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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
DynamicEnergy Budget Theory - I

Tânia Sousa

withcontributionsfrom : Bas Kooijman

a deb organism feeding assimilation
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

feeding assimilation
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
slide5

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

intra taxon predation efficient conversion y ex a high yield of reserve on food
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

a deb organism mobilization
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

mobilization of reserve
Mobilization of Reserve
  • The mobilizationof reserve isused to fuel theorganism’sactivities

- energyconductance

  • Empiricalpattern: organisms are capableofspendingenergyongrowth, maintenance, reproduction in theabsenceoffood
  • Empiricalpattern: eggsspendenergyonmaturationbut do notfeed.
  • Mobilizationfrom reserve -> highercontroloverthemetabolism (independencefromtheenvironment)
  • Mobilizationisuncoupledfromassimilation & feeding: makesevolutioneasier
  • Weakhomeostasis & stronghomeostasis & independenceofmobilizationfromtheenvironment mobilizationisproportional to C-moles of reserve per unitoflength
notation 2
Notation 2

General

Indices for compounds

Indices for transformations

notation 3
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
mobilization of reserve1
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

a deb organism the kappa rule a fixed allocation rule
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

kappa rule
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

a deb organism p riority allocation rules
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

priority maintenance rule
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
a deb organism
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

somatic maintenance
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)
somatic maintenance1
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

reserve pays no maintenance embryonic development
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

a deb organism1
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

growth
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

exercises
Exercises
    • Obtainexpressionsthatdependonlyonstatevariablesandparametersfor
    • 1) growthand
    • 2) growthatconstantfood(weakhomeostasis)
  • Suggestion use the:
    • followingequations for 1)
    • Use thefollowingdefinition for 2)

- reserve density

exercises1
Exercises
  • Theexpressionsthatdependonlyonstatevariablesandparametersfor
  • 1) growthis
  • 2) growthatconstantfoodis
exercises2
Exercises
  • Is thisVonBertallanffygrowth?
    • Yes, with
    • Ultimatelengthdependsonspecificmaintenanceneedsandincreaseswiththe reserve density

- heatinglength

von bertalanffy growth at constant food
Von Bertalanffy: growth at constant food

length, mm

Von Bert growth rate -1, d

time, d

ultimate length, mm

Von Bertalanffy growth curve:

extremes in relative growth rate in insects
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