Introduction to DEB theory applications in fishery sciences

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 Contents: • What is DEB theory? • Evolution & homeostasis • Standard model & calorimetry • Product formation • Allocation • Unexpected links • Social behaviour • Reconstruction • Body size scaling Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio. vu. nl http: //www. bio. vu. nl/thb/ 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 year author model 1780 Lavoisier multiple regression of heat against mineral fluxes 1950 Emerson cube root growth of bacterial colonies 1825 Gompertz 1889 DEB theory is axiomatic, 1951 Huggett & Widdas Survival probability for aging based on mechanisms temperature dependence of Arrhenius 1951 Weibull physiological rates not meant to glue empirical models foetal growth survival probability for aging Huxley allometric growth of body parts 1955 Best diffusion limitation of uptake 1902 Henri Michaelis--Menten kinetics 1957 Smith embryonic respiration 1905 Blackman 1973 Droop reserve (cell quota) dynamics 1891 1920 Since many empirical models bilinear functional response microbial product formation 1959 Leudeking & Piret to binding be special cases of DEB theory Cooperative hyperbolic functional response Hill turn out 1959 Holling von Bertalanffy growth ofthese 1962 maintenance in yields of biomass behind models support DEB theory Pütter the data Marr & Pirt 1927 Pearl 1928 Fisher & Tippitt 1932 Kleiber 1910 1932 individuals logistic population growth This makes DEB theory very tested against data Weibull aging water loss in bird eggs 1974 well Rahn & Ar respiration scales with body digestion 1975 Hungate DEB theory reveals when to expect deviations weight root growth of tumours development of salmonid embryos Mayneord 1977 Beer & Anderson from cube these empirical models 3/ 4

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 1 strong homeostasis for structure 2 delay of use of internal substrates 3 increase of maintenance costs 4 inernalization of maintenance 5 7 Kooijman & Troost 2007 Biol Rev, 82, 1 -30 reproduction juvenile embryo + adult animals 8 strong homeostasis for reserve installation of maturation program prokaryotes variable structure composition 6 plants 9 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 feeding defecation faeces assimilation somatic maintenance growth structure reserve 1 - maturity maintenance maturation reproduction maturity offspring Definition of standard model: Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) Extensions of standard model: • more types of food and food qualities reserve (autotrophs) structure (organs, plants) • changes in morphology • different number of life stages

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, CO 2, H 2 O, O 2, NH 3 Indirect calorimetry: heat = D O 2 -flux + E CO 2 -flux + F NH 3 -flux

Product Formation According to Dynamic Energy Budget theory: For pyruvate: w. G<0 glycerol throughput rate, h-1 Glucose-limited growth of Saccharomyces Data from Schatzmann, 1975 pyruvate, mg/l te va ru py glycerol, ethanol, g/l Product formation rate = w. A. Assimilation rate + w. M. Maintenance rate + w. G. Growth rate ethanol

volume, m 3 Bacillus = 0. 2 Collins & Richmond 1962 time, min Fusarium = 0 Trinci 1990 time, h volume, m 3 hyphal length, mm Static Mixtures of V 0 & V 1 morphs Escherichia = 0. 28 Kubitschek 1990 time, min Streptococcus = 0. 6 Mitchison 1961 time, min

-rule for allocation Ingestion rate, 105 cells/h O 2 consumption, g/h Respiration Length, mm • 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 Age, d in juveniles? Length, mm Cum # of young Reproduction Ingestion Growth: Von Bertalanffy Age, d

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

Tumour growth Dynamic generalization of -rule food defecation feeding Allocation to tumour relative maint workload faeces assimilation somatic maintenance growth structure reserve maint 1 - u 1 - u tumour maturity maintenance maturation reproduction maturity offspring Isomorphy: [p. MU] = [p. M] 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 Van Leeuwen et al. , 2003 British J Cancer 89, 2254 -2268

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

Organ size & function Kidney removes N-waste from body At constant food availability JN = a. L 2 + b. L 3 Strict isomorphy: kidney size L 3 If kidney function kidney size: work load reduces with size If kidney function L 2 + c. L 3 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 E 0 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/E 0 Reproduction buffer: buffer handling rules; clutch size

Embryonic development weight, g embryo yolk time, d ; O 2 consumption, ml/h Crocodylus johnstoni, Data from Whitehead 1987 time, d : scaled time l : scaled length e: scaled reserve density g: energy investment ratio

Daphnia Length, mm 1/yield, mmol glucose/ mg cells O 2 consumption, μl/h DEB theory reveals unexpected links Streptococcus 1/spec growth rate, 1/h 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 R 1 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. R 2 a food particle disappears at a constant probability rate, or because it is eaten by the individual(s). R 3 the individual of length L travels in a straight line to the nearest visible food particle at speed X 2/3 L 2, 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. R 4 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} LX 3/ L; Change of length L: 3 d/dt L = ({JXm} LX 3 e - L k. M g) (e + g)-1 At time t = 0: length L = Lb, ; reserve density e = f. R 5 a food particle becomes invisible for an individual of length L 1, if an individual of length L 1 is within a distance Ls (L 2/ L 1)2 from the food particle, irrespective of being aimed at.

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

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

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

Scaling of metabolic rate 8. 2. 2 Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Structure ; = length; endotherms intra-species maintenance growth inter-species

Metabolic rate 2 curves fitted: 0. 0226 L 2 + 0. 0185 L 3 0. 0516 L 2. 44 Log metabolic rate, w O 2 consumption, l/h slope = 1 endotherms ectotherms slope = 2/3 unicellulars Length, cm Intra-species (Daphnia pulex) Log weight, g Inter-species

von Bert growth rate, a-1 Von Bertalanffy growth rate 8. 2. 2 10 log 25 °C TA = 7 k. K 10 log ultimate length, mm At 25 °C : maint rate coeff k. M = 400 a-1 energy conductance v = 0. 3 m a-1 10 log ultimate length, mm ↑ ↑ 0

DEB tele course 2009 http: //www. bio. vu. nl/thb/deb/ Cambridge Univ Press 2000 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: Ph. D 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/ Vacancy Ph. D-position on DEB theory http: //www. bio. vu. nl/thb/ Audience: thank you for your attention Organizers: thank you for the invitation