1. Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thbhttp://www.bio.vu.nl/thb/ Life history events in DEB theory for metabolic organisation Oslo, 2008/03/13

2. Contents : What is DEB theory? Homeostasis Standard model & calorimetry Allocation Embryonic development Unexpected links Body size scaling relationships Parameter estimation Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thbhttp://www.bio.vu.nl/thb/ Oslo, 2008/03/13 Life history events in DEB theory for metabolic organisation

3. Dynamic Energy Budget theory 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 for metabolic organization

4. Empirical special cases of DEB 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 DEB theory reveals when to expect deviations from these empirical models

5. 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

6. 1-  maturity maintenance maturity offspring maturation reproduction Standard DEB model foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth  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

7. 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

8. Mixtures of V0 & V1 morphs 3.7.2 volume,  m 3 hyphal length, mm time, h time, min Fusarium  = 0 Trinci 1990 Bacillus  = 0.2 Collins & Richmond 1962 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961

9.  -rule for allocation 3.5 Age, d Length, mm Cum # of young Length, mm Ingestion rate, 10 5 cells/h O 2 consumption,  g/h 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? Respiration  Ingestion  Reproduction  Growth: Von Bertalanffy

10. Initial amount of reserve 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 ) J ER /E 0 Reproduction buffer: buffer handling rules; clutch size

11. Embryonic development 3.7.1 time, d weight, g O 2 consumption, ml/h ;  : scaled time l : scaled length e: scaled reserve density g: energy investment ratio Crocodylus johnstoni, Data from Whitehead 1987 yolk embryo

12. Respiration ontogeny in birds 3.7.1 age, d ml CO 2 d -1 ml O 2 d -1 altricial Troglodytes aëdon precocial Gallus domesticus Observations: just prior to hatching respiration shows a plateau in precocial, not in altricial birds pore size and frequency in egg shell is such that O 2 flux has constant resistance Conclusion : ontogeny is constrained by diffusion limitation in precocial birds (Rahn et al 1990) DEB theory : reserve dynamics controls ontogeny (same pattern in species without shells) Minimization of water loss causes observed constant flux resistance

13. Foetal development 3.7.1 weight, g time, d Mus musculus Foetes develop like eggs, but rate not restricted by reserve (because supply during development) Reserve of embryo “added” at birth Initiation of development can be delayed by implantation egg cell Nutritional condition of mother only affects foetus in extreme situations Data: MacDowell et al 1927

14. Pupal development time, d pupal weight, mg green-veined white butterfly, Pieris napi Data from Forsberg & Wiklund 1988 17 °C pupa = embryo in DEB theory no uptake of resources start of development with very small amount of structure initiation & termination linked to maturity

15. Metamorphosis The larval malphigian tubes are clearly visible in this emerging cicada They resemble a fractally-branching space-filling tubing system, according to Jim Brown, but judge yourself …. Java, Nov 2007

16. Reduction of initial reserve 3.7.1 1 0.8 0.5 scaled age scaled maturity scaled struct volume scaled reserve

17. DEB theory reveals unexpected links Length, mm O 2 consumption, μl/h 1/yield, mmol glucose/ mg cells 1/spec growth rate, 1/h Daphnia Streptococcus 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

18. Primary scaling relationships assimilation {J EAm } max surface-specific assim rate  L m feeding {b} surface- specific searching rate digestion y EX yield of reserve on food growth y VE yield of structure on reserve mobilization venergy conductance heating,osmosis {J ET } surface-specific somatic maint. costs turnover,activity [J EM ] volume-specific somatic maint. costs regulation,defencek J maturity maintenance rate coefficient allocation  partitioning fraction egg formation  R reproduction efficiency life cycle[M H b ] volume-specific maturity at birth life cycle [M H p ] volume-specific maturity at puberty aging h a aging acceleration maximum length L m =  {J EAm } / [J EM ] Kooijman 1986 J. Theor. Biol. 121: 269-282

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

20. Metabolic rate Log weight, g Log metabolic rate, w endotherms ectotherms unicellulars slope = 1 slope = 2/3 Length, cm O 2 consumption,  l/h Inter-species Intra-species 0.0226 L 2 + 0.0185 L 3 0.0516 L 2.44 2 curves fitted: (Daphnia pulex)

21. Growth at constant food 3.7 time, dultimate length, mm length, mm time Length L. at birth ultimate L. von Bert growth rate energy conductance maint. rate coefficient shape coefficient Von Bert growth rate -1, d Von Bertalanffy growth curve:

22. At 25 °C : maint rate coeff k M = 400 a -1 energy conductance v = 0.3 m a -1 25 °C T A = 7 kK 10 log ultimate length, mm 10 log von Bert growth rate, a -1 ↑ ↑ 0 Von Bertalanffy growth rate 8.2.2

23. Length at puberty 8.2.2  Clupea Brevoortia ° Sprattus  Sardinops Sardina  Sardinella + Engraulis * Centengraulis  Stolephorus Data from Blaxter & Hunter 1982 Clupoid fishes Length at first reproduction L p  ultimate length L 

24. Feeding rate 8.2.2 slope = 1 poikilothermic tetrapods Data: Farlow 1976 Inter-species: J Xm  V Intra-species: J Xm  V 2/3 Mytilus edulis Data: Winter 1973 Length, cm Filtration rate, l/h

25. log zoom factor, z log scaled initial reserve log scaled age at birth log scaled length at birth approximate slope at large zoom factor Scaling relationships 8.2.2

26. Two-sample case: D. magna 20°C Optimality of life history parameters?

27. measured quantities  primary pars Standard DEB model (isomorph, 1 reserve, 1 structure) reserve & maturity: hidden variables measured for 2 food levels primary parameters

28. DEB tele course 2009 http://www.bio.vu.nl/thb/deb/ Free of financial costs; some 250 h effort investment Program for 2009: Feb/Mar general theory April 18-22 symposium in Brest 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 Stig Omholt : thank you for the invitation