1. Introduction to DEB theory Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb Oslo 2012/02/09-10

2. Contents preliminary concepts required to link predictions to data standard DEB model for a 1-food, 1-reserve, 1-structure isomorph implications & extensions covariation of parameter values

3. Energy Budgets Basic processes Feeding Digestion Storing Growth Maturation Maintenance Reproduction Product formation Aging All have ecological implications All interact during the life cycle Life history events zero: start of development birth: start of feeding start of acceleration metamorphosis: end of acceleration puberty: end of maturation start of reproduction Life stages embryo juvenile adult

4. 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

5. Supply-demand spectrum 1.2.5

6. 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

7. These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake : These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake Not age, but size: Trichopsis vittatus

8. 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/ 4 1975Hungate 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

9. 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

10. Reserve vs structure 2.3 Reserve does not mean: “set apart for later use” compounds in reserve can have active functions 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 Important difference between reserve and structure: no maintenance costs for reserve Empirical evidence: freshly laid eggs consist of reserve and do not respire

11. 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

12. Body size length: depends on shape and choice (shape coefficient) volumetric length: cubic root of volume; does not depend on shape contribution of reserve in lengths is usually small use of lengths unavoidable because of role of surfaces and volumes weight: wet, dry, ash-free dry contribution of reserve in weights can be substantial easy to measure, but difficult to interpret C-moles (number of C-atoms as multiple of number of Avogadro) 1 mol glucose = 6 Cmol glucose useful for mass balances, but destructive measurement Problem: with reserve and structure, body size becomes bivariate We have only indirect access to these quantities

13. Flux vs Concentration concept “concentration” implies spatial homogeneity (at least locally) biomass of constant composition for intracellular compounds concept “flux” allows spatial heterogeneity classic enzyme kinetics relate production flux to substrate concentration Synthesizing Unit kinetics relate production flux to substrate flux in homogeneous systems: flux  conc. (diffusion, convection) concept “density” resembles “concentration” but no homogeneous mixing at the molecular level density = ratio between two amounts

14. Macrochemical reaction eq 3.5

15. Synthesizing units Are enzymes that follow classic enzyme kinetics E + S  ES  EP  E + P With two modifications: back flux is negligibly small E + S  ES  EP  E + P specification of transformation is on the basis of arrival fluxes of substrates rather than concentrations The concept concentration is problematic in spatially heterogeneous environments, such as inside cells In spatially homogeneous environments, arrival fluxes are proportional to concentrations

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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, 1-30 543 21 specialization of structure 7 8 animals 6 prokaryotes 9 plants

22. Symbiogenesis 2.7 Ga2.1 Ga 1.27 Ga phagocytosis

23. Arrhenius relationship ln rate 10 4 T -1, K -1 reproduction young/d ingestion 10 6 cells/h growth, d -1 aging, d -1 Daphnia magna

24. Arrhenius relationship 10 3 /T, K -1 ln pop growth rate, h -1 10 3 /T H 10 3 /T L r 1 = 1.94 h -1 T 1 = 310 K T H = 318 K T L = 293 K T A = 4370 K T AL = 20110 K T AH = 69490 K

25. Assumptions of auxiliary theory A well-chosen physical length  (volumetric) structural length for isomorphs Volume, wet/dry weight have contributions from structure, reserve, reproduction buffer Constant specific mass & volume of structure, reserve, reproduction buffer Constant chemical composition of juvenile growing at constant food

26. Compound parameters

27. Concept overview empirical facts supply-demand spectrum reserve & structure 5 types of homeostasis body size: weight, Cmol,.. body composition flux vs concentration macrochemical reactions Synthesizing Units surface area/volume iso-, V0-, V1-morphs shape correction function evolutionary aspects effects of temperature auxiliary theory compound parameters