Laure Pecquerie Laboratoire des Sciences de l’Environnement Marin UMR LEMAR, IRD 21 st -22 nd 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 O 2 consumption and CO 2 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 : 10 th 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 = aL b = L Allometric model = 2 parameters

Respiration rate as a function of length R = aL b = L R = aL 2 + bL 3 = L L 3 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 = aL b = L R = aL 2 + bL 3 = L L 3 Daphnia pulex (Kooijman, 2010) Assimilation proportional to L 2 Dissipation prop to L 3 Growth prop. to L 2 and L 3

Respiration in DEB theory Weighted sum of L 2 and L 3 processes as product formation is a weighted sum of : – Assimilation (L 2 ), – Dissipation(L 3 - and L 2 ) and – Growth (L 3 and L 2 ) 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

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

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 O 2 /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 * w with 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!