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Dynamic Energy Budget Theory - I

Dynamic Energy Budget Theory - I. Tânia Sousa with contributions from : Bas Kooijman. A DEB organism Feeding & Assimilation. Metabolism in a DEB individual. Rectangles are state variables

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Dynamic Energy Budget Theory - I

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

  2. A DEB organismFeeding & Assimilation • 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

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

  4. Notation 1

  5. Feeding & Assimilation • Proportionaluitybetweenassimilationandingestion rate for MytilusEdulis for differentsizes

  6. 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

  7. 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

  8. 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

  9. 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?

  10. Notation 2 General Indices for compounds Indices for transformations

  11. 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

  12. 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

  13. 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

  14. 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: organisms do not stop growingafterreproductionhasstarted Von Bertalanffy Age, d Age, d

  15. A DEB organismPriorityallocation rules • 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) • The full circles are the priority maintenance rules. Feeding ME- Reserve Mobilisation Assimilation Offspring MER Maturity Maintenance Reproduction Growth Somatic Maintenance Maturation MV - Structure MH - Maturity

  16. Priority maintenance rule • The priority maintenance rulestates that maintenance has priority: (1) from somatic maintenance is paid first and the rest goes to growth while (2) from maturitymaintenanceispaidfirstandtherestgoes to maturation/reproduction • Theprioritymaintenance rule resultsfromthekappa rule andthedemanddrivenbehaviorofmaintenance

  17. 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 • The full square is a fixed allocation rule (the kappa rule) • The full circles are the priority maintenance rule. Feeding ME- Reserve Mobilisation Assimilation Offspring MER Maturity Maintenance Reproduction Growth Somatic Maintenance Maturation MV - Structure MH - Maturity

  18. Somatic maintenance • Collection of processes that maintain the organism alive: • protein turnover (synthesis, but no net synthesis) • maintaining conc. gradients across membranes (proton leak) • (some) product formation (leaves, hairs, skin flakes, moults) • movement (usually less than 10% of maintenance costs)

  19. Somatic maintenance • Reserve compounds have no maintenance needs because they have a limited lifetime • Somatic maintenance is paid from flux JE,C: •  structural volume (most costs) •  surface area: heating (endotherms), osmo-regulation (fresh water organisms) • Specificsomaticmaintenancecosts are constantbecausethechemicalandthermodynamicpropertiesofthestructure are constant (stronghomeostasis) • Empiricalpattern: Freshlyproducedeggsconsistprimarlyof reserve andhardly respire - volume specificmaintenancecosts - surfacespecificmaintenancecosts

  20. Reserve pays no maintenance embryonic development Carettochelys insculpta Data from Web et al 1986 embryo yolk O2 consumption, ml/h weight, g time, d time, d

  21. 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 • The full square is a fixed allocation rule (the kappa rule) • The full circles are the priority maintenance rule. Feeding ME- Reserve Mobilisation Assimilation Offspring MER Maturity Maintenance Reproduction Growth Somatic Maintenance Maturation MV - Structure MH - Maturity

  22. Growth • Growthistheincreaseoftheamountofstructure (conversionof reserve intostructure) • Allocation to growth (supplydriven): • Stronghomeostasisimposes a fixedconversionefficiency • Stronghomeostasisimposes a constantdensity - numberof C-moles per unitofstructure body volume -yield of reserve onstructure

  23. Notation 1

  24. Exercises • Obtainexpressionsthatdependonlyonstatevariablesandparametersfor growthusingthefollowingequations

  25. Exercises • Theexpressionthatdependonlyonstatevariablesandparametersfor growthis

  26. Exercises • Obtainexpressionsthatdependonlyonstatevariablesandparametersfor growthatconstantfood(weakhomeostasis) usingthefollowingdefinition for reserve density: • Whathappens to atconstantfooddensity? - reserve density

  27. Exercises • Theexpressionsthatdependonlyonstatevariablesandparametersfor growthatconstantfooddensity are: • Is thisVonBertallanffygrowth?

  28. Exercises • Is thisVonBertallanffygrowth? • Yes, with - heatinglength

  29. Von Bertalanffy: growth at constant food • VonBertallanffygrowthin DEB theory • DEB theorypredicts: • decreaseswithspecificmaintenanceneedsandincreaseswiththe reserve density (foodlevel) • decreaseswith

  30. Von Bertalanffy: growth at constant food length, mm Von Bert growth rate -1, d time, d ultimate length, mm Alowerfoodlevelimplies a smallerultimatesizeand a shorter time to reachit. • Empiricalfact: organismsofthesamespeciesatdifferentfoodlevelsexhibitvonBertallanfygrowth rates that are inverselyproportional to ultimatelength

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