Estimation of DEB parameters Bas Kooijman Dept theoretical

Estimation of DEB parameters Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio. vu. nl http: //www. bio. vu. nl/thb/ Nantes, 2007/04/24

Auxiliary theory Quantities that are easy to measure (e. g. respiration, body weight) have contributions form several processes they are not suitable as variables in explenatory models Variables in explenatory models are not directly measurable we need auxiliary theory to link core theory to measurements Standard DEB model: isomorph with 1 reserve & 1 structure that feeds on 1 type of food

DEB parameters • primary parameters determine food uptake changes of state variables (reserve, maturity, structure) • compound parameters: functions of primary parameters • composition parameters food, reserve, structure, products (feaces, N-waste) • thermodynamic parameters free energies (chemical potentials) entropies dissipating heat

Reserve & maturity: hidden Maturity: information, not mass or energy quantified as cumulated mass of reserve that is invested Scale reserve & maturity

3. 7 Von Bert growth rate -1, d length, mm Growth at constant food time, d Von Bertalanffy growth curve: ultimate length, mm time Length L. at birth ultimate L. von Bert growth rate energy conductance maint. rate coefficient shape coefficient

measured quantities primary pars Standard DEB model (isomorph, 1 reserve, 1 structure) reserve & maturity: hidden variables measured for 2 food levels primary parameters

One-sample case

Two-sample case: D. magna 20°C Optimality of life history parameters?

Primary thermodynamic pars Given primary parameters: • get composition parameters • get mass fluxes (respiration) • get entropies, free energies

Reserve vs structure Kcal/g wet weight cumulative fraction structure time, d carbohydrate lipid reserve protein time of reserve depletion, d Body mass in starving pacific oyster Crassooestrea gigas at 10°C Data from Whyte J. N. C. , Englar J. R. & Carswell (1990). Aquaculture 90: 157 -172.

Reserve E vs structure V

Reserve E vs structure V 100 g wet weight total protein lipid carbohydrate CMC 0, kcal 64. 81 30. 54 16. 80 16. 87 C JCM, kcal/d 0. 1042 0. 0408 0. 0200 0. 0358 401 616 516 0. 319 0. 114 0. 137 JCM, mmol/d 0. 426 0. 136 0. 290 MCE =ME , mol/mol 0. 500 0. 159 0. 341 C, k. J/C-mol MC 0, C-mol 0. 570 MCV =MV , mol/mol t 0 = 200 d 0. 546 0. 191 0. 263 MCV =MV , mol/mol t 0 = 400 d 0. 537 0. 185 0. 278 MCV =MV , mol/mol t 0 = 600 d 0. 531 0. 181 0. 288

Food density from reprod data Data from Stella Berger, univ München, on Daphnia hyalina Observed in enclosure (1 haul per week): • length of individuals • # eggs in brood pouch • length, width of an egg: test of maternal effects fdaughter(birth) = fmother(egg laying) “Given” par values derived from Daphnia magna = 0. 8; v = 3. 24 mm d-1; k. J = 1. 7 d-1; k. M = 1. 7 d-1; g = 0. 69; UHb = 0. 0046 d mm 2; UHp = 0. 042 d mm 2 Reconstruction: • one scaled functional response per individual • one scaled functional response per haul Observation: • min egg volume = 16 max egg volume increases

Food density from reprod data Reconstruction basis:

1 -18 1 -19 2 -16 2 -17 2_20 2 -21 1 -21 N 1 -17 2 -18 N 1 -23 2 -22 N 2 -19 3 -20 3 -21 N 3 -17 L L

3 -25 4 -16 4 -19 4 -20 4 -17 N 3 -23 4 -21 N 4 -18 L 4 -24 4 -25 N 4 -22 L L N: # eggs in brood pouch L: body length f : single estimated parameter per graph L

Food density from reprod data food the same for ind in one haul f f week scaled functional resp, f initial egg volume, mm 3 food different for each ind