1. Introduction to DEB theory & applications in fishery sciences
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam
Trondheim, 2007/11/01

2. Introduction to DEB theory & applications in fishery sciences
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam
Contents:
What is DEB theory?
Evolution & homeostasis
Standard model & calorimetry
Product formation
Allocation
Unexpected links
Social behaviour
Reconstruction
Body size scaling
Trondheim, 2007/11/01

3. Dynamic Energy Budget theory
for metabolic organization
consists of a set of consistent and coherent assumptions
uses framework of general systems theory
links levels of organization
scales in space and time: scale separation
quantitative; first principles only
equivalent of theoretical physics
interplay between biology, mathematics,
physics, chemistry, earth system sciences
fundamental to biology; many practical applications

4. Research strategy
1) use general physical-chemical principles to
develop an educated quantitative expectation for the
eco-physiological behaviour of a generalized species
2) estimate parameters for any specific case
compare the values with expectations from scaling relationships
deviations reveal specific evolutionary adaptations
3) study deviations from model expectations
learn about the physical-chemical details that matter in this case
but had to be ignored because they not always apply
Deviations from a detailed generalized expectation provide
access to species-specific (or case-specific) modifications

5. Empirical special cases of DEB
DEB theory is axiomatic,
based on mechanisms
not meant to glue empirical models
Since many empirical models
turn out to be special cases of DEB theory
the data behind these models support DEB theory
This makes DEB theory very well tested against data
DEB theory reveals when to expect deviations
from these empirical models
year
author
model
1780
Lavoisier
multiple regression of heat against mineral fluxes
1950
Emerson
cube root growth of bacterial colonies
1825
Gompertz
Survival probability for aging
1951
Huggett & Widdas
foetal growth
1889
Arrhenius
temperature dependence of physiological rates
Weibull
survival probability for aging
1891
Huxley
allometric growth of body parts
1955
Best
diffusion limitation of uptake
1902
Henri
Michaelis--Menten kinetics
1957
Smith
embryonic respiration
1905
Blackman
bilinear functional response
1959
Leudeking & Piret
microbial product formation
1910
Hill
Cooperative binding
Holling
hyperbolic functional response
1920
Pütter
von Bertalanffy growth of individuals
1962
Marr & Pirt
maintenance in yields of biomass
1927
Pearl
logistic population growth
1973
Droop
reserve (cell quota) dynamics
1928
Fisher & Tippitt
Weibull aging
1974
Rahn & Ar
water loss in bird eggs
1932
Kleiber
respiration scales with body weight3/ 4
1975
Hungate
digestion
Mayneord
cube root growth of tumours
1977
Beer & Anderson
development of salmonid embryos

6. Individual  Ecosystem
population dynamics is derived from
properties of individuals + interactions between them
evolution according to Darwin:
variation between individuals + selection
material and energy balances:
most easy for individuals
individuals are the survival machines of life

7. Evolution of DEB systems
variable
structure
composition
strong
homeostasis
for structure
delay of use of
internal substrates
increase of
maintenance costs
inernalization of
maintenance
installation of
maturation program 1 2 3 4 5 6
prokaryotes 7 9
plants 8
animals
Kooijman & Troost 2007
Biol Rev, 82, 1-30
reproduction
juvenile  embryo + adult
strong homeostasis
for reserve
specialization
of structure

8. Homeostasis strong homeostasis
constant composition of pools (reserves/structures)
generalized compounds, stoichiometric contraints on synthesis
weak homeostasis
constant composition of biomass during growth in constant environments
determines reserve dynamics (in combination with strong homeostasis)
structural homeostasis
constant relative proportions during growth in constant environments
isomorphy .work load allocation
ectothermy  homeothermy  endothermy
supply  demand systems
development of sensors, behavioural adaptations

9. Standard DEB model food faeces reserve structure  offspring
Definition of standard model:
Isomorph
with 1 reserve & 1 structure
feeds on 1 type of food
has 3 life stages
(embryo, juvenile, adult)
food
faeces
assimilation
reserve
feeding
defecation
Extensions of standard model:
more types of
food and food qualities
reserve (autotrophs)
structure (organs, plants)
changes in morphology
different number of life stages
structure
somatic
maintenance
growth 
1-
maturity
maintenance
offspring
maturation
reproduction

10. Three basic fluxes assimilation: substrate  reserve + products
linked to surface area
dissipation: reserve  products
somatic maintenance: linked to surface area & structural volume
maturity maintenance: linked to maturity
maturation or reproduction overheads
growth: reserve  structure + products
Product formation = A  assimilation + B  dissipation + C  growth
Examples: heat, CO2, H2O, O2, NH3
Indirect calorimetry: heat = D  O2-flux + E  CO2-flux + F  NH3-flux

11. Product Formation ethanol pyruvate glycerol According to
Dynamic Energy Budget theory:
Product formation rate =
wA . Assimilation rate +
wM . Maintenance rate +
wG . Growth rate
For pyruvate: wG<0
ethanol
pyruvate, mg/l
glycerol, ethanol, g/l
pyruvate
glycerol
throughput rate, h-1
Glucose-limited growth of Saccharomyces
Data from Schatzmann, 1975

12. Static Mixtures of V0 & V1 morphs
volume, m3
hyphal length, mm
Bacillus  = 0.2
Collins & Richmond 1962
Fusarium  = 0
Trinci 1990
time, h
time, min
volume, m3
volume, m3
Escherichia  = 0.28
Kubitschek 1990
Streptococcus  = 0.6
Mitchison 1961
time, min
time, min

13. -rule for allocation Ingestion  Respiration  Reproduction  Growth:
Ingestion rate, 105 cells/h
O2 consumption, g/h
Length, mm
Length, mm
Reproduction 
Length, mm
Cum # of young
large part of adult budget
to reproduction in daphnids
puberty at 2.5 mm
No change in
ingest., resp., or growth
Where do resources for
reprod. come from? Or:
What is fate of resources
in juveniles?
Growth:
Von Bertalanffy
Age, d
Age, d

14. Size of body parts Static generalization of -rule whole body heart
weight, g
time, d
time, d
Data: Gille & Salomon 1994 on mallard

15. Tumour growth Dynamic generalization of -rule food faeces reserve 
Allocation to tumour
 relative maint workload
defecation
feeding
food
faeces
assimilation
Isomorphy: [pMU] = [pM]
Tumour tissue:
low spec growth & maint costs
Growth curve of tumour depends on pars
no maximum size is assumed a priori
Model explains dramatic
tumour-mediated weight loss
If tumour induction occurs late,
tumours grow slower
Caloric restriction reduces tumour growth
but the effect fades
reserve
somatic
maintenance
maturity
maintenance 
1-
maint
maturation
reproduction u
1-u
growth
maturity
offspring
structure
tumour
Van Leeuwen et al., 2003
British J Cancer 89,

16. Katja Philipart (NIOZ)
Organ growth
fraction of
catabolic flux
Allocation to velum vs gut
 relative workload
Macoma
low food
Macoma
high food
Relative organ size is weakly homeostatic
Collaboration:
Katja Philipart (NIOZ)

17. Organ size & function Kidney removes N-waste from body
At constant food availability JN = aL2 + bL3
Strict isomorphy: kidney size  L3
If kidney function  kidney size: work load reduces with size
If kidney function  L2 + cL3 for length L of kidney or body
work load can be constant for appropriate weight coefficients
This translates into a morphological design constraint for kidneys

18. Initial amount of reserve
Initial amount of reserve E0 follows from
initial structural volume is negligibly small
initial maturity is negligibly small
maturity at birth is given
reserve density at birth equals that of mother at egg formation
Accounts for
maturity maintenance costs
somatic maintenance costs
cost for structure
allocation fraction  to somatic maintenance + growth
Mean reproduction rate (number of offspring per time):
R = (1-R) JER/E0
Reproduction buffer: buffer handling rules; clutch size

19. Embryonic development
Crocodylus johnstoni,
Data from Whitehead 1987
embryo
yolk
O2 consumption, ml/h
weight, g
time, d
time, d ;
: scaled time
l : scaled length
e: scaled reserve density
g: energy investment ratio

20. DEB theory reveals unexpected links
Streptococcus
O2 consumption, μl/h
Daphnia
1/yield, mmol glucose/ mg cells
1/spec growth rate, 1/h
Length, mm
respiration  length in individual animals & yield  growth in pop of prokaryotes have a lot in common, as revealed by DEB theory
Reserve plays an important role in both relationships,
but you need DEB theory to see why and how

21. Not age, but size:
: These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake
Trichopsis vittatus

22. Rules for feeding R1 a new food particle appears at a random site
within the cube at the moment one of the resident
particles disappears.
The particle stays on this site till it disappears;
the particle density X remains constant.
R2 a food particle disappears
at a constant probability rate, or
because it is eaten by the individual(s).
R3 the individual of length L travels in a straight line to the nearest visible food particle at speed  X2/3 L2, eats the particle upon arrival and waits at this site for a time th = {JXm}-1 L-2.
Direction changes if the aimed food particle
disappears or a nearer new one appears.
Speed changes because of changes in length.
R4 If an individual of length L feeds:
scaled reserve density jumps:
e  e + (LX/ L)3
Change of scaled reserve density e:
d/dt e = - e {JXm} LX3/ L;
Change of length L:
3 d/dt L = ({JXm} LX3 e - L kM g) (e + g)-1
At time t = 0:
length L = Lb,; reserve density e = f.
R5 a food particle becomes invisible for an individual of length L1, if an individual of length L1 is within a distance Ls (L2/ L1)2 from the food particle, irrespective of being aimed at.

23. Social interaction  Feeding 2.1.2
determin
expectation
length
reserve density
1 ind
time
time
2 ind
length
reserve density
time
time

24. Otolith growth & opacity
standard DEB model: otolith is a product
otolith growth has contributions from
growth & dissipation
(= maintenance + maturation + reprod overheads)
opacity  relative contribution from growth
DEB theory allows reconstruction
of functional response from opacity data
as long as reserve supports growth
Reconstruction is robust for deviations from
correct temperature trajectory
Laure Pecquerie 2007: reading the otolith

25. Otolith opacity  Functional response
temp correction
functional response
time, d
opacity
time, d
otolith length, m
body length, cm
reserve density
otolith length, m
time, d
time, d
time, d
Laure Pecquerie 2007: reading the otolith

26. Primary scaling relationships
assimilation {JEAm} max surface-specific assim rate  Lm
feeding {b} surface- specific searching rate
digestion yEX yield of reserve on food
growth yVE yield of structure on reserve
mobilization v energy conductance
heating,osmosis {JET} surface-specific somatic maint. costs
turnover,activity [JEM] volume-specific somatic maint. costs
regulation,defence kJ maturity maintenance rate coefficient
allocation  partitioning fraction
egg formation R reproduction efficiency
life cycle [MHb] volume-specific maturity at birth
life cycle [MHp] volume-specific maturity at puberty
aging ha aging acceleration
Kooijman 1986
J. Theor. Biol.
121:
maximum length Lm =  {JEAm} / [JEM]

27. Scaling of metabolic rate 8.2.2
Respiration: contributions from growth and maintenance
Weight: contributions from structure and reserve
Structure ; = length; endotherms
intra-species
inter-species
maintenance
growth

28. Metabolic rate 2 curves fitted: Intra-species Inter-species slope = 1
Log metabolic rate, w
O2 consumption, l/h
2 curves fitted:
endotherms
L L3
L2.44
ectotherms
slope = 2/3
unicellulars
Log weight, g
Length, cm
Intra-species
Inter-species
(Daphnia pulex)

29. Von Bertalanffy growth rate 8.2.2
25 °C
TA = 7 kK
10log von Bert growth rate, a-1
10log ultimate length, mm
10log ultimate length, mm
At 25 °C :
maint rate coeff kM = 400 a-1
energy conductance v = 0.3 m a-1 ↑ ↑

30. DEB tele course 2009 Audience: Organizers:
Free of financial costs; some 250 h effort investment
Program for 2009:
Feb/Mar general theory
April symposium in Brest (2-3 d)
Sept/Oct case studies & applications
Target audience: PhD students
We encourage participation in groups
that organize local meetings weekly
Software package DEBtool for Octave/ Matlab
freely downloadable
Slides of this presentation are downloadable from
Cambridge Univ Press 2000
Audience:
thank you for your attention
Organizers:
thank you for the invitation
Vacancy PhD-position on DEB theory