DEB theory ecotox applications Bas Kooijman Dept theoretical

DEB theory & ecotox applications Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio. vu. nl http: //www. bio. vu. nl/thb/ Lyon, 2008/09/19

DEB theory & ecotox applications Contents: • What is DEB theory? • Evolution & body size scaling Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio. vu. nl http: //www. bio. vu. nl/thb/ • Unexpected links & reconstructions • Applications of DEB theory • Effects of chemical compounds Lyon, 2008/09/19

Dynamic Energy Budget theory for metabolic organization • consists of a set of consistent and coherent assumptions • uses framework of general systems theory • links levels of organization scales in space and time: scale separation • quantitative; first principles only equivalent of theoretical physics • interplay between biology, mathematics, physics, chemistry, earth system sciences • fundamental to biology; many practical applications

Research strategy 1) use general physical-chemical principles to develop an educated quantitative expectation for the eco-physiological behaviour of a generalized species 2) estimate parameters for any specific case compare the values with expectations from scaling relationships deviations reveal specific evolutionary adaptations 3) study deviations from model expectations learn about the physical-chemical details that matter in this case but had to be ignored because they not always apply Deviations from a detailed generalized expectation provide access to species-specific (or case-specific) modifications

Empirical special cases of DEB year author model 1780 Lavoisier multiple regression of heat against mineral fluxes 1950 Emerson cube root growth of bacterial colonies 1825 Gompertz 1889 DEB theory is axiomatic, 1951 Huggett & Widdas Survival probability for aging based on mechanisms temperature dependence of Arrhenius 1951 Weibull physiological rates not meant to glue empirical models foetal growth survival probability for aging Huxley allometric growth of body parts 1955 Best diffusion limitation of uptake 1902 Henri Michaelis--Menten kinetics 1957 Smith embryonic respiration 1905 Blackman 1973 Droop reserve (cell quota) dynamics 1891 1920 Since many empirical models bilinear functional response microbial product formation 1959 Leudeking & Piret to binding be special cases of DEB theory Cooperative hyperbolic functional response Hill turn out 1959 Holling von Bertalanffy growth ofthese 1962 maintenance in yields of biomass behind models support DEB theory Pütter the data Marr & Pirt 1927 Pearl 1928 Fisher & Tippitt 1932 Kleiber 1910 1932 individuals logistic population growth This makes DEB theory very tested against data Weibull aging water loss in bird eggs 1974 well Rahn & Ar respiration scales with body digestion 1975 Hungate DEB theory reveals when to expect deviations weight root growth of tumours development of salmonid embryos Mayneord 1977 Beer & Anderson from cube these empirical models 3/ 4

Individual Ecosystem • population dynamics is derived from properties of individuals + interactions between them • evolution according to Darwin: variation between individuals + selection • material and energy balances: most easy for individuals • individuals are the survival machines of life

Evolution of DEB systems strong homeostasis for structure variable structure composition 1 3 2 5 6 inernalization of maintenance delay of use of internal substrates increase of maintenance costs 4 7 installation of maturation program 5 8 strong homeostasis for reserve reproduction juvenile embryo + adult Kooijman & Troost 2007 Biol Rev, 82, 1 -30

Standard DEB model Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) Extensions: • more types of food and food qualities • more types of reserve (autotrophs) • more types of structure (organs, plants) • changes in morphology • different number of life stages

Primary scaling relationships assimilation feeding digestion growth mobilization heating, osmosis turnover, activity regulation, defence allocation egg formation life cycle aging {JEAm} {b} y. EX y. VE v {JET} [JEM] k. J R [MHb] [MHp] ha max surface-specific assim rate Lm surface- specific searching rate yield of reserve on food yield of structure on reserve energy conductance surface-specific somatic maint. costs volume-specific somatic maint. costs maturity maintenance rate coefficient partitioning fraction reproduction efficiency volume-specific maturity at birth volume-specific maturity at puberty aging acceleration maximum length Lm = {JEAm} / [JEM] Kooijman 1986 J. Theor. Biol. 121: 269 -282

Metabolic rate 2 curves fitted: 0. 0226 L 2 + 0. 0185 L 3 0. 0516 L 2. 44 Log metabolic rate, w O 2 consumption, l/h slope = 1 endotherms ectotherms slope = 2/3 unicellulars Length, cm Intra-species (Daphnia pulex) Log weight, g Inter-species

Daphnia Length, mm 1/yield, mmol glucose/ mg cells O 2 consumption, μl/h DEB theory reveals unexpected links Streptococcus 1/spec growth rate, 1/h respiration length in individual animals & yield growth in pop of prokaryotes have a lot in common, as revealed by DEB theory Reserve plays an important role in both relationships, but you need DEB theory to see why and how

Otolith growth & opacity • standard DEB model: otolith is a product • otolith growth has contributions from growth & dissipation (= maintenance + maturation + reprod overheads) • opacity relative contribution from growth DEB theory allows reconstruction of functional response from opacity data as long as reserve supports growth Reconstruction is robust for deviations from correct temperature trajectory Laure Pecquerie 2007: reading the otolith

time, d opacity functional response temp correction Otolith opacity Functional response reserve density body length, cm otolith length, m time, d Laure Pecquerie 2007: reading the otolith

Applications of DEB theory Fundamental knowledge • bioproduction: agronomy, aquaculture, fisheries • pest control • biotechnology, sewage treatment, biodegradation • (eco)toxicology, pharmacology • medicine: cancer biology, obesity, nutrition biology • global change: biogeochemical climate modeling • conservation biology; biodiversity • economy; sustainable development of metabolic organisation has many practical applications

Biology based methods Effects based on internal concentrations One compartment accumulation-elimination Hazard rate or physiological target parameter is linear in internal concentration (small effects only) Dynamic Energy Budget theory is used to identify potential target parameters translate change in parameter to change in endpoint Interaction of compounds in mixture product of internal concentrations similar to analysis of variance

Modes of action of toxicants assimilation food defecation feeding somatic maintenance structure growth costs reproduction costs maint 1 - 7 growth faeces assimilation reserve maintenance costs u tumour 6 hazard to embryo maturity maintenance maturation reproduction maturity offspring 6 tumour induction 7 endocr. disruption 8 lethal effects: hazard rate Mode of action affects translation to pop level

body length, mm indirect effects mg kg-1 0, 0, 64, 139 300 646 1392 3000 body length, mm assimilation maintenance time, d Effects on growth Triphenyltin on Folsomia candida at 20°C direct effects growth time, d

indirect effects cum # offspring/♀ Effects on reproduction assimilation maintenance cost/offspring cum # offspring/♀ mg L-1 0, 320 560 1000 growth hazard 1800 3200 time, d Phenol on Daphnia magna at 20°C direct effects time, d

Population effects can depend on food density 3, 4 -dichloroaniline direct effect on reproduction 6. 4. 7 potassium metavanadate effect on maintenance Population growth of rotifer Brachionus rubens at 20˚C for different algal concentrations

Hazard model Suppose that the elimination rate is large internal conc is fast at equilibrium, hazard rate is constant Conclusion: effect on survival concentration exposure time well known in pharmacology desinfection of buildings, green houses

Effect on survival for single compound Effects of Dieldrin on survival of Poecilia NEC 4. 49 g l-1 killing rate 0. 038 l g-1 d-1 elimination rate 0. 712 d-1

Effect on survival for mixture Model for survival in time for a binary mixture: 8 parameters in total using data for all observation times control mortality rate, interaction parameter 2 (NEC, killing rate, elimination rate) Model tested for 6 binary mixtures of metals (Cu, Cd, Pb & Zn) on Folsomia candida (Collembola) Survival measurements daily for 21 days 6 6 concentrations 22 6 6 = 792 data points for each mixture

Cd & Cu survival of Folsomia Interaction Cu, Cd, Pb, Zn: Cu & Pb: slightly antagonistic Other combinations: nill Folsomia candida Data: Bart van Houte Theory: Bas Kooijman Fit: Jan Baas Movie: Jorn Bruggeman

DEB tele course 2009 Cambridge Univ Press 2000 http: //www. bio. vu. nl/thb/deb/ Free of financial costs; some 250 h effort investment Program for 2009: Feb/Mar general theory April symposium in Brest (2 -3 d) Sept/Oct case studies & applications Target audience: Ph. D students We encourage participation in groups that 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/ Audience: thank you for your attention Organizers: thank you for the invitation