estimation of deb parameters bas kooijman dept theoretical biology vrije universiteit amsterdam...

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

0000

00

0

000

00

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