Post on 20-Dec-2015
Estimation of DEB parametersBas Kooijman
Dept theoretical biologyVrije Universiteit Amsterdam
Bas@bio.vu.nlhttp://www.bio.vu.nl/thb/
Marseille, 2007/01/18
Auxiliary theoryQuantities 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, d ultimate length, mm
leng
th, m
m
M
M
δfVfLLvLδkr
trLLLtL
mm
MB
Bb
//33
)exp()()(
3/1
11
LLLt
b
Mδkvr
M
BtimeLengthL. at birthultimate L.
von Bert growth rateenergy conductancemaint. rate coefficientshape coefficient
vδ /3 M
Von
Ber
t gro
wth
rat
e -1, d
13 Mk
Von Bertalanffy growth curve:
measured quantities primary parsStandard DEB model (isomorph, 1 reserve, 1 structure)reserve & maturity: hidden variables
measuredfor 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
Kca
l/g
wet
wei
ght
cum
ulat
ive
frac
tion
time, d time of reserve depletion, d
protein
lipid
carbohydrate
Data from Whyte J.N.C., Englar J.R. &Carswell (1990). Aquaculture 90: 157-172.
Body mass in starving pacific oyster Crassooestrea gigas at 10°C
reserve
structure
Reserve E vs structure V
n)compositio structure fixes (this/)(/
n)compositio reserve fixes (this//
;known; is / that Suppose
compounds allfor ,for estimatesin results Regressionconstant /,/ rate;own itsat decreasecan compoundEach
;)/(; timedepletion reserve and compoundfor ))(/()(
00
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VMCCVVC
i i MCCVi EMVC
i j EECMCMCEMMC
i VVCi EECi MCi C
iMCC
VCVECE
CVCVCEMECECMCMC
EMECECVC
MJtMMM
JtMMtJMM
MMJJJJ
MMMMJMt
CJMMMMM
tJMMJMMJtJMtCJttMMMtM
iii
iii
iiii
iiii
ii
Reserve E vs structure V
100 g wet weight
total protein lipid carbohydrate
CMC0, kcal 64.81 30.54 16.80 16.87
C JCM, kcal/d 0.1042 0.0408 0.0200 0.0358
C, kJ/C-mol 401 616 516
MC0, C-mol 0.570 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
MCV =MV , mol/mol
t0 = 200 d 0.546 0.191 0.263
MCV =MV , mol/mol
t0 = 400 d 0.537 0.185 0.278
MCV =MV , mol/mol
t0 = 600 d 0.531 0.181 0.288