What is DEB theory?

What is DEB theory? Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb Melbourne 2012/08/06

What is DEB theory? Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb • Contents • What is DEB theory? • Stylised facts • Supply/demand systems • How was it invented? • Selection of concepts • DEBs vs SEBs Melbourne 2012/08/06

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. B365: 3413-3428

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 O2 The use of O2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O2 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: CO2, O2 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 Weight1/3, g1/3 Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 time, h time, h Weight1/3, g1/3 Toxostoma recurvirostre Ricklefs 1968 length, mm Pleurobrachia pileus Greve 1971 time, d time, d

DEB – ontogeny - IBM Daphnia von Foerster ecotox application embryos 1980 body size scaling epidemiol applications time dependence morph dynamics indirect calorimetry bifurcation analysis micro’s numerical methods 1990 food chains Global bif-analysis DEB 1 aging Synthesizing Units NECs integral formulations DEBtox multivar plants adaptive dynamics 2000 tumour induction ecosystem dynamics DEB 2 adaptation organ function symbioses ISO/OECD QSARs evolution entropy production ecosystem effects par estimation ecosystem self-orginazation molecular organisation DEB 3 mixtures 2010

system earth space ecosystem population individual cell time molecule Space-time scales Each process has its characteristic domain of 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

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  volume2/3 volumetric length = volume1/3 Mucor Ceratium Merismopedia V0-morph: surface area  volume0 V1-morph: surface area  volume1

Shape correction function actual surface area at volume V isomorphic surface area at volume V Shape correction function at volume V = for • 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 V0-morph V1-morph isomorph Static mixtures between V0- and V1-morphs for aspect ratio

Biofilms solid substrate biomass Isomorph: V1= 0 mixture between iso- & V0-morph V0-morph: V1=  biomass grows, but surface area that is involved in nutrient exchange does not

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

3 4 5 1 2 prokaryotes 7 plants 9 animals 6 8 Evolution of DEB systems variable structure composition strong homeostasis for structure increase of maintenance costs delay of use of internal substrates inernalization of maintenance installation of maturation program strong homeostasis for reserve Kooijman & Troost 2007 Biol Rev, 82, 1-30 reproduction juvenile  embryo + adult specialization of structure

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 apparent assimilated urine gross metabolised spec dynamic action net metabolised maintenance work production somatic maintenance activity growth products thermo regulation 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 http://www.bio.vu.nl/thb/research/bib/Kooy2010_n.pdf

Notation 2 General Indices for compounds Indices for transformations

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 http://www.bio.vu.nl/thb/deb/

What is DEB theory?