Estimation of DEB parameters

1. 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

2. 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

3. 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

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

5. Growth at constant food 3.7 length, mm Von Bert growth rate -1, d time, d ultimate length, mm Von Bertalanffy growth curve: time Length L. at birth ultimate L. von Bert growth rate energy conductance maint. rate coefficient shape coefficient

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

7. One-sample case

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

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

10. Reserve vs structure structure carbohydrate lipid cumulative fraction reserve Kcal/g wet weight protein time, d 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.

11. Reserve Evs structure V

12. Reserve Evs structure V

13. 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; kJ = 1.7 d-1; kM = 1.7 d-1; g = 0.69; UHb = 0.0046 d mm2; UHp = 0.042 d mm2 • Reconstruction: • one scaled functional response per individual • one scaled functional response per haul • Observation: • min egg volume = 16 max egg volume  volume increases

14. Food density from reprod data Reconstruction basis:

15. 1-18 1-19 1-17 1-21  N 2-16 2-17 2-18 1-23  N 2-19 2_20 2-21 2-22  N 3-17 3-19 3-20 3-21  N  L  L  L  L

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

17. Food density from reprod data food different for each ind food the same for ind in one haul initial egg volume, mm3  f  f scaled functional resp, f  week  week