DEB theory, an introduction Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam 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:

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 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 Bertalanffy growth rate increases linearly with ultimate length The von Bertalanffy growth rate of different species decreases almost linearly with the maximum body length Fetuses increase in weight approximately proportional to cubed time Reproduction Reproduction increases with size intra-specically, but decreases with size inter-specifically 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) Stoichiometry The chemical composition of organisms depends on the nutritional status (starved vs well-fed) The chemical composition of organisms growing at constant food density becomes constant Energy Dissipating heat is a weighted sum of 3 mass flows: carbon dioxide, dioxygen and nitrogenous waste From Sousa et al 2008 Phil. Trans. R. Soc. Lond. B 363:

Empirical special cases of DEB 11.1 yearauthormodelyearauthormodel 1780Lavoisier multiple regression of heat against mineral fluxes 1950Emerson cube root growth of bacterial colonies 1825Gompertz Survival probability for aging 1951Huggett & Widdas foetal growth 1889Arrhenius temperature dependence of physiological rates 1951Weibull survival probability for aging 1891Huxley allometric growth of body parts 1955Best diffusion limitation of uptake 1902Henri Michaelis--Menten kinetics 1957Smith embryonic respiration 1905Blackman bilinear functional response 1959Leudeking & Piret microbial product formation 1910Hill Cooperative binding 1959Holling hyperbolic functional response 1920Pütter von Bertalanffy growth of individuals 1962Marr & Pirt maintenance in yields of biomass 1927Pearl logistic population growth 1973Droop reserve (cell quota) dynamics 1928Fisher & Tippitt Weibull aging 1974Rahn & Ar water loss in bird eggs 1932Kleiber respiration scales with body weight 3/ Hungate digestion 1932Mayneord cube root growth of tumours 1977Beer & Anderson development of salmonid embryos DEB theory is axiomatic, based on mechanisms not meant to glue empirical models Since many empirical models turn out to be special cases of DEB theory the data behind these models support DEB theory 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 Chemical reaction: 1A + 1B 1C Poisson arrival events for molecules A and B blocked time intervals acceptation event ¤ rejection event production Kooijman, 1998 Biophys Chem 73:

Interactions of substrates 3.7.3b Kooijman, 2001 Phil Trans R Soc B 356:

Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) Processes: Balances: mass, energy, entropy, time Standard DEB model 2a 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 feeding digestion maintenance storage product formation maturation growth reproduction aging

1-  maturity maintenance maturity offspring maturation reproduction Standard DEB scheme 2b 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

Reserve residence time 2.3.1b

Embryonic development 2.6.2d time, d weight, g O 2 consumption, ml/h Crocodylus johnstoni, Data from Whitehead 1987 yolk embryo

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

Change in body shape Isomorph: surface area  volume 2/3 volumetric length = volume 1/3 V0-morph: surface area  volume 0 V1-morph: surface area  volume 1 Ceratium Mucor Merismopedia

Isomorphic growth 2.6c diameter,  m Weight 1/3, g 1/3 length, mm time, h time, d Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 Pleurobrachia pileus Greve 1971 Toxostoma recurvirostre Ricklefs 1968 Weight 1/3, g 1/3

Mixtures of V0 & V1 morphs 4.2.3a volume,  m 3 hyphal length, mm time, h time, min Fusarium  = 0 Trinci 1990 Bacillus  = 0.2 Collins & Richmond 1962 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961

Mixtures of changes in shape 4.2.4a Lichen Rhizocarpon V1- iso- V0-morph

Dynamic mixtures of V0- & V1-morphs V1-morph V0-morph Respiration: assim + maint + growth Assim, maint  mass Growth in diam  time at constant food

White at al 2011 Am. Nat., to appear Dynamic mixtures of V0- & V1-morphs 0.5 cm/yr cm/yr cm/yr cm/yr cm/yr cm/yr Celleporella

Dynamic mixtures of V0- & V1-morphs White at al 2011 Am. Nat., to appear Celleporella 0.5 cm/yr , 24 cm/yr

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 Augustine et al 2011 Comp. Biochem. Physiol. A 159 :275–283 Danio rerio 28.5°C Data: Lauwrence et al 2008 caloric restiction Data: Augustine < birth : isomorph birth-metamorphosis: V1-morph > metamorphosis : isomorph

add_my_pet Collection of data, DEB-parameters, properties: Species.xls 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 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 course at NIOZ (Texel, NL) April 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 Cambridge Univ Press 2009 Audience : thank you for your attention Seb Lefebvre : thank you for the invitation