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DEB theory, an introduction Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam [email protected] http://www.bio.vu.nl/thb/ Wimereux, 2011/05/11 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 2010 Phil. Trans. R. Soc. Lond. B 365: 3413-3428 Empirical patterns 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 Respiration Animal eggs and plant seeds initially hardly use dioxygen The use of dioxygen increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of dioxygen 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) 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 The chemical composition of organisms depends on Bertalanffy growth rate increases linearly with ultimate length the nutritional status (starved vs well-fed) The von Bertalanffy growth rate of different species The chemical composition of organisms growing decreases almost linearly with the maximum at constant food density becomes constant body length Fetuses increase in weight approximately proportional to cubed time Dissipating heat is a weighted sum of 3 mass flows: carbon dioxide, dioxygen and nitrogenous waste Stoichiometry Energy Reproduction Reproduction increases with size intra-specically, but decreases with size inter-specifically From Sousa et al 2008 Phil. Trans. R. Soc. Lond. B 363: 2453-2463 Empirical special cases of DEB 11.1 year author model year author model 1780 Lavoisier multiple regression of heat against mineral fluxes 1950 Emerson cube root growth of bacterial colonies 1825 Gompertz 1891 Survival probability for aging DEB theory is axiomatic, 1951 Huggett & Widdas temperature dependence of Arrhenius 1951 Weibull based on mechanisms physiological rates allometric growth of body parts Huxleynot meant 1955 Best to glue empirical models 1902 Henri 1905 Blackman 1889 1910 1920 Michaelis--Menten kinetics 1957 Smith foetal growth survival probability for aging diffusion limitation of uptake embryonic respiration bilinear functional response 1959 Leudeking & Piret microbial product formation Since many empirical models Cooperative binding hyperbolic functional response Hill 1959 Holling turn out to be special cases of DEB theory von Bertalanffy growth of maintenance in yields of biomass Pütter 1962 Marr & Pirt individuals the data behind these models support DEB theory 1927 Pearl logistic population growth 1973 Droop reserve (cell quota) dynamics 1928 Fisher & Tippitt Weibull aging 1974 Rahn & Ar water loss in bird eggs 1932 Kleiber respiration scales with body weight3/ 4 1975 Hungate digestion 1932 Mayneord cube root growth of tumours 1977 Beer & Anderson development of salmonid embryos This makes DEB theory very well tested against data Homeostasis 1.2 strong homeostasis constant composition of pools (reserves/structures) generalized compounds, stoichiometric contraints on synthesis weak homeostasis constant composition of biomass during growth in constant environments determines reserve dynamics (in combination with strong homeostasis) structural homeostasis constant relative proportions during growth in constant environments isomorphy .work load allocation thermal homeostasis ectothermy homeothermy endothermy acquisition homeostasis supply demand systems development of sensors, behavioural adaptations Simultaneous Substrate Processing 3.7c production production Chemical reaction: 1A + 1B 1C Poisson arrival events for molecules A and B blocked time intervals • acceptation event ¤ rejection event Kooijman, 1998 Biophys Chem 73: 179-188 Interactions of substrates 3.7.3b Kooijman, 2001 Phil Trans R Soc B 356: 331-349 Standard DEB model 2a Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) Processes: feeding digestion maintenance storage product formation maturation Balances: mass, energy , entropy, time 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 growth reproduction aging Standard DEB scheme 2b 1 food type, 1 reserve, 1 structure, isomorph food feeding defecation faeces assimilation reserve somatic maintenance growth structure 1- maturity maintenance maturation reproduction maturity offspring 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 Reserve residence time 2.3.1b Crocodylus johnstoni, Data from Whitehead 1987 weight, g embryo yolk O2 consumption, ml/h Embryonic development 2.6.2d time, d time, d Scaling of respiration 8.2.2d Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Kooijman 1986 J Theor Biol 121: 269-282 Metabolic rate 8.2.2e slope = 1 0.0226 L2 + 0.0185 L3 0.0516 L2.44 Log metabolic rate, w O2 consumption, l/h 2 curves fitted: endotherms ectotherms slope = 2/3 unicellulars Length, cm Intra-species (Daphnia pulex) Data: Richman 1958; curve fitted from DEB theory Log weight, g Inter-species Data: Hemmingson 1969; curve fitted from DEB theory Change in body shape 4.2.2 Isomorph: surface area volume2/3 volumetric length = volume1/3 Mucor Ceratium V0-morph: surface area volume0 Merismopedia V1-morph: surface area volume1 Weight1/3, g1/3 diameter, m Isomorphic growth 2.6c Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 time, h Weight1/3, g1/3 length, mm time, h Toxostoma recurvirostre Ricklefs 1968 Pleurobrachia pileus Greve 1971 time, d time, d volume, m3 4.2.3a Bacillus = 0.2 Collins & Richmond 1962 time, min Fusarium = 0 Trinci 1990 time, h volume, m3 volume, m3 hyphal length, mm Mixtures of V0 & V1 morphs Escherichia = 0.28 Kubitschek 1990 time, min Streptococcus = 0.6 Mitchison 1961 time, min Mixtures of changes in shape 4.2.4a Lichen Rhizocarpon V1- iso- V0-morph Dynamic mixtures of V0- & V1-morphs Respiration: assim + maint + growth Assim, maint mass Growth in diam time at constant food V0-morph V1-morph Dynamic mixtures of V0- & V1-morphs Celleporella 15 cm/yr 33 33 16 16 5 5 2 2 0.5 cm/yr 0.5 cm/yr White at al 2011 Am. Nat., to appear Dynamic mixtures of V0- & V1-morphs Celleporella 33, 24 cm/yr 33 16 5 2 0.5 cm/yr White at al 2011 Am. Nat., to appear Stage transitions at maturity thresholds Danio rerio 28.5°C Augustine et al 2011 Comp. Biochem. Physiol. A 159 :275–283 Stage transitions at maturity thresholds < birth : isomorph birth-metamorphosis: V1-morph > metamorphosis : isomorph Danio rerio 28.5°C Data: Lauwrence et al 2008 caloric restiction Data: Augustine Augustine et al 2011 Comp. Biochem. Physiol. A 159 :275–283 add_my_pet Collection of data, DEB-parameters, properties: Species.xls http://www.bio.vu.nl/thb/deb/deblab/ 3 files per species, about 60 species at 2011/05/10 mydata_my_pet real & pseudo-data, par-estimation, prediction-presentation, FIT predict_my_pet computes predictions given parameters pars_my_pet presents >100 implied properties Uses DEBtool (Matlab, Octave): add_my_pet.pdf (> 1000 functions & scripts) DEB tele course 2013 http://www.bio.vu.nl/thb/deb/ Free of financial costs; some 200 h effort investment Program for 2013: Feb 1 wk pre-course in tele-mode Feb/Mar 5 wk general theory in tele-mode April 15-23 course at NIOZ (Texel, NL) April 24-26 symposium at NIOZ (Texel, NL) 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 Seb Lefebvre: thank you for the invitation