1. Theoretical Ecology course 2012 DEB theory
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam

2. Contents of 4 lectures on DEB theory
Preliminary concepts
required to link predictions to data
Outline of basic theory
for a 1-reserve, 1-structure isomorph
Implications of theory
for mass fluxes, body size scaling relationships
Population consequences
interactions between individuals

3. Dynamic Energy Budget theory
for metabolic organization
links levels of organization
molecules, cells, individuals, populations, ecosystems
scales in space and time: scale separation
interplay between biology, mathematics,
physics, chemistry, earth system sciences
framework of general systems theory
quantitative; first principles only
equivalent of theoretical physics
fundamental to biology; many practical applications
(bio)production, medicine, (eco)toxicity, climate change

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

5. Some DEB principles life as coupled chemical transformations
life cycle perspective of individual as primary target
energy & mass balances
stoichiometric constraints via Synthesizing Units
surface area/ volume relationships
spatial structure & transport
synthrophy (basis for symbioses)
homeostasis
intensive/extensive parameters: scaling
evolutionary perspective

6. Empirical patterns Feeding During starvation, organisms are able to
reproduce, grow and survive for some time
At abundant food, the feeding rate is at some
maximum, independent of food density
Growth
Many species continue to grow after
reproduction has started
Growth of isomorphic organisms at abundant
food is well described by the von Bertalanffy
For different constant food levels the inverse von
Bertalanffy growth rate increases linearly with
ultimate length
The von Bertalanffy growth rate of different species
decreases almost linearly with the maximum
body length
Fetuses increase in weight approximately
proportional to cubed time
Reproduction
Reproduction increases with size intra-specifically,
but decreases with size inter-specifically
Respiration
Animal eggs and plant seeds initially hardly use O2
The use of O2 increases with decreasing
mass in embryos and increases with mass in
juveniles and adults
The use of O2 scales approximately with
body weight raised to a power close to 0.75
Animals show a transient increase in metabolic
rate after ingesting food (heat increment of feeding)
Stoichiometry
The chemical composition of organisms depends on
the nutritional status (starved vs well-fed)
The chemical composition of organisms growing
at constant food density becomes constant
Energy
Dissipating heat is a weighted sum of 3 mass flows:
CO2, O2 and N-waste

7. Supply-demand spectrum 1.2.5
Species can be ranked in the gradient from supply to demand systems as stages in the evolution toward a high level of homeostasis.
Extreme supply or demand systems don’t exist, all species represent a mixture of these extremes.
Plants come close to the supply-end of the spectrum and can adapt their metabolism to the local environment relatively well.
Demand systems adapt their metabolism much less and compensate that by a high level of behavioural flexibility.
The characterizing property of demand systems is that the use of resources (growth, reproduction) is `pre-programmed’, which causes a particular need for food and growth curves that are given functions of age.

8. Energy Budgets Basic processes All have ecological implications
Feeding
Digestion
Storing
Growth
Maturation
Maintenance
Reproduction
Product formation
Aging
All have ecological implications
All interact during the life cycle

9. 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

10. Surface area/volume interactions
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 environment
food availability for daphnids: amount of algae per volume environment
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

11. 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

12. Shape correction function
at volume V
actual surface area at volume V
isomorphic surface area at volume V =
for
V1-morphs are special because
surfaces do not play an explicit role
their population dynamics reduce to
an unstructured dynamics; reserve densities
of all individuals converge to the same value
in homogeneous environments
V0-morph
V1-morph
isomorph
Static mixtures between V0- and V1-morphs for aspect ratio

13. 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

14. Mixtures of changes in shape 2
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

15. Biomass: reserve(s) + structure(s)
Reserve(s), structure(s): generalized compounds,
mixtures of proteins, lipids, carbohydrates: fixed composition
Reasons to delineate reserve, distinct from structure
metabolic memory
biomass composition depends on growth rate
explanation of
respiration patterns (freshly laid eggs don’t respire)
method of indirect calorimetry
fluxes are linear sums of assimilation, dissipation and growth
fate of metabolites
(e.g. conversion into energy vs buiding blocks)
inter-species body size scaling relationships

16. Reserve vs structure 2.3
Reserve does not mean: “set apart for later use”
compounds in reserve can have active functions
Life span of compounds in
reserve: limited due to turnover of reserve
all reserve compounds have the same mean life span
structure: controlled by somatic maintenance
structure compounds can differ in mean life span
Important difference between reserve and structure:
no maintenance costs for reserve
Empirical evidence:
freshly laid eggs consist of reserve and do not respire

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

18. Body size length: depends on shape and choice (shape coefficient)
volumetric length: cubic root of volume; does not depend on shape
contribution of reserve in lengths is usually small
use of lengths unavoidable because of role of surfaces and volumes
weight: wet, dry, ash-free dry
contribution of reserve in weights can be substantial
easy to measure, but difficult to interpret
C-moles (number of C-atoms as multiple of number of Avogadro)
1 mol glucose = 6 Cmol glucose
useful for mass balances, but destructive measurement
Problem: with reserve and structure, body size becomes bivariate
We have only indirect access to these quantities

19. Storage Plants store water and carbohydrates,
Animals frequently store lipids
Many reserve materials
are less visible
specialized
Myrmecocystus
serves as
adipose tissue
for the ant colony

20. Flux vs Concentration concept “concentration” implies
spatial homogeneity (at least locally)
biomass of constant composition for intracellular compounds
concept “flux” allows spatial heterogeneity
classic enzyme kinetics relate
production flux to substrate concentration
Synthesizing Unit kinetics relate
production flux to substrate flux
in homogeneous systems: flux  conc. (diffusion, convection)
concept “density” resembles “concentration”
but no homogeneous mixing at the molecular level
density = ratio between two amounts

21. Macrochemical reaction eq 3.5

22. Synthesizing units Are enzymes that follow classic enzyme kinetics
E + S  ES  EP  E + P
With two modifications:
back flux is negligibly small
E + S  ES  EP  E + P
specification of transformation is on the basis of
arrival fluxes of substrates rather than concentrations
The concept concentration is problematic in
spatially heterogeneous environments, such as inside cells
In spatially homogeneous environments,
arrival fluxes are proportional to concentrations

23. 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

24. Symbiogenesis
2.7 Ga
2.1 Ga
1.27 Ga
phagocytosis

25. Life stages embryo juvenile adult fertilization birth death puberty
baby
infant
weaning
fertilization
birth
death
puberty
Essential: switch points, not periods
birth: start of feeding
puberty: start of allocation to reproduction
Switch points sometimes in reversed order (aphids)

26. Arrhenius relationship
ln rate
reproduction
young/d
ingestion
106 cells/h
Daphnia magna
growth, d-1
aging, d-1
104 T-1, K-1

27. Arrhenius relationship
ln pop growth rate, h-1
r1 = h-1
T1 = K
TH = K
TL = K
TA = K
TAL = K
TAH = K
103/T, K-1
103/TH
103/TL

28. Concept overview supply-demand spectrum not age, but size
surface area/volume
iso-, V0-, V1-morphs
shape correction function
reserve & structure
5 types of homeostasis
body size: weight, Cmol, ..
body composition
flux vs concentration
macrochemical reactions
Synthesizing Units
evolutionary aspects
life stages
effects of temperature