1. Physical & Chemical Constraints on Population Dynamics
25 year research on
Dynamic Energy Budget
theory for
metabolic organisation
Bas Kooijman
Dept of Theoretical Biology
Vrije Universiteit, Amsterdam
embryo
adult
juvenile
Leiden, 2004/12/10
Hans Metz 60th birthday

2. DEB – ontogeny - IBM 1980 1990 2000 Daphnia von Foerster ecotox
application
1980
embryos
body size
scaling
epidemiol
applications
morph
dynamics
indirect
calorimetry
bifurcation
analysis
micro’s
numerical
methods
1990
food chains
Global
bif-analysis
DEB 1
aging
Synthesizing
Units
NECs
integral
formulations
DEBtox 1
multivar
plants
adaptive
dynamics
tumour
induction
ecosystem
dynamics
DEB 2
2000
adaptation
organ
function
symbioses
ISO/OECD
ecosystem
Self-orginazation
molecular
organisation

3. Space-time scales
Each process has its characteristic domain of space-time scales
system earth
space
ecosystem
population
When changing the space-time scale,
new processes will become important
other will become less important
Individuals are special because of
straightforward energy/mass balances
individual
cell
time
molecule

4. 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
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

5. Some DEB pillars
life cycle perspective of individual as primary target
embryo, juvenile, adult (levels in metabolic organization)
life as coupled chemical transformations (reserve & structure)
time, energy, entropy & mass balances
surface area/ volume relationships (spatial structure & transport)
homeostasis (stoichiometric constraints via Synthesizing Units)
syntrophy (basis for symbioses, evolutionary perspective)
intensive/extensive parameters: body size scaling

6. Basic DEB scheme food faeces reserve structure  offspring defecation
assimilation
reserve
feeding
defecation
structure
somatic
maintenance
growth 
1-
maturity
maintenance
offspring
maturation
reproduction

7. Competitive tumour growth
Allocation to tumour
 relative maint workload
defecation
feeding
food
faeces
assimilation
Isomorphy:
is constant
Tumour tissue:
low spec growth costs
low spec maint costs
reserve
somatic
maintenance
maturity
maintenance 
1-
maint
maturation
reproduction u
1-u
growth
maturity
offspring
Van Leeuwen et al., 2003
The embedded tumour: host physiology
is important for the evaluation of
tumour growth.
British J Cancer 89,
structure
tumour

8. Biomass: reserve(s) + structure(s)
Reserve(s), structure(s): generalized compounds,
mixtures of proteins, lipids, carbohydrates: fixed composition
Compounds in
reserve(s): equal turnover times, no maintenance costs
structure: unequal turnover times, maintenance costs
Reasons to delineate reserve, distinct from structure
metabolic memory
explanation of respiration patterns (freshly laid eggs don’t respire)
biomass composition depends on growth rate
fluxes are linear sums of assimilation, dissipation and growth
basis of method of indirect calorimetry
explanation of inter-species body size scaling relationships

9. Biomass composition nHW nOW O2 nNW CO2
Data Esener et al 1982, 1983; Kleibsiella on glycerol at 35°C
nHW
•μE-1 pA pM pG JC
0.14
1.00
-0.49 JH
1.15
0.36
-0.42 JO
-0.35
-0.97
0.63 JN
-0.31
0.31
0.02
Entropy J/C-mol.K
Glycerol 69.7
Reserve 74.9
Structure 52.0
Sousa et al 2004
Interface, subm
Relative abundance
nOW O2
nNW
Weight yield, mol.mol-1
Spec prod, mol.mol-1.h-1
Spec growth rate, h-1
CO2
Spec growth rate
kE h-1 kM h-1
yEV yXE 1.490
rm h-1 g = 1
nHE 1.66 nOE nNE 0.312
nHV 1.64 nOV nNV 0.189
Spec growth rate, h-1

10. Yield vs growth Streptococcus bovis, Russell & Baldwin (1979)
Marr-Pirt
(no reserve)
DEB
1/yield, mmol glucose/ mg cells
spec growth rate
yield
1/spec growth rate, 1/h
Russell & Cook (1995): this is evidence for down-regulation
of maintenance at low growth rates
DEB theory: high reserve density gives high growth rates
structure requires maintenance, reserves not

11. Inter-species body size scaling
parameter values tend to co-vary across species
parameters are either intensive or extensive
ratios of extensive parameters are intensive
maximum body length is
allocation fraction to growth + maint. (intensive)
volume-specific maintenance power (intensive)
surface area-specific assimilation power (extensive)
conclusion : (so are all extensive parameters)
write physiological property as function of parameters
(including maximum body weight)
evaluate this property as function of max body weight
Kooijman 1986
Energy budgets can explain body size scaling relations
J. Theor. Biol. 121:

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

13. 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)

14. Synthesizing Unit dynamics
SU: Generalized enzyme that operates on fluxes of metabolites
Typical form for changes in bounded fractions
Typical flux of metabolites for
Mixing of types:
Example of mixture between sequential & complementary substrates:

15. Interactions of substrates
Kooijman, 2001
Phil Trans R Soc B
356:

16. Co-metabolism Co-metabolic degradation of
3-chloroaniline by Rhodococcus
with glucose as primary substrate
Data from Schukat et al, 1983
Brandt et al, 2003
Water Research
37,

17. Aggressive competition
V structure; E reserve; M maintenance substrate
priority E  M; posteriority V  M
JE flux mobilized from reserve
specified by DEB theory
JV flux mobilized from structure
 amount of structure (part of maint.)
excess returns to structure
kV dissociation rate SU-V complex
kE dissociation rate SU-E complex
kV kE depend on  such that
kM = yMEkE(E. + EV)+yMVkV .V is constant
JEM, JVM
kV = kE
JEM, JVM
kV < kE
Collaboration:
Tolla, Poggiale, Auger, Kooi, Kooijman JE

18. Behaviour  Energetics
DEB fouraging module: time budgeting
Fouraging feeding + food processing, food selection
feeding  surface area (intra-species), volume (inter-species)
Sleeping repair of damage by free radicals  respiration
respiration scales between surface area & volume
Social interaction feeding efficiency (schooling)
resource partitioning (territory)
mate selection (gene quality  energetic parameter values)
Migration traveling speed and distance: body size
spatial pattern in resource dynamics (seasonal effects)
environmental constraints on reproduction

19. Social inhibition of x  e
sequential
parallel
substrate conc.
No socialization
Implications:
stable co-existence of
competing species
“survival of the fittest”?
absence of paradox of enrichment
x substrate
e reserve
y species 1
z species 2
biomass conc.
Collaboration:
Van Voorn, Gross, Feudel, Kooi, Kooijman
dilution rate

20. Significance of co-existence
Main driving force behind evolution:
Darwin: Survival of the fittest (internal forces)
involves out-competition argument
Wallace: Selection by environment (external forces)
consistent with observed biodiversity
Mean life span of typical species: Ma
Sub-optimal rare species:
not going extinct soon (“sleeping pool of potential response”)
environmental changes can turn rare into abundant species

21. Surface area/volume interactions 2.2
biosphere: thin skin wrapping the earth
light from outside, nutrient exchange from inside is across surfaces
production (nutrient concentration)  volume of environment
food availability for cows: amount of grass per surface area environ
food availability for daphnids: amount of algae per volume environ
feeding rate  surface area; maintenance rate  volume (Wallace, 1865)
many enzymes are only active if linked to membranes (surfaces)
substrate and product concentrations linked to volumes
change in their concentrations gives local info
about cell size; ratio of volume and surface area gives a length

22. Change in body shape Isomorph: surface area  volume2/3
volumetric length = volume1/3
Mucor
Ceratium
Merismopedia
V0-morph:
surface area  volume0
V1-morph:
surface area  volume1

23. Shape correction function
at volume V
actual surface area at volume V
isomorphic surface area at volume V =
for
V0-morph
V1-morph
isomorph
Static mixtures between V0- and V1-morphs for aspect ratio

24. Mixtures of changes in shape
Dynamic mixtures between morphs
V V0-morph
outer annulus behaves as a V1-morph,
inner part as a V0-morph. Result: diameter increases  time
Lichen Rhizocarpon
V iso V0-morph

25. Biofilms solid substrate biomass Isomorph: V1 = 0 mixture between
iso- & V0-morph
V0-morph: V1 = 
biomass grows, but
surface area that is involved
in nutrient exchange does not

26. Size-structured  Unstructured Population Dynamics
Isomorphs: individual-based or pde formulation
V1-morphs: unstructured (ode) formulation
Effect of individuality becomes small if
ratio between largest and smallest body size reduces
This suggest a perturbation method to approximate
a pde with an ode formulation
Need for simplification of ecosystem dynamics

27. Cells, individuals, colonies
vague boundaries
plasmodesmata connect cytoplasm; cells form a symplast: plants
pits and large pores connect cytoplasm: fungi, rhodophytes
multinucleated cells occur; individuals can be unicellular:
fungi, Eumycetozoa, Myxozoa, ciliates, Xenophyophores, Actinophryids, Biomyxa, diplomonads,
Gymnosphaerida, haplosporids, Microsporidia, nephridiophagids, Nucleariidae, plasmodiophorids,
Pseudospora, Xanthophyta (e.g. Vaucheria), most classes of Chlorophyta (Chlorophyceae, Ulvophyceae,
Charophyceae (in mature cells) and all Cladophoryceae, Bryopsidophyceae and Dasycladophyceae))
cells inside cells: Paramyxea
uni- and multicellular stages: multicellular spores in unicellular myxozoa, gametes
individuals can remain connected after vegetative propagation: plants, corals, bryozoans
individuals in colonies can strongly interact
and specialize for particular tasks:
syphonophorans, insects, mole rats
Kooijman, Hengeveld The symbiontic nature
of metabolic evolution In: Reydon, Hemerik (eds)
Current themes in theor biol. Springer, Dordrecht
rotifer
Conochilus
hippocrepis
Heterocephalus glaber

28. Transitions between these types
Trophic interactions
Competition for same resources
size/age-dependent diet choices
Syntrophy on products
faeces, leaves, dead biomass
Parasitism (typically small, relative to host)
biotrophy, milking, sometimes lethal (disease)
interaction with immune system
Predation (typical large, relative to prey)
living individuals, preference for dead/weak
specialization on particular life stages (eggs, juveniles)
inducible defense systems; cannibalism
Transitions between these types
frequently occur

29. Symbiosis
substrate
product

30. Symbiosis
substrate
substrate

31. Steps in symbiogenesis
1 substrate
+ 1 product
taken up each
2 substrates taken up
products degrade
to physiol role
Free-living, homogeneous
Free-living, clustering
Internalization
Structures merge
Reserves merge

32. Symbiogenesis
symbioses: fundamental organization of life based on syntrophy
ranges from weak to strong interactions; basis of biodiversity
symbiogenesis: evolution of eukaryotes (mitochondria, plastids)
DEB model is closed under symbiogenesis:
it is possible to model symbiogenesis of two initially independently
living populations that follow the DEB rules by incremental changes
of parameter values such that a single population emerges that
again follows the DEB rules
essential property for models that apply to all organisms
Kooijman, Auger, Poggiale, Kooi 2003
Quantitative steps in symbiogenesis and the evolution of homeostasis
Biological Reviews 78:

33. Resource dynamics
Typical approach

34. Prey/predator dynamics
Usual form
for densities prey x and predator y:
Problems:
Not clear how dynamics depends on properties of individuals,
which change during life cycle
If i(x) depends on x: no conservation of mass; popular: i(x)  x(1-x/K)
If yield Y is constant: no maintenance, no realism If
feeding function f(cx,cy)  cf(x,y) and/or
input function i(cx)  ci(x) and/or
output function o(cx)  co(x)
for any c>0: no spatial scaling (amount  density)
Conclusions:
include inert zero-th trophic level (substitutable by mass conservation)
need for mechanistic individual-based population models
Kooi et al 1997 J. Biol. Systems, 1: 77-85

35. Resource dynamics
Nutrient

36. Resource dynamics
Nutrient

37. Resource dynamics
Nutrient

38. Effects of parasites On individuals: Many parasites
increase  (chemical manipulation)
harvest (all) allocation to dev./reprod.
Results
larger body size  higher food intake
reduced reproduction
On populations: Many small parasites
convert healthy (susceptible) individuals to affected ones on contact
convert affected individuals into non-susceptible ones
Globif project NWO-CLS program
Van Voorn, Kooi, Kooijman

39. Producer/consumer dynamics
: hazard rate
nutr reserve
of producer
: total nutrient in
closed system
spec growth
of consumer
special case:
consumer is not nutrient limited
Kooijman et al 2004
Ecology, 85,

40. Producer/consumer dynamics
nutrient limited
Consumer not
nutrient limited
homoclinic
bifurcation
tangent
bifurcation
transcritical
Hopf
bifurcation

41. 1-species mixotroph community
Mixotrophs are
producers, which live
off light and nutrients
as well as
decomposers, which live
off organic compounds
which they produce by
aging
Simplest community with
full material cycling
Kooijman, Dijkstra, Kooi 2002 J. Theor. Biol. 214:

42. Canonical community Short time scale: Long time scale: Mass recycling
in a community
closed for mass
open for energy
Long time scale:
Nutrients leaks and influxes
Memory is controlled by
life span (links to body size)
Spatial coherence is controlled by
transport (links to body size)
Kooijman, Nisbet 2000 How light and nutrients affect life in a closed bottle. In:
Jørgensen, S. E (ed) Thermodynamics and ecological modelling. CRC, 19-60

43. Self organisation of ecosystems
homogeneous environment, closed for mass
start from mono-species community of mixotrophs
parameters constant for each individual
allow incremental deviations across generations
link extensive parameters (body size segregation)
study speciation using adaptive dynamics
allow cannibalism/carnivory
study trophic food web/piramid:
coupling of structure & function
study co-evolution of life, geochemical dynamics , climate
adaptive dynamics applied to multi-character DEB models
Troost et al 2004 Math Biosci, to appear; Troost et al 2004 Am Nat, submitted
Collaboration: Metz, Troost, Kooi, Kooijman

44. DEB tele-course 2005 Feb – April 2005, 10 weeks, 200 h
no financial costs