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Introductionauxconceptsdelathorie DEB(Dynamic Energy
Budget);Applicationspourltudedes cyclesdeviedepoissons
LaurePECQUERIEIRD/LEMAR [email protected]
NOTA: de (trs) nombreuses diapos sont tires du cours
dintroduction la thorie DEB de Y. Thomas aux Master 1 du Ple
Halieutique dAgrocampus Ouest (2012)
mailto:[email protected]
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PLANDELEXPOS
1. ConceptsdelathorieDEB
2. LemodleDEBstandard(+codeR)
3. Lotolithe=unexemplede DEBproduct
4. Pourallerplusloin
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Unpeudhistoire
BasKooijman,en1979 Deuxquestions:
Commentpeutonquantifierleffetdecomposantstoxiquessurlareproductiondesdaphnies?
Quelestleffetdunerductionfaibledelareproductiondunindividusurladynamiquedelapopulation?
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Observations:Croissanceasymptotique
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Hypothses
Ptter
(1920):lacroissanceestlersultatdunediffrenceentreprocessusdesynthse(anabolisme)etdedgradation(catabolisme)croissance=surface
volumeet
Kleiber (1932):tauxmtaboliquessontproportionnelsW3/4
von Bertalanffy (1938)db cWaW
dtdW
=1
43,
32
=
c
b
WV
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Equationdevon Bertalanffy
K.L.von Bertalanffy (19011972)
L : longueur asymptotiquek : taux de croissance de VBL0 :
longueur t0
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Equationdevon Bertalanffy
Croissance=Anabolisme catabolisme
f(surface) f(volume)
EquationdiffrentielledeVBenmasse
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Modlesstatiques,ScopeforGrowth
Modlesbionergtiques
ModlesdynamiquesdeproductionnetteetmodlesDEB
)( RFEGCdt
dW+++=
C consommationG reproductionE excrtionF faecesR respiration
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Diffusiondelathorie
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1.LESCONCEPTSDELATHORIEDEB
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ObjectifsdelathorieDEB
Dcrirelacquisition dnergieetutilisation
decettenergieparunorganismeaucoursdesoncycledevie
pourralisersesdiffrentesfonctionsbiologiques(croissance,reproduction)demaniremcaniste
etenfonctiondelenvironnement.
Comprendrelespointscommunsentrelesespces
dunpointdevuebionergtique,enlienaveclvolution
UnmodleDEB=unensembledhypothsesprincipales(modlestandard)+hypothsessecondaires(spcifiquesdelapplication)
Bactries,champignons,plantesetanimaux
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Transfertsdchelles
Individu
Population
EcosystmeEspace
Temps
Climat
Anthropisation
Cellule
Toxiques
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Consommationdoxygne Empirique R=aLbKleiber (1932)b=2.25
Thorique R=cL2 +dL3(Kooijman,2000)
Dmarchedemodlisation
a = 0.0516 ; b = 2.4367
c = 0.0336 ; d = 0.0185
Daphnia pulexdaprs Kooijman (2000)
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WhyDynamicEnergyBudget(DEB)theory?
Simplestfulllifecyclemodel:singlesetofequationsandparameterstodescribeindividualgrowth,development
andreproductioninadynamicenvironment
Bodysizescalingrelationships
todescribewhichphysiologicalparametersdifferamongrelatedspecies
Integrationofmultiplestressors(e.g.ageandsizeateverystagetransitionwilldependontemperature,foodconditions,pollutants,parasites,encounteredbytheindividual)
(Kooijman2010)
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Cycledeviedunindividu
Modlestandard=3stades
Embryon,quinesenourritpasetnesereproduitpas
Juvnile:quisenourritmaisnesereproduitpas
Adulte:quisenourritetsereproduit(1)
(2)
(3)
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maturity
1-maturity
maintenance
development
food faecesassimilation
reserve
structure
somaticmaintenance
growth
LifeeventsinastandardDEBmodel
reproductionbuffer
reproduction
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Modelsimulations
INPUTS DEB MODEL
Food density
Temperature
Flow
Weight
Fecundity / egg size
OUTPUTS
Length
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Schmaconceptuel
Modle
Equations Variables dtatParamtres
Variables secondaires
(longueur, masse)
Environnement
Donnes de calibration / validation
Organisme
Variablesforantes
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Bodysizescalingrelationships basedonlengthatspawning
(Lsp =87cm)
(Lsp =68cm)
(Lsp =64cm)
(Lsp =53cm)
(Lsp =55cm)
Pink
Sockeye
Coho
Chum
Chinookz=1
z=68/87=0.78
z=64/87=0.74
z=53/87=0.6
z=55/87=0.63
(Quinn, 2005)
Some parameters vary:
Assimilation Development thresholds
Other parameters stay constant
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(FromBeachamandMurray,1993)
Step1:Reproductionweightfollowspredictionsfrombodysizescalingrelationships
DataAnalysis
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(Pecquerie etal.2011)
Step1:Reproductionweightfollowspredictionsfrombodysizescalingrelationships
SimulationsData(FromBeachamandMurray,1993)
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Step1:Lengthatemergenceasafunctionofeggweightisalsowellreproduced
(Pecquerie etal.2011)
SimulationsData(FromBeachamandMurray,1990)
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Step2:Variationamongindividuals(Chinook)
5C
7.5C
10C
High food
Average food
Low food
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5C
7.5C
10C
High food
Average food
Low food
Step2:Variationamongindividuals(Chinook)
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Step2:Qualitatively,themodelcapturesvariationsinlifehistorytraitsamongindividuals(Chinook)
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2.LEMODELEDEBSTANDARD
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Notations
{ } : Surface dpendant (.cm-2)
[ ] : Volume spcifique (.cm-3)
: Taux (j-1)
CodificationDEB:
Exemples :&pAm{ }
max. journalier d 'assimilation surface spcifique (J . j1. cm2
)Em[ ]
Densit max. de l 'nergie rserve (J . cm3)
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Volumestructurel
Lalongueur(L,cm),ou volumestructurel(V,cm3) pluttquelge.AvecV =
(L)3
Kooijman(2000)
2individusdunemmecohorteUnpincentenaire
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Larserve
Unorganismeragitlentementauxvariationdumilieu,ilfautun
filtre
Eestprsentdans(1)lesorganesdestockageet(2)danschaquecellule(vacuole,lysosome)
E=protine,glucide,lipide,ARN
W = d.V + E.E
d = densit de la structureE = contenu nergtique
des rserves
L
W1V E1
L
W2V E2
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Ladensitderserve
[E] = E / V
[E] 0 [Em]
[Em] : capacit maximale de stockage dun organisme (J.cm-3)
En conditions constantes, la densit de rserve dun organisme
reste constant: hypothse fondamentale de la thorie = contrle la
dynamique des rserves
.V
EEE
V V
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Equationsdumodle
3quationsdiffrentielles
0 else, if ,)1(
0 else, if ,)1(
]/[)(
==
=
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Effetdelatemprature
Daphnia magna(daprs Kooijman, 2010)
Toutfluxphysiologiquedpenddelatemprature (drivedela
loidArrhnius,1889,quidcritlavitesseduneractionchimiqueenfonctiondelatemprature)
&k(T ) = &k(T1 ).expTAT1
TAT
TA :Temprature d ' Arrhnius (K ) = f (espce)T1 :Temprature de
rfrence (K )
Danslagammedetolrance ona:
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Effetdelatemprature
Audeldelagammedetolrance :
Limiteinfrieure:entreenphasedequiescence
Limitesuprieure:dgradationdesprotines
&k(T ) = &k(T1 ).expTAT1
TAT
1+ exp TAL
T TAL
TL
+ exp TAH
TH TAH
T
1
Escherichia coli(daprs Kooijman, 2010)
TA
TAHTAL
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Assimilation
Lingestionsuituneloidesaturation Letauxdingestiondpend:
delasurface delindividu
delatemprature
deladensitennourriture
Unefraction decequiestingrseraassimil
XXk
MichaelisMenten
+
=KXX
Xf
E
X FpX
pA
&pX{ }
&pXm{ }
0.5 &pXm{ } = rponse fonctionnelle
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Assimilation
Lingestionsuituneloidesaturation Letauxdingestiondpend:
delasurface delindividu
delatemprature
deladensitennourriture
Unefraction
decequiestingrseraassimil(fonctiondutypedenourriture)
&pA =V2/3 f &pXm{ } X &k(T )
V : volume structurel (cm3)f : rponse fonctionnelle
(01)&pXm{ } : max. d 'ingestion (J.cm2. j1)
X : efficacit d 'assimilation (%)
XK : coefficient de demie saturation
E
X FpX
pA
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Utilisationdesrserves
E
pA
pcdEdt
= &pA &pCE
&pA
&pC = f ( E[ ],V )
Em
&pC =EG[ ]V 1/3 &pAm{ }
Em[ ]+ &pM[ ]
EG[ ]E
+ V
1
Cot de construction dune unit de V (J.cm-3)
Max. de rserve par unit de V (J.cm-3)
Cot de maintenance dune unit de V (J.cm-3)
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Allocationdelnergie
V ER
pc
pMpG pR
pJPC (1 - ) PC
ruleUne fraction constante de
lnergie de rserve est alloue la croissance et maintenance
somatique, le reste tant allou la maturit/reproduction
Sous certaines conditions, peut varier :entre les sexes
(dimorphisme sexuel);en fonction de la photopriode (e.g.
vgtaux);dans les conditions de jeun extrme (remobilisation de la
structure);en cas dinfection et de pollution (perturbation
endocrinienne).
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Maintenancesomatique
Lamaintenancesomatiquedpend:
Duvolume structurel Delatemprature
Prioritaire surlacroissance!
&pM =V &pM[ ] &k(T )
V
pMpG
PCLa maintenance somatique permet le maintient en vie :Maintien
des gradients cellulaires de concentration
Turnover des protines et des enzymes
Tension moyenne des muscles
Mouvements minimaux
Production de phanres (poil, plume, caille, coquille), demucus
et de mue
Osmorgulation
&pM[ ] : taux de maintenancepar unit de V (J . cm3. j1)
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Croissance
[ ]GG
MCG
Ep
dtdV
ppp&
&&&
=
= V
pMpG
PC
EG[ ] : nergie alloue la construction d 'une unit de V (J .
cm31)
Cecot,[EG] revtuncaractreuniversel : acell is acell ;du
mmeordredegrandeur pourleseucaryotes:(100010000J.cm3)
Lnergieallouelacroissancesomatiqueest:
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Dveloppement/maturit
Dveloppement etacquisitiondelamaturit :
DveloppementdusystmeimmunitaireMiseenplacedusystmedergulationhormonaleDveloppementdescaractressexuelsprimairesetsecondairesMtamorphose
/...
EH
pR
pJ(1 - ) PC
HJJ Ekp && =
Max la pubert , i.e. EH = EHp
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Reproduction
ER
pR
pJ(1 - ) PC
&pR = (1 ) &pC &pJ
Lnergieallouelareproduction est:
Lagestiondelnergieallouelaproductionpuislmissiondesgamtesestextrmementvariable
danslergneanimal:
DesespcessereproduisentdslorsqueER
estsuffisantpourproduireunuf;
Dautresattendrontquunecertainequantitdnergiesoitdisponible;
LebufferER
peutnepastrevidtotalementaprslareproduction(pontepartielle);
Gamtes
La synthse des gamtes se fera partir de lnergie stocke pour la
reproduction, avec une certaine efficacit (R).
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Enrsum
Pour le modle standard :
3 stades de vie
4 variables dtat2 variables forantes
3 quations diffrentielles
10aine de paramtres primaires
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3.Lotolithe=unexemplede DEBproduct
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Fishotoliths=biocalcifiedstructures
Environment
Fish metabolism (growth + maintenance)
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Biocarbonate=metabolicproduct
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Biocarbonate=metabolicproduct
Assumption: biocarbonate formation coupled to growth +
maintenance fluxes
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Biocarbonate =metabolicproduct
Assumption: biocarbonate formation coupled to growth +
maintenance fluxes
OG D
dV p pdt
= +& &
G
G D
pOp p
=
+&
& &
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Biocarbonate =metabolicproduct
Assumption: biocarbonate formation coupled to growth +
maintenance fluxes
OG D
dV p pdt
= +& &
G
G D
pOp p
=
+&
& &
Simulation for a constant environment
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Otolith modeling : individual history
Environment
Data
Simulation
Otolith growth and opacity
LengthDEB model
(Pecquerie et al. 2012)
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Otolith modeling : individual history
Environment
Otolith growth and opacity
LengthDEB model
Slow growing fish have larger otoliths
We can reproduce main observations on otolith growth and opacity
with simple mechanisms
(Pecquerie et al. 2012)
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Food history reconstruction from otolith
Reconstruction of length
DEB model
Assimilated food +
We can theoretically reconstruct both growthand assimilated
food
from temperature and otolith data
extraction of new information from data difficult to obtain
new information = food in natural conditions, at the individual
scale
DEBtool routine: animal/o2f.m(Pecquerie et al. 2012)
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Two age-3 individuals ?
Individual 2
Individual 1
(Pecquerie et al. 2012)
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3 years-old
2 years-old
False check
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Application:North Sea (NS)cod otolithsat odds withBarentssea
(BS)cod otoliths
(Beckman etal. 1996,Hoie etal.2009)
Classicpattern:translucentedgeinwinter
Slowgrowthinwinter
Oppositepattern:translucentedgeinsummerSlowgrowthinsummer?
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Modelextensiontotake into account temperatureeffect onCaCO3
precipitation
Fablet etal.2011,PLoS ONE
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Modelextensiontotake into account temperatureeffect onCaCO3
precipitation
OM:OrganicMatrix
Fablet etal.2011,PLoS ONE
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Modelextensiontotake into account temperatureeffect onCaCO3
precipitation
Fablet etal.2011,PLoS ONE
Otolithaccretion =CaCO3 (VC)flux+OM(VP)flux
Specific temperature effect ondVC/dt
[ ]MCGCCC ppTcdtdV += )(
MCGC
MPGP
CC
P
C
P
pppp
Tcdt
dVdt
dV
VVO
++
=
=)(
1
LO =VC
1/ 3
O
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Modelcalibrationandvalidationwith longterm experimental data
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4.POURALLERPLUSLOIN
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O trouver plusdinfos?
Artwork: Yoan Eynaud
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O trouver plusdinfos?
BasKooijman,Departmenttheoreticalbiology,VrijeUniversiteit
Amsterdam
http://www.bio.vu.nl/thb/deb/
Introduction aux concepts de la thorie DEB: 4 vidos ralises par
Roger Nisbet (UC Santa Barbara) peuvent tre
tlcharges([email protected])
Site AquaDEB http://www.ifremer.fr/aquadeb
BreizhDEB: Marianne Alunno-Bruscia, Cedric Bacher, Fred Jean,
Jonathan Flye Sainte Marie, Laure Pecquerie + Veronique Loizeau,
Yoann Thomas
DEB course tous les 2 ans (fev 2015)
http://www.bio.vu.nl/thb/deb/course/
http://www.bio.vu.nl/thb/deb/mailto:[email protected]://www.ifremer.fr/aquadebhttp://www.bio.vu.nl/thb/deb/course/
Slide Number 1PLAN DE LEXPOSUn peu dhistoireObservations :
Croissance asymptotiqueHypothsesEquation de von BertalanffyEquation
de von BertalanffyModles bionergtiquesDiffusion de la thorie1. LES
CONCEPTS DE LA THORIE DEBObjectifs de la thorie DEBTransferts
dchellesDmarche de modlisationWhy Dynamic Energy Budget (DEB)
theory?Cycle de vie dun individuSlide Number 16Model
simulationsSchma conceptuelBody-size scaling relationships based on
length at spawningStep 1: Reproduction weight follows predictions
from body-size scaling relationshipsSlide Number 21Slide Number
22Slide Number 23Slide Number 24Slide Number 252. LE MODELE DEB
STANDARDNotationsVolume structurelLa rserveLa densit de
rserveEquations du modleEffet de la tempratureEffet de la
tempratureAssimilationAssimilationUtilisation des rservesAllocation
de lnergieMaintenance
somatiqueCroissanceDveloppement/maturitReproductionEn rsum3.
Lotolithe = un exemple de DEB productFish otoliths = bio-calcified
structuresSlide Number 45Slide Number 46Slide Number 47Slide Number
48Otolith modeling : individual historyOtolith modeling :
individual historyFood history reconstruction from otolithSlide
Number 52Slide Number 53Application: North Sea (NS) cod otoliths at
odds with Barents sea (BS) cod otolithsModel extension to take into
account temperature effect on CaCO3 precipitationModel extension to
take into account temperature effect on CaCO3 precipitationModel
extension to take into account temperature effect on CaCO3
precipitationModel calibration and validation with long-term
experimental dataSlide Number 59Slide Number 604. POUR ALLER PLUS
LOINO trouver plus dinfos? O trouver plus dinfos?
