What is DEB theory? Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Melbourne 2012/08/06

What is DEB theory? Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Melbourne 2012/08/06 Contents What is DEB theory? Stylised facts Supply/demand systems How was it invented? Selection of concepts DEBs vs SEBs

Empirical cycle 1.1

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: stylised facts 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-specifically, but decreases with size inter-specifically Respiration Animal eggs and plant seeds initially hardly use O 2 The use of O 2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O 2 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: CO 2, O 2 and N-waste

Supply-demand spectrum 1.2.5

Historical roots Aug 1979 Two questions: How should we quantify effects of chemical compounds on reproduction of daphnids? reproduction  energy budget How bad is it for the environment if daphnid reproduction is a bit reduced due to toxic stress? individual  population  ecosystem prediction outside observed range: first principles

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

DEB – ontogeny - IBM Daphnia ISO/OECD von Foerster molecular organisation DEB 1 DEB 2 DEBtox NECs embryos body size scaling morph dynamics indirect calorimetry food chains Synthesizing Units multivar plants adaptation tumour induction epidemiol applications bifurcation analysis Global bif-analysis integral formulations adaptive dynamics ecosystem self-orginazation numerical methods symbioses ecosystem dynamics organ function aging micro’s DEB ecotox application mixtures QSARs evolution ecosystem effects time dependence par estimation entropy production

molecule cell individual population ecosystem system earth time space Space-time scales When changing the space-time scale, new processes will become important other will become less important This can be used to simplify models, by coupling space-time scales Complex models are required for small time and big space scales and vv Models with many variables & parameters hardly contribute to insight Each process has its characteristic domain of space-time scales

Homeostasis strong constant composition of pools (reserves/structures) generalized compounds, stoichiometric constraints on synthesis weak constant composition of biomass during growth in constant environments determines reserve dynamics (in combination with strong homeostasis) structural constant relative proportions during growth in constant environments isomorphy.work load allocation thermal ectothermy  homeothermy  endothermy acquisition supply  demand systems; development of sensors, behavioural adaptations

Biomass: reserve(s) + structure(s) Reserve(s), structure(s): generalized compounds, mixtures of proteins, lipids, carbohydrates: fixed composition Reasons to delineate reserve, distinct from structure metabolic memory biomass composition depends on growth rate explanation of respiration patterns (freshly laid eggs don’t respire) method of indirect calorimetry fluxes are linear sums of assimilation, dissipation and growth fate of metabolites (e.g. conversion into energy vs buiding blocks) inter-species body size scaling relationships

Reserve vs structure 2.3 Differences between reserve & structure Life span of compounds in reserve: limited due to turnover of reserve all reserve compounds have the same mean life span structure: controlled by somatic maintenance structure compounds can differ in mean life span no maintenance costs for reserve freshly laid eggs consist of reserve and do not respire Reserve does not mean: “set apart for later use’: compounds in reserve can have active functions lipids: the rest would be structure and lipids cannot convert to protein `material that does not require maintenance’: can also apply to compounds in structure `material that is synthesize from assimilates’: indirectly applies to all compounds

Reserve residence time 2.3.1b

Surface area/volume interactions biosphere: thin skin wrapping the earth light from outside, nutrient exchange from inside is across surfaces production (nutrient concentration)  volume of environment food availability for cows: amount of grass per surface area environment food availability for daphnids: amount of algae per volume environment feeding rate  surface area; maintenance rate  volume (Wallace, 1865) many enzymes are only active if linked to membranes (surfaces) substrate and product concentrations linked to volumes change in their concentrations gives local info about cell size ratio of volume and surface area gives a length

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

Shape correction function at volume V actual surface area at volume V isomorphic surface area at volume V = for V0-morph V1-morph isomorph Static mixtures between V0- and V1-morphs for aspect ratio V1-morphs are special because surfaces do not play an explicit role their population dynamics reduce to an unstructured dynamics; reserve densities of all individuals converge to the same value in homogeneous environments

Biofilms Isomorph: V 1 = 0 V0-morph: V 1 =  mixture between iso- & V0-morph biomass grows, but surface area that is involved in nutrient exchange does not solid substrate biomass

Mixtures of changes in shape 2 Dynamic mixtures between morphs Lichen Rhizocarpon V1- V0-morph V1- iso- V0-morph outer annulus behaves as a V1-morph, inner part as a V0-morph. Result: diameter increases  time

Evolution of DEB systems variable structure composition strong homeostasis for structure delay of use of internal substrates increase of maintenance costs inernalization of maintenance installation of maturation program strong homeostasis for reserve reproduction juvenile  embryo + adult Kooijman & Troost 2007 Biol Rev, 82, specialization of structure 7 8 animals 6 prokaryotes 9 plants

Static Energy Budgets (SEBs) Differences with DEBs overheads interpretation of respiration interpretation of urination metabolic memory life cycle perspective change in states gross ingested faeces urine apparent assimilated gross metabolised net metabolised spec dynamic action workmaintenance somatic maintenance activity thermo regulation production growth products reproduction

Concept overview empirical facts supply-demand spectrum 5 types of homeostasis reserve & structure residence time surface area/volume iso-, V0-, V1-morphs shape correction function evolutionary perspective

Notation 1

Indices for compounds Indices for transformations General Notation 2

Notation 3 Some symbols have more than one meaning: V as symbol stands for volume, and without index for volume of structure, as index stands for the compound structure E as symbol stands for energy, and without index for energy in reserve, as index stands for the compound reserve C,H,O,N as indices stand for mineral compounds as well as chemical elements the context defines the meaning Dots are used to distinguish rates from states (dimension check) allow scaling of time without the need to introduce new symbols if time is scaled to a dimensionless quantity, the dot is removes

DEB resources DEB book 2010 (DEB3, 500 p) + erratum-list summary of concepts for each of the sections of DEB3 notation document, including notation for new developments comments to DEB3 (250 p) DEBtool: software package for Matlab and Octave (> 1000 functions) add my pet document on par estimation for the standard DEB model add_my_pet library of data and par values, implied properties (130 spec) micro-lectures, a collection of ppt’s for DEB3 phylogenetic survey of living organisms, frequently updated ppt’s exercises that follow DEB3 quizzes, to monitor progress in mastering DEB concepts assays, written by participants of DEB tele-courses questions and answers on DEB theory from previous DEB tele-courses bibliography of DEB papers (via the DEB information page) Basic Methods for Theoretical Biology on methodology, modelling & math