Dynamic Energy Budget Theory - I

1. DynamicEnergy Budget Theory - I Tânia Sousa withcontributionsfrom : Bas Kooijman

2. A TheoryofMetabolism • Whatismetabolism?

3. A TheoryofMetabolism • Whatismetabolism? • “Using resources (energy and materials) to make new cells, to repair old ones, and to get rid of wastes requires the assemblage of biochemical pathways that we call metabolism. Metabolism is a universal feature of life that links organisms with their environment, and with each other.”

4. A TheoryofMetabolism • Whatismetabolism? • “Using resources (energy and materials) to make new cells, to repair old ones, and to get rid of wastes requires the assemblage of biochemical pathways that we call metabolism. Metabolism is a universal feature of life that links organisms with their environment, and with each other.” • Whatshould a theoryofmetabolism look like?

5. A TheoryofMetabolism • Whatismetabolism? • Whatshould a theoryofmetabolism look like? • Itshouldbe a qualitativeandquantitativedescriptionofhoworganisms use massandenergy to do thethingstheyneed to do to stay alive

6. A TheoryofMetabolism • Whatismetabolism? • Whatshould a theoryofmetabolism look like? • Itshouldbe a qualitativeandquantitativedescriptionofhoworganisms use massandenergy to do thethingstheyneed to do to stay alive • Whichtypeofquestions can a theoryofmetabolismhelpyouwith?

7. A TheoryofMetabolism • Whatismetabolism? • Whatshould a theoryofmetabolism look like? • Whichtypeofquestions can a theoryofmetabolismhelpyouwith? • Why do weakaccidshaveaneffectonthegrowthofyeasts? • Whatistheminimumamountoffood (andhabitat) a panda needs to survive? • Ifthetemperatureofoceanincreasesby 0.5ºC whatwillhappen to thesurvivalofthesardinelarvae?

8. EnvironmentalApplications • Toxicology • Which is the toxicity of the environmental concentration of a compound? • Which are the toxic effects of a compound? • Climate Change • Will an increase in 1ºC have a drastic impact on the distribution range of a species? • Waste water treatment plant • What are the necessary conditions to mantain an healthy microbian comunity in the biological reactors? • Fisheries Management • Whatisthesustainablefishing quota?

9. MinimataDisaster: Mercury Poisoning • Minamata is a small factory town facing the Shiranui Sea, and Minamata Bay is part of this sea. • Chisso Corporation in Minimatawhich produced plastics, drugs, and perfumes • released methylmercuryfrom 1932 to 1968in the industrial wastewater whichbioaccumulated in shellfish and fish in eaten by the local people. • In the mid-1950's people begin to notice a "strange disease". Victimswere diagnosed as having a degeneration of their nervous systems.

10. Whatis DEB theory? • It captures thequantitativeaspectsofmetabolismatthe individual level for allspecies • Whythehope for generality? • universalityofphysicsandevolution • Entropyproductionis >=0 • celluniversality: • cells are metabolically very similar, independently of the organism orits size • widespreadbiologicalempiricalpatterns

11. A widespreadbiologicalempiricalfact: VonBertalanffygrowth • Growth as a function of time • Depends on length at birth, maximum length and growth rate • It was proposed in 1929 by Putter and in 1938 by Von Bertalanffy

12. A widespreadbiologicalempiricalfact:Kleiber’sLaw • Metabolism (respiration or heat production) as a function of mass • Metabolism increases with weight raised to the power 3/4 • Max Kleiber originally formulated this basic relationship back in the 1930s. Whatistherelationshipbetweenspecificmetabolismandweight?

13. A widespreadbiologicalempiricalfact:Kleiber’sLaw • Relationshipbetweenspecificmetabolismandweight?

14. A widespreadbiologicalempiricalfact:IndirectCalorimetry • Indirect calorimetry calculates heat that living organisms produce from their production of carbon dioxide and nitrogen waste and from their consumption of oxygen. • Lavoisiernoted in 1780 that heat production can be predicted from oxygen consumption this way, using multiple regression.

15. Basic Concepts in DEB Theory • Consistencywithotherscientificknowledge (thermodynamics, evolution, etc) • Consistencywithempirical data • Life-cycleapproach: embryo, juvenileandadult • Occam’srazor: the general modelshouldbe as simple as possible (andnot more) • Occam’sbiologicalrazor: organisms increasedtheir control over metabolism duringevolution

16. Basic Concepts in DEB Theory • The individual: time andspatialscales

17. A DEB organism – massdescription • Metabolism in a DEB individual. • The boundary of the organism • Rectangles are state variables ME- Reserve MV - Structure MH - Maturity

18. DEB model: theStateVariables • What defines a DEB organism? • Biomass • Mv - MassofStructure • ME - MassofReserve • Life-Cycleapproach: differentlifestages • MH - LevelofMaturity (itrepresentsneithermassnorenergy) • Whataboutotherpossiblesstatevariablessuch as age?

19. Why not age as a state variable? Trichopsis vittatus These gouramis are from the same nest, they have the same age and lived in the same tankSocial interaction during feeding caused the huge size differenceAge-based models for growth are bound to fail; growth depends on food intake

20. Notation General Indices for compounds Indices for transformations

21. DEB model: Reserve andStructure • Stronghomeostasis • Reserve & structurehaveconstantaggregatedchemicalcomposition

22. DEB model: Reserve andStructure • Stronghomeostasis • Reserve & structurehaveconstantaggregatedchemicalcomposition What does a variableaggregatedchemicalcompositionimplies? • Why more than 1 statevariable to define thebiomass? • Theaggregatedchemicalcompositionoforganismsisnotconstant – itchangeswiththegrowthrate • Whynot more than 2 statevariables to define biomass? • Two are sufficient (in animalsandbacteria) to capture thechange in aggregatedchemicalcompositionwiththegrowth rate • Stronghomeostasis -> highercontrolovermetabolism

23. Whynot use thousandsofchemicalspeciesandchemicalreactions to define theorganism? • Metabolismatthechemicallevelisverycomplex • Itisnotpossible to imposemassconservationwithoutmodelingallchemicalreactions (whichisimpossible). • “Knowledge on motors of cars is of little help to solve queuing problems”

24. DEB model: Reserve andStructure • Weakhomeostasis • Atconstantfoodorganismstend to constantaggregatedchemicalcomposition Whathas to betherelationshipbetween MVand ME to ensure a constantaggregatedchemicalcomposition? • Empiricalsupport: growingbiomasstends to constantchemicalcompositionatconstantfood • Weakhomeostasis -> highercontrolovermetabolism

25. DEB model: Maturity • LifeStages (darkblue) andtransitions (light blue) • Essentialswitchpoints for metabolicbehavior • Birth (startoffeeding) • Puberty (startofallocation to reproduction) • Switchpointssometimes in reversedorder (aphids) embryo juvenile adult baby infant weaning fertilization birth death puberty MHb- thresholdofmaturityatbirth MHp- thresholdofmaturityatpuberty

26. Life-stages: Metamorphosis

27. MHb - Extremes in relative maturity at birth Didelphus marsupiales (Am opossum) ♂, ♀ 0.5 + 0.5 m, 6.5 kg At birth: <2 g; ab = 8-13 d 10-12 (upto 25) young/litter, 2 litters/a Ommatophoca rossii (Ross Seal) ♂ 1.7-2.1 m, 129-216 kg ♀ 1.3-2.2 m, 159-204 kg At birth: 1 m, 16.5 kg; ab = 270 d

28. A DEB organism – energydescription • Metabolism in a DEB individual. • The boundary of the organism • Rectangles are state variables ME- Reserve MV - Structure MH - Maturity Whyisthechemicalpotentialof reserve a parameter? - chemicalpotentialof reserve - chemicalpotentialofstructure MHb- thresholdofmaturityatbirth MHp- thresholdofmaturityatpuberty EHb- thresholdofmaturityatbirth EHp- thresholdofmaturityatpuberty

29. A DEB organism – energydescription • Metabolism in a DEB individual. • The boundary of the organism • Rectangles are state variables ME- Reserve MV - Structure MH - Maturity • Chemicalandthermodynamicpropertiesofthestructureand reserve are constant (stronghomeostasis) - chemicalpotentialof reserve - chemicalpotentialofstructure MHb- thresholdofmaturityatbirth MHp- thresholdofmaturityatpuberty EHb- thresholdofmaturityatbirth EHp- thresholdofmaturityatpuberty

30. A DEB organism • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of foodJXA, reserveJEA, JEC, JEM, JET, JEG, JER, JEJor structureJVG. • Circles are processes Feeding ME- Reserve Assimilation MV - Structure MH - Maturity

31. Notation for mass flows 1

32. Notation for mass flows 2 General Indices for compounds Indices for transformations

33. Feeding & Assimilation • Feeding: theuptakeoffood • Assimilation: conversionofsubstrate (food, nutrients, light) into reserve(s) • Dependonsubstrateavailability& structuralsurfacearea (e.g. surfaceareaofthegut) Are alltheseparametersindependent? - surfacemaximumfeeding rate - surfacemaximumassimilation rate -yield of reserve onfood • Empiricalpattern: theheatincrementoffeedingsuggeststhatthere are processes onlyassociatedwithfoodprocessing • Consistencywithotherfields: masstransfer (needed for acquisition, digestionandfoodprocessing) isproportional to area Whyisthe yield of reserve onfood a parameter?

34. Feeding & Assimilation • Feeding: theuptakeoffood • Assimilation: conversionofsubstrate (food, nutrients, light) into reserve(s) • Dependonsubstrateavailability& structuralsurfacearea (e.g. surfaceareaofthegut) - surfacemaximumfeeding rate - surfacemaximumassimilation rate -yield of reserve onfood • Empiricalpattern: theheatincrementoffeedingsuggeststhatthere are processes onlyassociatedwithfoodprocessing • Stronghomeostasisimposes a fixedconversionefficiency • Consistencywithotherfields: masstransfer (needed for acquisition, digestionandfoodprocessing) isproportional to area

35. Feeding rate • Iffoodavailabilityisconstant (orabundant) feedingincreasesproportional to areaor L2 (for isomorphs) Filtration rate, l/h Mytilus edulis Data: Winter 1973 Length, cm

36. Intra-taxon predation: efficient conversionyEX a high yield of reserve on food Hemiphractus fasciatus is a frog-eating frog Beroe sp is a comb jelly-eating comb jelly Solaster papposus is a starfish-eating starfish Chrysaora hysoscella is a jelly fish-eating jelly fish Coluber constrictor is a snake-eating snake Euspira catena is a snail-eating snail

37. Intra-taxon predation: efficient conversionyEX a high yield of reserve on food Asplanchna girodi is a rotifer-eating rotifer Didinium nasutum is a ciliate-eating ciliate Esox lucius is a fish-eating fish Acinonyx jubatus is a mammal-eating mammal Enallagma carunculatum is a insect-eating insect Falco peregrinus is a bird-eating bird

38. Feeding & Assimilation • Proportionalitybetweenassimilationandingestion rate for MytilusEdulis for differentsizes

39. A DEB organism – energydescription • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of foodJXA, reserveJEA, JEC, JEM, JET, JEG, JER, JEJor structureJVG. • Circles are processes Feeding ME- Reserve Assimilation MV - Structure MH - Maturity How do weobtaintheenergydescription? - surfacemaximumfeeding rate - surfacemaximumassimilation rate -yield of reserve onfood

40. A DEB organism – energydescription • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of foodJXA, reserveJEA, JEC, JEM, JET, JEG, JER, JEJor structureJVG. • Circles are processes Feeding ME- Reserve Assimilation MV - Structure MH - Maturity - surfacemaximumfeeding rate - surfacemaximumassimilation rate -yield of reserve onfood

41. A DEB organismMobilization • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of foodJXA, reserveJEA, JEC, JEM, JET, JEG, JER, JEJor structureJVG. • Circles are processes Feeding ME- Reserve Mobilisation Assimilation MV - Structure MH - Maturity

42. Mobilization of Reserve • The mobilizationof reserve isused to fuel theorganism’sactivities - energyconductance • Empiricalpattern: organisms are capableofspendingenergyongrowth, maintenanceandreproduction in theabsenceoffood • Empiricalpattern: eggsspendenergyonmaturationbut do notfeed. • Mobilizationfrom reserve -> highercontroloverthemetabolism (independencefromtheenvironment) • Mobilizationisuncoupledfromassimilation & feeding: makesevolutioneasier • Weakhomeostasis & stronghomeostasis & independenceofmobilizationfromtheenvironment mobilizationisproportional to C-moles of reserve per unitoflength • What are theunitsof?

43. Notation 2 General Indices for compounds Indices for transformations

44. Notation 3 • Notice that 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 removed

45. Mobilization of Reserve Some populations of humpback whale Megaptera novaeangliae (36 Mg) migrate 26 Mm anuallywithout feeding, A 15 m mother gets a 6 m calf in tropical waters, gives it 600 l milk/d for 6 months and together return to cold waters to resume feeding in summer

46. A DEB organism– energydescription Feeding • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of foodJXA, reserveJEA, JEC, JEM, JET, JEG, JER, JEJor structureJVG. • Circles are processes ME- Reserve Mobilisation Assimilation MV - Structure MH - Maturity Writetheenergydescription

47. A DEB organism– energydescription Feeding • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of foodJXA, reserveJEA, JEC, JEM, JET, JEG, JER, JEJor structureJVG. • Circles are processes ME- Reserve Mobilisation Assimilation MV - Structure MH - Maturity = Writetheenergydescription

48. A DEB organismThekappa rule – a fixedallocation rule • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of foodJXA, reserveJEA, JEC, JEM, JET, JEG, JER, JEJor structureJVG. • Circles are processes • The full square is a fixed allocation rule (the kappa rule) Feeding ME- Reserve Mobilisation Assimilation MV - Structure MH - Maturity

49. Kappa rule • A fixed fraction  of mobilised reserve is allocated to somatic maintenance and growth,the rest to maturity maintenance and maturation (juveniles) or reproduction (adults).  - kappa Length, mm Growth: Cum # of young Reproduction  • Empiricalpattern: some species do not stop growingafterreproductionhasstarted Von Bertalanffy Age, d Age, d

50. A DEB organism– energydescription • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of foodJXA, reserveJEA, JEC, JEM, JET, JEG, JER, JEJor structureJVG. • Circles are processes • The full square is a fixed allocation rule (the kappa rule) Feeding ME- Reserve Mobilisation Assimilation MV - Structure MH - Maturity