomorphic surface area at volume V=

1)( VΜ for dVV

V0-morphV1-morph isomorph 0

3/1

3/2

)/()(

)/()(

)/()(

d

d

d

VVV

VVV

VVV

Μ

Μ

Μ

3/13/2

3/13/2

)/(2

2)/(

2)(

)/(3

3)/(

3)(

dd

dd

VVδ

VVδ

δV

VVδ

VVδ

V

Μ

Μ

Static mixtures between V0- and V1-morphs for aspect ratioδ

V1-morphs are special because• surfaces do not play an explicit role• their population dynamics reduce to an unstructured dynamics; reserve densities of all individuals converge to the same value in homogeneous environments

Biofilms

Isomorph: V1 = 0

V0-morph: V1 =

mixture between iso- & V0-morph

biomass grows, butsurface area that is involvedin nutrient exchange does not

solid substratebiomass

3/2

1

1)(

d

d

VV

VV

V

VVΜ

Mixtures of changes in shape 2

Dynamic mixtures between morphs

Lichen Rhizocarpon

V1- V0-morph

V1- iso- V0-morph

outer annulus behaves as a V1-morph, inner part as a V0-morph. Result: diameter increases time

Evolution of DEB systemsvariable structure

composition

strong homeostasisfor structure

delay of use ofinternal substrates

increase ofmaintenance costs

inernalization of maintenance

installation ofmaturation program

strong homeostasisfor reserve

reproductionjuvenile embryo + adult

Kooijman & Troost 2007 Biol Rev, 82, 1-30

54321

specialization of structure

7

8

an

ima

ls

6

pro

ka

ryo

tes

9plants

Static Energy Budgets (SEBs)

Differences with DEBs• overheads interpretation of respiration interpretation of urination• metabolic memory• life cycle perspective change in states

gross ingested

faeces

urine

apparent assimilated

gross metabolised

net metabolised

spec dynamic action

workmaintenance

somaticmaintenance

activity

thermo regulation

production

growth productsreproduction

Concept overview

• empirical facts• supply-demand spectrum

• 5 types of homeostasis• reserve & structure• residence time

• surface area/volume• iso-, V0-, V1-morphs• shape correction function

• evolutionary perspective

Notation 1

http://www.bio.vu.nl/thb/research/bib/Kooy2010_n.pdf

Indices for compounds

Indices for transformations

GeneralNotation 2

Notation 3Some symbols have more than one meaning:V as symbol stands for volume, and without index for volume of structure, as index stands for the compound structureE as symbol stands for energy, and without index for energy in reserve, as index stands for the compound reserveC,H,O,N as indices stand for mineral compounds as well as chemical elements the context defines the meaning

Dots are used to • distinguish rates from states (dimension check)• allow scaling of time without the need to introduce new symbols if time is scaled to a dimensionless quantity, the dot is removes

DEB resources• DEB book 2010 (DEB3, 500 p) + erratum-list• summary of concepts for each of the sections of DEB3• notation document, including notation for new developments• comments to DEB3 (250 p)• DEBtool: software package for Matlab and Octave (> 1000 functions)• add my pet document on par estimation for the standard DEB model• add_my_pet library of data and par values, implied properties (130 spec)• micro-lectures, a collection of ppt’s for DEB3• phylogenetic survey of living organisms, frequently updated ppt’s• exercises that follow DEB3• quizzes, to monitor progress in mastering DEB concepts• assays, written by participants of DEB tele-courses• questions and answers on DEB theory from previous DEB tele-courses• bibliography of DEB papers (via the DEB information page)• Basic Methods for Theoretical Biology on methodology, modelling & math

http://www.bio.vu.nl/thb/deb/