Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par valuesCo-variation of par values 9 Living together 10 Evolution 11 Evaluation

Scales of life 8a Life span 10 log a Volume 10 log m 3 earth whale bacterium water molecule life on earth whale bacterium ATP molecule

Selection for reproduction White Leghorn Red Jungle fowl Indian River broiler

Bergmann

Dwarfing in Platyrrhini 8.1.2a Perelman et al 2011 Plos Genetics 7, 3, e MYA Callitrix Cebuella Mico Leontopithecus Aotus Saimiri Cebus g g g g 3500 g g g 130 g 180 g Callimico Saguinus Cebidae

parameter values tend to co-vary across species parameters are either intensive or extensive ratios of extensive parameters are intensive maximum body length is allocation fraction to growth + maint. (intensive) volume-specific maintenance power (intensive) surface area-specific assimilation power (extensive) conclusion : (so are all extensive parameters) write physiological property as function of parameters (including maximum body weight) evaluate this property as function of max body weight Inter-species body size scaling 8.2 Kooijman 1986 Energy budgets can explain body size scaling relations J. Theor. Biol. 121:

Intra -  Inter-specific scaling 8.2a intrainter feedingL2L2 L3L3 reproductionL 2.5 L -1

Primary parameters standard DEB model Kooijman 1986 J. Theor. Biol. 121:

Inter-species zoom factor 8.2.1a

Feeding strategies are adaptable 8.2.1b basking shark (Cetorhinus maximus) whale shark (Rhincodon typus) white shark, (Carcharodon carcharias) cookiecutter shark (Isistius brasiliensis) filter feeding big prey

Compound vs primary parameters 8.2.1c

Body weight Body weight has contributions from structure and reserve If reserve allocated to reproduction hardly contributes:

West-Brown: scaling of respiration 8.2.2b Explanation: Minimizing of transportation costs in space-filling fractally branching tube systems results in ¾ - “law” West et al 1997 Science 276: Problems: Protostomes have open circulation system, no tube system scaling of respiration also applies to protostomes Flux in capillaries is much less than in big tubes, not equal Transport rate must match peak metabolic requirements rather than standard No differentiation between inter- and intra-specific scaling Transport costs are tiny fraction of maintenance costs minimum argument is not convincing (nor demonstrated) Scaling of respiration does not explain all other scaling “laws” nor “the growth curve” of demand systems

Banavar: scaling of respiration 8.2.2c Explanation: Dilution of biomass with transport material between maintenance-requiring nodes in efficient networks results in ¾ -”law”; Banavar et al 1999 Nature 399: Problems: Transport rate must match peak metabolic requirements rather than standard No differentiation between inter- and intra-specific scaling criterion Assumption about the scaling of mass involved in transport is not tested; tubing material does not dominate in whales Efficiency criterion is anthropomorphic

Scaling of respiration 8.2.2d Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Kooijman 1986 J Theor Biol 121:

Metabolic rate 8.2.2e Log weight, g Log metabolic rate, w endotherms ectotherms unicellulars slope = 1 slope = 2/3 Length, cm O 2 consumption,  l/h Inter-species Intra-species L L L curves fitted: (Daphnia pulex) Data: Hemmingson 1969; curve fitted from DEB theoryData: Richman 1958; curve fitted from DEB theory

Feeding rate 8.2.2f slope = 1 poikilothermic tetrapods Data: Farlow 1976 Inter-species: J Xm  V Intra-species: J Xm  V 2/3 Mytilus edulis Data: Winter 1973 Length, cm Filtration rate, l/h

log zoom factor, z log scaled initial reserve log scaled age at birth log scaled length at birth approximate slope at large zoom factor Scaling relationships 8.2.2g

Length at puberty 8.2.2h  Clupea Brevoortia ° Sprattus  Sardinops Sardina  Sardinella + Engraulis * Centengraulis  Stolephorus Data from Blaxter & Hunter 1982 Clupoid fishes Length at first reproduction L p  ultimate length L 

25 °C T A = 7 kK 10 log ultimate length, mm 10 log von Bert growth rate, a -1 ↑ ↑ 0 Von Bertalanffy growth rate 8.2.2i

Body temperature of Maiasaurs 8.2.2j determine v Bert growth rate & max length convert length to weight (shape) obtain v Bert growth rate for that weight at 25 °C (inter-spec) calculate ratio with observed v Bert growth rate convert ratio to body temperature (inverse Arrhenius) result: 37 °C age, a length, cm

Incubation time 8.2.2k 10 log egg weight, g 10 log incubation time, d l b equal ° tube noses slope = 0.25 Data from Harrison 1975 European birds Incubation time Egg weight tube noses

Gestation time 8.2.2l 10 log adult weight, g 10 log gestation time, d Data from Millar 1981 Mammals * Insectivora + Primates  Edentata  Lagomorpha  Rodentia  Carnivora  Proboscidea Hyracoidea  Perissodactyla  Artiodactyla slope = 0.33 Kooijman 1986 J Theor Biol 121:

Reproduction rate 8.2.2o

Costs for movement 8.2.2m slope = -1/3 Walking costs: 5.39 ml O 2 cm -2 km -1 Swimming costs: 0.65 ml O 2 cm -2 km -1 Movement costs per distance  V 2/3 Investment in movement  V included in somatic maintenance Home range  V 1/3 Data: Fedak & Seeherman, 1979 Data: Beamish, 1978

Ageing among species 8.2.2n Conclusion for life span hardly depends on max body size of ectotherms increases with length in endotherms slope 1/3, 1/5 Right whale Ricklefs & Finch 1995

Abundance feeding rate  V food production constant  Abundance  V -1 Data: Peters, 1983 Kooijman 1986 J Theor Biol 121:

1,1 compartment model Suppose and while Kooijman et al 2004 Chemosphere 57:

Elimination rate & partition coeff log P 01 log 10% saturation time 1 film 2 film diffusivities low high Transition: film  1,1-compartment model Kooijman et al 2004 Chemosphere 57:

QSARs for tox parameters log NEC, mM 10 log elim rate, d log kill rate, mM -1 d log P ow Slope = -1 Slope = 1Slope = -0.5 Hazard model for survival : one compartment kinetics hazard rate linear in internal concentration Alkyl benzenes in Pimephales Data from Geiger et al 1990 Assumption: Each molecule has same effect Kooijman et al 2004 Chemosphere 57:

QSARs for tox parameters 8.3.4a 10 log NEC, mM 10 log elim rate, d log kill rate, mM -1 d log P ow Slope = -1 Slope = 1Slope = -0.5 Benzenes, alifates, phenols in Pimephales Data from Mackay et al 1992, Hawker & Connell 1985 Assumption: Each molecule has same effect Hazard model for survival : one compartment kinetics hazard rate linear in internal concentration Kooijman et al 2004 Chemosphere 57:

Covariation of tox parameters 8.3.4b 10 log NEC, mM 10 log killing rate, mM -1 d -1 Slope = -1 Pimephales Data from Gerritsen 1997 Kooijman et al 2004 Chemosphere 57:

10 log P ow 10 log LC50.14d,  M LC50.14d of chlorinated hydrocarbons for Poecilia. Data: Könemann, 1980 QSARs for LC50’s 8.3.4c

Similarities QSAR  body size scaling compartment model: partition coefficient (= state) is ratio between uptake and elimination rate DEB-model: maximum length (= state) is ratio between assimilation and maintenance rate Parameters are constant for a system, but vary between systems in a way that follows from the model structure

Interactions QSAR  body size scaling 8.4a uptake, elimination fluxes, food uptake  surface area (intra-specifically) elimination rate  length -1 (exposure time should depend on size) food uptake  structural volume (inter-specifically) dilution by growth affects toxicokinetics max growth  length 2 (inter-specifically) elimination via reproduction: max reprod mass flux  length 2 (inter-specifically) chemical composition: reserve capacity  length 4 (inter-specifically) in some taxa reserve are enriched in lipids chemical transformation, excretion is coupled to metabolic rate metabolic rate scales between length 2 and length 3 juvenile period  length, abundance  length -3, pop growth rate  length -1 links with risk assessment strategies

Dynamic Energy Budget theory 1 Basic ConceptsBasic Concepts 2 Standard DEB modelStandard DEB model 3 MetabolismMetabolism 4 Univariate DEB modelsUnivariate DEB models 5 Multivariate DEB modelsMultivariate DEB models 6 Effects of compoundsEffects of compounds 7 Extensions of DEB modelsExtensions of DEB models 8 Co-variation of par valuesCo-variation of par values 9 Living togetherLiving together 10 EvolutionEvolution 11 EvaluationEvaluation