Applications of DEB theory Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam 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-  maturity maintenance maturity offspring maturation reproduction Standard DEB model foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth  time: searching & handling feeding  surface area weak & strong homeostasis κ-rule for allocation to soma maintenance has priority somatic maint  structure maturity maint  maturity stage transition: maturation embryo: no feeding, reprod juvenile: no reproduction adult: no maturation maternal effect: reserve density at birth equals that of mother initially: zero structure, maturity 1 food type, 1 reserve, 1 structure, isomorph

Food intake from weights age, d weight 1/3, g 1/3 Small-bodied pinguins synchronise breeding with food peak and grow von Bertalanffy Large-bodied pinguins: fit spline through weights reconstruct food intake, given DEB parameters Pygoscelis adelidae Aptenodytes forsteri food intake, cm 2 Kooijman 1993 Cambridge Univ Press

Arrhenius relationship 10 3 /T, K -1 ln pop growth rate, h /T H 10 3 /T L Escherichia coli Arrhenius Kooijman 2000 Cambridge Univ Press

age, d Body temperature from weights age, d weight 1/3, g 1/3 fit generalised logistic growth through weights assume abudant food reconstruct body temperature, given DEB parameters and Arrhenius relationship Catharacta skua Furness 1987 Uria aalge Mahoney & Trelfall 1981 body temperature, °C Kooijman 1993 Cambridge 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 2010 Cambridge Univ Press

Food density from reproduction  f  week initial egg volume, mm 3 scaled functional resp, f food different for each indfood the same for ind in one haul

Analysis of otolith data Fablet et al 2010, in prep North Sea cod Barents Sea cod observed simulated Otolith formation : organic matrix (OM) has contributions from dissipation and growth CaCO 3 is stoichiometrically coupled in a temperature-dependent way opacity reflects the CaCO 3 -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 observed fitted 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 cumulative offspring time body length TPT Jager et al (2004) Environ Sci Technol 38: Folsomia candida Tri-Phenyl-Tin

Increase in cost for offspring time cumulative offspring time body length Chlorpyrifos Jager et al (2007) Environ Pollut 145: Folsomia candida

Increase in cost for structure time body length time cumulative offspring Pentachlorobenzene Alda Álvarez et al (2006) Environ Sci Technol 40: Caenorhabditis elegans

Interaction Cu,Cd, Pb, Zn: Cu & Pb: slightly antagonistic Other combinations: nill Folsomia candida Cd & Cu  survival of Folsomia Baas et al 2007 Eviron Tox Chem 26:

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 2003 Brit J Cancer 89:

Yield vs growth 1/spec growth rate, h 1/yield, mmol glucose/ 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 rates DEB theory: high reserve density gives high growth rates structure requires maintenance, reserves do not Kooijman & Troost 2007 Biol 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 2006 J Sea Res 56:

DEB tele course Course is free of financial costs; some 100 h effort Program for 2011: Feb/Mar general theory (5w) 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 Cambridge Univ Press 2009 Audience : thank you for your attention