Introduction to DEB theory & applications in fishery sciences Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb/ Trondheim, 2007/11/01

Introduction to DEB theory & applications in fishery sciences Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb/ Contents: What is DEB theory? Evolution & homeostasis Standard model & calorimetry Product formation Allocation Unexpected links Social behaviour Reconstruction Body size scaling Trondheim, 2007/11/01

Dynamic Energy Budget theory for metabolic organization consists of a set of consistent and coherent assumptions uses framework of general systems theory links levels of organization scales in space and time: scale separation quantitative; first principles only equivalent of theoretical physics interplay between biology, mathematics, physics, chemistry, earth system sciences fundamental to biology; many practical applications

Research strategy 1) use general physical-chemical principles to develop an educated quantitative expectation for the eco-physiological behaviour of a generalized species 2) estimate parameters for any specific case compare the values with expectations from scaling relationships deviations reveal specific evolutionary adaptations 3) study deviations from model expectations learn about the physical-chemical details that matter in this case but had to be ignored because they not always apply Deviations from a detailed generalized expectation provide access to species-specific (or case-specific) modifications

Empirical special cases of DEB 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 DEB theory reveals when to expect deviations from these empirical models year author model 1780 Lavoisier multiple regression of heat against mineral fluxes 1950 Emerson cube root growth of bacterial colonies 1825 Gompertz Survival probability for aging 1951 Huggett & Widdas foetal growth 1889 Arrhenius temperature dependence of physiological rates Weibull survival probability for aging 1891 Huxley allometric growth of body parts 1955 Best diffusion limitation of uptake 1902 Henri Michaelis--Menten kinetics 1957 Smith embryonic respiration 1905 Blackman bilinear functional response 1959 Leudeking & Piret microbial product formation 1910 Hill Cooperative binding Holling hyperbolic functional response 1920 Pütter von Bertalanffy growth of individuals 1962 Marr & Pirt maintenance in yields of biomass 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 Mayneord cube root growth of tumours 1977 Beer & Anderson development of salmonid embryos

Individual  Ecosystem population dynamics is derived from properties of individuals + interactions between them evolution according to Darwin: variation between individuals + selection material and energy balances: most easy for individuals individuals are the survival machines of life

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 1 2 3 4 5 6 prokaryotes 7 9 plants 8 animals Kooijman & Troost 2007 Biol Rev, 82, 1-30 reproduction juvenile  embryo + adult strong homeostasis for reserve specialization of structure

Homeostasis 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 ectothermy  homeothermy  endothermy supply  demand systems development of sensors, behavioural adaptations

Standard DEB model food faeces reserve structure  offspring Definition of standard model: Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) food faeces assimilation reserve feeding defecation Extensions of standard model: more types of food and food qualities reserve (autotrophs) structure (organs, plants) changes in morphology different number of life stages structure somatic maintenance growth  1- maturity maintenance offspring maturation reproduction

Three basic fluxes assimilation: substrate  reserve + products linked to surface area dissipation: reserve  products somatic maintenance: linked to surface area & structural volume maturity maintenance: linked to maturity maturation or reproduction overheads growth: reserve  structure + products Product formation = A  assimilation + B  dissipation + C  growth Examples: heat, CO2, H2O, O2, NH3 Indirect calorimetry: heat = D  O2-flux + E  CO2-flux + F  NH3-flux

Product Formation ethanol pyruvate glycerol According to Dynamic Energy Budget theory: Product formation rate = wA . Assimilation rate + wM . Maintenance rate + wG . Growth rate For pyruvate: wG<0 ethanol pyruvate, mg/l glycerol, ethanol, g/l pyruvate glycerol throughput rate, h-1 Glucose-limited growth of Saccharomyces Data from Schatzmann, 1975

Static Mixtures of V0 & V1 morphs volume, m3 hyphal length, mm Bacillus  = 0.2 Collins & Richmond 1962 Fusarium  = 0 Trinci 1990 time, h time, min volume, m3 volume, m3 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961 time, min time, min

-rule for allocation Ingestion  Respiration  Reproduction  Growth: Ingestion rate, 105 cells/h O2 consumption, g/h Length, mm Length, mm Reproduction  Length, mm Cum # of young large part of adult budget to reproduction in daphnids puberty at 2.5 mm No change in ingest., resp., or growth Where do resources for reprod. come from? Or: What is fate of resources in juveniles? Growth: Von Bertalanffy Age, d Age, d

Size of body parts Static generalization of -rule whole body heart weight, g time, d time, d Data: Gille & Salomon 1994 on mallard

Tumour growth Dynamic generalization of -rule food faeces reserve  Allocation to tumour  relative maint workload defecation feeding food faeces assimilation Isomorphy: [pMU] = [pM] Tumour tissue: low spec growth & maint costs Growth curve of tumour depends on pars no maximum size is assumed a priori Model explains dramatic tumour-mediated weight loss If tumour induction occurs late, tumours grow slower Caloric restriction reduces tumour growth but the effect fades reserve somatic maintenance maturity maintenance  1- maint maturation reproduction u 1-u growth maturity offspring structure tumour Van Leeuwen et al., 2003 British J Cancer 89, 2254-2268

Katja Philipart (NIOZ) Organ growth fraction of catabolic flux Allocation to velum vs gut  relative workload Macoma low food Macoma high food Relative organ size is weakly homeostatic Collaboration: Katja Philipart (NIOZ)

Organ size & function Kidney removes N-waste from body At constant food availability JN = aL2 + bL3 Strict isomorphy: kidney size  L3 If kidney function  kidney size: work load reduces with size If kidney function  L2 + cL3 for length L of kidney or body work load can be constant for appropriate weight coefficients This translates into a morphological design constraint for kidneys

Initial amount of reserve Initial amount of reserve E0 follows from initial structural volume is negligibly small initial maturity is negligibly small maturity at birth is given reserve density at birth equals that of mother at egg formation Accounts for maturity maintenance costs somatic maintenance costs cost for structure allocation fraction  to somatic maintenance + growth Mean reproduction rate (number of offspring per time): R = (1-R) JER/E0 Reproduction buffer: buffer handling rules; clutch size

Embryonic development Crocodylus johnstoni, Data from Whitehead 1987 embryo yolk O2 consumption, ml/h weight, g time, d time, d ; : scaled time l : scaled length e: scaled reserve density g: energy investment ratio

DEB theory reveals unexpected links Streptococcus O2 consumption, μl/h Daphnia 1/yield, mmol glucose/ mg cells 1/spec growth rate, 1/h Length, mm respiration  length in individual animals & yield  growth in pop of prokaryotes have a lot in common, as revealed by DEB theory Reserve plays an important role in both relationships, but you need DEB theory to see why and how

Not age, but size: : 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 Trichopsis vittatus

Rules for feeding R1 a new food particle appears at a random site within the cube at the moment one of the resident particles disappears. The particle stays on this site till it disappears; the particle density X remains constant. R2 a food particle disappears at a constant probability rate, or because it is eaten by the individual(s). R3 the individual of length L travels in a straight line to the nearest visible food particle at speed  X2/3 L2, eats the particle upon arrival and waits at this site for a time th = {JXm}-1 L-2. Direction changes if the aimed food particle disappears or a nearer new one appears. Speed changes because of changes in length. R4 If an individual of length L feeds: scaled reserve density jumps: e  e + (LX/ L)3 Change of scaled reserve density e: d/dt e = - e {JXm} LX3/ L; Change of length L: 3 d/dt L = ({JXm} LX3 e - L kM g) (e + g)-1 At time t = 0: length L = Lb,; reserve density e = f. R5 a food particle becomes invisible for an individual of length L1, if an individual of length L1 is within a distance Ls (L2/ L1)2 from the food particle, irrespective of being aimed at.

Social interaction  Feeding 2.1.2 determin expectation length reserve density 1 ind time time 2 ind length reserve density time time

Otolith growth & opacity standard DEB model: otolith is a product otolith growth has contributions from growth & dissipation (= maintenance + maturation + reprod overheads) opacity  relative contribution from growth DEB theory allows reconstruction of functional response from opacity data as long as reserve supports growth Reconstruction is robust for deviations from correct temperature trajectory Laure Pecquerie 2007: reading the otolith

Otolith opacity  Functional response temp correction functional response time, d opacity time, d otolith length, m body length, cm reserve density otolith length, m time, d time, d time, d Laure Pecquerie 2007: reading the otolith

Primary scaling relationships assimilation {JEAm} max surface-specific assim rate  Lm feeding {b} surface- specific searching rate digestion yEX yield of reserve on food growth yVE yield of structure on reserve mobilization v energy conductance heating,osmosis {JET} surface-specific somatic maint. costs turnover,activity [JEM] volume-specific somatic maint. costs regulation,defence kJ maturity maintenance rate coefficient allocation  partitioning fraction egg formation R reproduction efficiency life cycle [MHb] volume-specific maturity at birth life cycle [MHp] volume-specific maturity at puberty aging ha aging acceleration Kooijman 1986 J. Theor. Biol. 121: 269-282 maximum length Lm =  {JEAm} / [JEM]

Scaling of metabolic rate 8.2.2 Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Structure ; = length; endotherms intra-species inter-species maintenance growth

Metabolic rate 2 curves fitted: Intra-species Inter-species slope = 1 Log metabolic rate, w O2 consumption, l/h 2 curves fitted: endotherms 0.0226 L2 + 0.0185 L3 0.0516 L2.44 ectotherms slope = 2/3 unicellulars Log weight, g Length, cm Intra-species Inter-species (Daphnia pulex)

Von Bertalanffy growth rate 8.2.2 25 °C TA = 7 kK 10log von Bert growth rate, a-1 10log ultimate length, mm 10log ultimate length, mm At 25 °C : maint rate coeff kM = 400 a-1 energy conductance v = 0.3 m a-1 ↑ ↑

DEB tele course 2009 Audience: Organizers: http://www.bio.vu.nl/thb/deb/ Free of financial costs; some 250 h effort investment Program for 2009: Feb/Mar general theory April symposium in Brest (2-3 d) Sept/Oct case studies & applications Target audience: PhD students We encourage participation in groups that 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 2000 Audience: thank you for your attention Organizers: thank you for the invitation Vacancy PhD-position on DEB theory http://www.bio.vu.nl/thb/