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Dynamic Energy Budget Theory - I

Dynamic Energy Budget Theory - I. Tânia Sousa with contributions from : Bas Kooijman. A DEB organism : growth. 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 organism: growth • 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 MaturityMaintenance Reproduction Growth SomaticMaintenance Maturation MV - Structure MH - Maturity

  3. 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

  4. Exercises • Obtainexpressionsthatdependonlyonstatevariablesandparametersfor • 1) growthand • 2) growthatconstantfood(weakhomeostasis) • Suggestion use the: • followingequations for 1) • Use thefollowingdefinition for 2) - reserve density

  5. Exercises • Theexpressionsthatdependonlyonstatevariablesandparametersfor • 1) growthis

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

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

  8. Von Bertalanffy: growth at constant food length, mm Von Bert growth rate -1, d time, d ultimate length, mm Alowerthefoodlevelimplies a smallerultimatesizeand a shorter time to reachit.

  9. Eggandfoetaldevelopment: differences • Growth in DEB: • Whathappens to the reserve density in anegg? • Itdecreases in time • Exercise: Whathappens to the reserve density in a foetus? • Ittends to infinity • Empiricalfact: Foetalweigthisproportional to cubed time

  10. Egg & Foetal development

  11. Competitionbetweengrowthandsomaticmaintenance • As theorganismgetsbiggeritgets more food (proportional to V2/3) butitgrowsslowerbecausesomaticmaintenance (proportional to V)iscompetingwithgrowth • Thehigherthespecificsomaticmaintenanceneedsthelowertheultimatesize

  12. Extremes in relative growth rate in insects Buprestis splendens (jewel beetle) Juveniles live in wood for 20-40 a Antheraea polyphemus (polyphemus moth) Juveniles increase weight 80000 × in 48 h

  13. Exercises • Obtain an expression for the dynamics of the reserve density mE • Suggestion use theequations for thedynamicsof MEand MVandfollowingequations: • Obtain na expression for themaximum reserve densitymEm • Set dmE/dt=0 (weakhomeostasis). • WhatisthevalueofmE? • WhatisthemaximumvalueofmE? • RewriteusingmEm. Whatisthemeaningof? - maximumlength -maximumreserve density

  14. A DEB organism: maturitymaintenance • 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 MaturityMaintenance Reproduction Growth SomaticMaintenance Maturation MV - Structure MH - Maturity

  15. Maturity maintenance • Collection of processes that maintain the level of maturity • Defense and regulating systems • Maturity maintenance is paid from flux (1-)JE,C: •  maturity level • It does not increase after the onset of reproduction • Specificmaturitymaintenancecosts are constantbecauseofthestronghomeostasis • Thecomplexitywoulddecrease in theabsenceofenergyspent in itsmaintenance(2ndLawofthermodynamics) • Empiricalpattern: no reproductionoccursatverylowfooddensities - maturitymaintenance rate coefficient

  16. A DEB organism: maturation/reproduction • 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 MaturityMaintenance Reproduction Growth SomaticMaintenance Maturation MV - Structure MH - Maturity

  17. Maturation/Reproduction • The use of reserve to increasethestateofmaturity (embryoandjuvenile) or to reproduce (adult) • Allocation to maturationin a juvenile (MH <MHp) or to reproduction in na adult (MH >=MHp) (supplydriven): • Empiricalpattern: organismskeptatlowfooddensityneverreachpubertyimplyingthattheywillnotreproduce • Stagetransitionsshouldnotbelinkedwithsize MHb- thresholdofmaturityatbirth MHp- thresholdofmaturityatpuberty

  18. Extremes in relative maturity at birth in mammals 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

  19. Extremes in relative maturity at birth in fish Mola mola (ocean sunfish) ♂,♀ 4 m, 1500 (till 2300) kg Egg: 3 1010 eggs in buffer At birth: 1.84 mm g; ab = ? d Feeds on jellyfish & combjellies Latimeriachalumnae (coelacanth) ♂, ♀ 1.9 m, 90 kg Egg: 325 g At birth: 30 cm; ab = 395 d Feeds on fish

  20. Reproduction • Theamountofenergycontinuouslyinvested in reproductionisaccumulated in a buffer andthenitisconvertedintoeggsprovidingtheinitialendowmentofthe reserve to theembryo • Initial amount of reserve follows from • Initial structural vol. and maturity are negligibly small and maturity at birth is given • Empirical fact: reserve density at birth equals that of mother at egg formation (egg size covaries with the nutritional state of the mother) - initial amountof reserve oftheegg - reproductionefficiency

  21. Reproduction: buffer handling rules • Rules for handling thereproduction buffer are species-specific (differentevolutionarystrategies) • Some speciesreproducewhenenoughenergy for a single egghasbeenaccumulated • Some speciesreproduce a largeclutch (some fisheshavethousandsofeggs) • Some species use environmentaltriggers for spawning (e.g., moluscs)

  22. Energyflows vs. Massflows =

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