Estimation of DEB parameters Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam 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

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

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 time, dtime of reserve depletion, d protein lipid carbohydrate Data from Whyte J.N.C., Englar J.R. & Carswell (1990). Aquaculture 90: Body mass in starving pacific oyster Crassooestrea gigas at 10°C reserve structure

Reserve E vs structure V

100 g wet weighttotalproteinlipidcarbohydrate  C M C0, kcal  C J CM, kcal/d  C, kJ/C-mol M C0, C-mol J CM, mmol/d M CE =M E, mol/mol M CV =M V, mol/molt 0 = 200 d M CV =M V, mol/molt 0 = 400 d M CV =M V, mol/molt 0 = 600 d

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 f daughter (birth) = f mother (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; U H b = d mm 2 ; U H p = d mm 2 Reconstruction: one scaled functional response per individual one scaled functional response per haul Observation : min egg volume = 16 max egg volume  volume increases

Food density from reprod data Reconstruction basis:

_  L  N

 L  N N: # eggs in brood pouch L: body length f : single estimated parameter per graph

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