Metabolic products
within a DEB context
Laure Pecquerie
Laboratoire des Sciences de l’Environnement Marin
UMR LEMAR, IRD
laure.pecquerie@ird.fr
21st -22nd April 2015,
DEB Course 2015, Marseille
Respiration in bioenergetic models
• The conceptual relationship between respiration and use of
energy has changed with time.
– Von Bertalanffy identified it with anabolic processes,
– while e.g. a Scope For model relates it to catabolic processes
• DEB theory relates it to the three transformations :
assimilation, dissipation and growth
(which all have an anabolic and a catabolic components)
• DEB theory defines O2 consumption and CO2 production as
product “formations” and not as mechanistic processes (ie
fluxes driving the dynamics of the state variables)
Outline
lecture 1 (Tue. 21. ) and 2 (Wed. 22.)
• [A bit of networking]
• Definition of products in a DEB context
• Example : Torpedo marmorata
– Univariate data t-L, L-W
– Respiration data L-JO
• Steps to calculate the respiration rate from the standard DEB
expressed in an energy-length-time framework
• Hard to believe at first (for me!) but true (and we gained a lot of
insights from it) : otoliths and other biocarbonates are also DEB
products
2005 2015 and next!
• Participant of the Brest group of the 2005 DEB telecourse : 10th DEB
anniversary for Jonathan, Fred, me and a few others you’ll meet
 Changed the direction of my anchovy PhD project
 Helped me getting an interview for a post-doc position in Santa Barbara with Roger
Nisbet
 Got me a job in Brest !
• Brest group: DEB applications inmarine ecology, aquaculture and fisheries
sciences:
16 people! 3 assistant professors, 6 researchers, 2 associated researchers, 1
post-doc, 4 PhD students
+ 5 Master and PhD students in the US, Peru and Mexico
 Call for Post-docs and PhD’s  contact us!
Grand merci : Bas, Roger, Brest group – Jonathan, Fred, Marianne, Cédric and
Véro - , and Starrlight, Dina and Gonçalo for taking me on board
Respiration rate as a function of length
Allometric model =
2 parameters
R = aLb = 0.0516 L2.437
Daphnia pulex (Kooijman, 2010)
Respiration rate as a function of length
Allometric model =
2 parameters
R = aLb = 0.0516 L2.437
R = aL2 + bL3
= 0.0336 L2 + 0.01845 L3
DEB model =
same number of
parameters
but parameters with
measureable
dimensions
Daphnia pulex (Kooijman, 2010)
Respiration rate as a function of length
Assimilation
proportional to L2
R = aLb = 0.0516 L2.437
R = aL2 + bL3
= 0.0336 L2 + 0.01845 L3
Dissipation prop to L3
Growth prop. to
L2 and L3
Daphnia pulex (Kooijman, 2010)
Respiration in DEB theory
• Weighted sum of L2 and L3 processes as product formation is a
weighted sum of :
– Assimilation (L2),
– Dissipation(L3 - and L2) and
– Growth (L3 and L2)
• Definition of Dissipation : sum of somatic maintenance,
maturity maintenance, development and reproduction
overheads
pD = pS + pJ + pR
For embryos and juveniles
pD = pS + pJ +(1- kapR )pR For adults
Definition of products in a DEB context
(a)
(b)
Food
(a)
Assimilation
Products
Assimilation pA
Food
(b)
Faeces
Reserve
Growth
Reserve
Products

Growth
Products
Growth pG
Growth pG
pC
1
Somatic
maintenance pM
Somatic
maintenance pM
Structure
Structure
Fa
pA
Assimilation
Products
Assimilation pA
Dissipation
Products
pC
1
(c)
Maturity
maintenance pJ
Maturity
maintenance pJ
Dissipation
Products
pA
(c)
CO2
(d)
ReproductionReproduction
pR
Reproduction
buffer
C
pA pD pG
Reproduction pR
buffer (d)
pA pD pG
pD pG
pD pG
Product formation can occur during one, two or all the three DEB
transformations : assimilation, dissipation and growth
(a)
(b)
Food
(a)
Assimilation
Products
Assimilation pA
Food
(b)
Faeces
Reserve
Growth
Reserve
Products

Growth
Products
Growth pG
Growth pG
pC
1
Somatic
maintenance pM
Somatic
maintenance pM
Structure
Structure
Fa
pA
Assimilation
Products
Assimilation pA
Dissipation
Products
pC
1
(c)
Maturity
maintenance pJ
Maturity
maintenance pJ
Dissipation
Products
pA
(c)
CO2
(d)
ReproductionReproduction
pR
Reproduction
buffer
C
pA pD pG
Reproduction pR
buffer (d)
pA pD pG
pD pG
pD pG
Torpedo marmorata example
• Constant food and temperature = 15°C
• Weight, length and respiration data from birth to max age
• Time (d), Wet weight (g) , Total length (cm), Respiration rate
(mg O2 /h)
• Let’s start with the first 2 univariate datasets: t-L and L-W
t-L and L-W predictions
• Defined in predict_Torpedo_marmorata.m
• Lw as a function of t?
– Constant food  von Bertalanffy growth
L_w = L_wi – (L_wi – L_wb) * exp( -r_BT * t)
– L_wi? L_wb? r_BT? t?
• Ww as a function of Lw ?
– Constant food  constant reserve density
– Ww = Ww_V + Ww_E (+ Ww_ER)
predict_Torpedo_marmorata.m
• t = time from birth to max age : defined in mydata_Torpedo_marmorata.m
• Parameters
–
–
–
–
v: primary parameter defined in pars_init_Torpedo_marmorata.m
T_A : environmental parameter
k_M, L_m, g, k, v_Hb: computed in parscomp_st.m
del_M :
auxiliary param defined in pars_init_Torpedo_marmorata.m
• Environment
– X  f:
treated as param defined in pars_init_Torpedo_marmorata.m
– T  TC_tL : calculated by tempcorr.m
TC_tL = tempcorr(temp.tL, T_ref, T_A);
• Initial conditions : at E_Hb defined in pars_init_Torpedo_marmorata.m
– L_b (NOTA : E_b = f [E_m]L_b, E_Rb = 0) calculated by get_lb.m
pars_lb = [g; k; v_Hb]
– Lw_b = get_lb(pars_lb, f) * L_m/ del_M;
• Von Bertalanffy parameters
– rB = 1 / (3 kM + 3 f L_m / v)
– Lw_i = f * L_m / del_M
predict_Torpedo_marmorata.m
• Calculation
– EL = Lw_i - (Lw_i - Lw_b) * exp( - TC_tL * r_B * tL(:,1));
– Ww_V = (EL * del_M)^3  assumption that d_V = 1 g/cm^3 for wet
weight
– Ww_E = (EL * del_M)^3 * f * w
with w = m_Em * w_E * d_E/ d_V/ w_V;
L-JO predictions
• Hold your breath, we’ll dive deeper into DEB notations!