Applications of DEB theory Bas Kooijman

Dept theoretical biologyVrije Universiteit Amsterdam

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

Iraklion, 2010/05/12

Contents

• Very short outline of standard DEB model• Reconstruction of food/temperature trajectories• Identification of mode of action of toxicants• Prediction of tumour growth

as affected by caloric restriction• Optimisation of bioproduction

yield of microbial biomass

prediction of spawning by pacific oysters

1- maturitymaintenance

maturityoffspring

maturationreproduction

Standard DEB model

food faecesassimilation

reserve

feeding defecation

structurestructure

somaticmaintenance

growth

time: searching & handlingfeeding surface areaweak & strong homeostasisκ-rule for allocation to somamaintenance has priority somatic maint structure maturity maint maturitystage transition: maturation embryo: no feeding, reprod juvenile: no reproduction adult: no maturationmaternal effect: reserve density at birth equals that of motherinitially: zero structure, maturity

1 food type, 1 reserve, 1 structure, isomorph

Food intake from weights

age, d age, d

wei

ght1/

3 , g

1/3

wei

ght1/

3 , g

1/3

Small-bodied pinguins synchronise breeding with food peak and grow von BertalanffyLarge-bodied pinguins: fit spline through weights reconstruct food intake, given DEB parameters

Pygoscelis adelidae Aptenodytes forsteri

food intake, cm2

Kooijman 1993Cambridge Univ Press

Arrhenius relationship

103/T, K-1

ln p

op g

row

th r

ate,

h-1

103/TH 103/TL

Escherichia coli

Arrhenius

Kooijman 2000Cambridge Univ Press

age, d

Body temperature from weights

age, d

wei

ght1/

3 , g

1/3

wei

ght1/

3 , g

1/3

fit generalised logistic growth through weights assume abudant food reconstruct body temperature, given DEB parameters and Arrhenius relationship

Catharacta skuaFurness 1987

Uria aalgeMahoney & Trelfall 1981

body temperature, °C

body temperature, °C

Kooijman 1993Cambridge Univ Press

Food density from reproduction Eggs in brood pouches of Daphnia hyalina were counted in weekly hauls in 4 mesocosms by Stella Berger (München) and eggs and body length are measured

Given DEB parameters for D. hyalina scaled functional response can be estimated as functions of time based on assumptions:• functional response is constant during a week and individuals are in pseudo-equilibrium• all individuals have equal parameters but experience different food densities (estimate is individual-specific for each time point) or individuals differ in parameters but experience the same food density

DEB elements:• handling rules for reproduction buffer comply to the molting cycle• maternal effect: reserve density at birth equals that of the mother at egg formation• eggs grow in volume during incubation due to uptake of water

Kooijman 2010Cambridge Univ Press

Food density from reproduction

f f

week week

initi

al e

gg

vo

lum

e, m

m3

sca

led

fun

ctio

na

l re

sp, f

food different for each ind food the same for ind in one haul

Analysis of otolith data

Fablet et al 2010, in prep

North Sea cod Barents Sea cod

obse

rved

sim

ulat

ed

Otolith formation: organic matrix (OM) has contributions from dissipation and growth CaCO3 is stoichiometrically coupled in a temperature-dependent way opacity reflects the CaCO3-OM ratio

Gadus morhua

Analysis of otolith data

simulated scenario’s

April 15

† May 1

checks

Fablet et al 2010, in prep

Food & temperature reconstruction from otolith data

observedfitted

fitted if food constant

Direct observation: feeding was low for low and high temperatures

Fablet et al 2010, in prep

Increase in maintenance costs

time

cum

ula

tive

off

spri

ng

time

bo

dy

len

gth

TPT

Jager et al (2004)

Environ Sci Technol 38: 2894-2900

Folsomia candidaTri-Phenyl-Tin

Increase in cost for offspring

time

cum

ula

tive

off

spri

ng

time

bo

dy

len

gth

Chlorpyrifos

Jager et al (2007)

Environ Pollut 145: 452-458

Folsomia candida

Increase in cost for structure

time

bo

dy

len

gth

time

cum

ula

tive

off

spri

ng Pentachlorobenzene

Alda Álvarez et al (2006)

Environ Sci Technol 40:2478-2484

Caenorhabditis elegans

Interaction Cu,Cd, Pb, Zn: Cu & Pb: slightly antagonistic Other combinations: nill

Folsomia candida

Cd & Cu survival of Folsomia

Baas et al 2007Eviron Tox Chem 26: 1320-1327

Tumour Growth: workload allocation

If tumour induction occurs late, tumours grows slower

Growth curve of tumour depends on pars no maximum size is assumed a priori

Van Leeuwen et al 2003Brit J Cancer 89: 2254-2263

Yield vs growth

1/spec growth rate, h

1/yi

eld,

mm

ol g

luco

se/

mg

cells

Streptococcus bovis, Russell & Baldwin (1979)

Marr-Pirt (no reserve)DEB

spec growth rate

yield

Russell & Cook (1995): this is evidence for down-regulation of maintenance at high growth ratesDEB theory: high reserve density gives high growth rates structure requires maintenance, reserves do not

Kooijman & Troost 2007Biol Rev 82: 1-30

Growth & reprod in Crassostrea gigas

Bay of Arcachon

DEB curves based on- measured temperature- measured chlorophyll- known DEB parameters

Spawings (jumps in weight) correctly predicted on the basis of temp trigger

Pouvreau et al 2006J Sea Res 56: 156-167

DEB tele course 2011http://www.bio.vu.nl/thb/deb/

Course is free of financial costs; some 100 h effort

Program for 2011: Feb/Mar general theory (5w) 13-15 April course + symposium in Lisbon (2w + 3 d) Target audience: PhD students

We encourage participation in groups who organize local meetings weekly

Software package DEBtool for Octave/ Matlab freely downloadable

Slides of this presentation are downloadable from http://www.bio.vu.nl/thb/users/bas/lectures/

Cambridge Univ Press 2009

Audience: thank you for your attention