Laure PecquerieLaboratoire des Sciences de l’Environnement Marin

UMR LEMAR, IRDlaure.pecquerie@ird.fr

21st -22nd April 2015,DEB Course 2015, Marseille

Metabolic products within a DEB context

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)

Outlinelecture 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

Daphnia pulex (Kooijman, 2010)

Respiration rate as a function of length

R = aLb = 0.0516 L2.437

Allometric model = 2 parameters

Respiration rate as a function of length

R = aLb = 0.0516 L2.437

R = aL2 + bL3

= 0.0336 L2 + 0.01845 L3

Daphnia pulex (Kooijman, 2010)

Allometric model = 2 parameters

DEB model = same number of parameters but parameters with measureable dimensions

Respiration rate as a function of length

R = aLb = 0.0516 L2.437

R = aL2 + bL3

= 0.0336 L2 + 0.01845 L3

Daphnia pulex (Kooijman, 2010)

Assimilation proportional to L2

Dissipation prop to L3

Growth prop. to L2 and L3

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

For embryos and juveniles

For adults

Definition of products in a DEB context

Reserve

Structure

1

Assimilation pA

Growth pG

Somaticmaintenance pM

Maturitymaintenance pJ

Reproduction pR

Food

pC

Reproductionbuffer

Assimilation Products

Dissipation Products

Growth Products

pDpA

pA

Faeces

CO2

pD pG

pG

(b)

(c)

(d)

(a)

Reserve

Structure

1

Assimilation pA

Growth pG

Somaticmaintenance pM

Maturitymaintenance pJ

Reproduction pR

Food

pC

Reproductionbuffer

Assimilation Products

Dissipation Products

Growth Products

pDpA

pA

Faeces

CO2

pD pG

pG

(b)

(c)

(d)

(a)

Reserve

Structure

1

Assimilation pA

Growth pG

Somaticmaintenance pM

Maturitymaintenance pJ

Reproduction pR

Food

pC

Reproductionbuffer

Assimilation Products

Dissipation Products

Growth Products

pDpA

pA

Faeces

CO2

pD pG

pG

(b)

(c)

(d)

(a)

Reserve

Structure

1

Assimilation pA

Growth pG

Somaticmaintenance pM

Maturitymaintenance pJ

Reproduction pR

Food

pC

Reproductionbuffer

Assimilation Products

Dissipation Products

Growth Products

pDpA

pA

Faeces

CO2

pD pG

pG

(b)

(c)

(d)

(a)

Product formation can occur during one, two or all the three DEB transformations : assimilation, dissipation and growth

Reserve

Structure

1

Assimilation pA

Growth pG

Somaticmaintenance pM

Maturitymaintenance pJ

Reproduction pR

Food

pC

Reproductionbuffer

Assimilation Products

Dissipation Products

Growth Products

pDpA

pA

Faeces

CO2

pD pG

pG

(b)

(c)

(d)

(a)

Reserve

Structure

1

Assimilation pA

Growth pG

Somaticmaintenance pM

Maturitymaintenance pJ

Reproduction pR

Food

pC

Reproductionbuffer

Assimilation Products

Dissipation Products

Growth Products

pDpA

pA

Faeces

CO2

pD pG

pG

(b)

(c)

(d)

(a)

Reserve

Structure

1

Assimilation pA

Growth pG

Somaticmaintenance pM

Maturitymaintenance pJ

Reproduction pR

Food

pC

Reproductionbuffer

Assimilation Products

Dissipation Products

Growth Products

pDpA

pA

Faeces

CO2

pD pG

pG

(b)

(c)

(d)

(a)

Reserve

Structure

1

Assimilation pA

Growth pG

Somaticmaintenance pM

Maturitymaintenance pJ

Reproduction pR

Food

pC

Reproductionbuffer

Assimilation Products

Dissipation Products

Growth Products

pDpA

pA

Faeces

CO2

pD pG

pG

(b)

(c)

(d)

(a)

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)

• 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 * wwith w = m_Em * w_E * d_E/ d_V/ w_V;

predict_Torpedo_marmorata.m

L-JO predictions

• Hold your breath, we’ll dive deeper into DEB notations!