1. The scaling of metabolism in the perspective of DEB theory
Bas Kooijman
Dept theoretical biology
VU University Amsterdam
Krakow, 2015/08/27/11:45

2. Dynamic Energy Budget
Start: Aug 1979 understanding effects of toxicants. Since then: 50 PhD’s
Now: bibliography of 500 DEB papers:
Dynamic:
Full life cycle: embryo, juvenile, adult
Energy:
Feeding
Digestion
Storing
Growth
Maturation
Maintenance
Reproduction
Product formation
Aging
Budget:
Conservation: energy, mass, time, isotopes

3. Standard DEB scheme food faeces reserve structure  offspring
1 food type, 1 reserve, 1 structure, isomorph
time: searching & handling
feeding  surface area
weak & strong homeostasis
κ-rule for allocation to soma
maintenance has priority
somatic maint  structure
maturity maint  maturity
stage transition: maturation
embryo: no feeding, reprod
juvenile: no reproduction
adult: no maturation
maternal effect: reserve density
at birth equals that of mother
initially: zero structure, maturity
egg = blob of reserve
food
faeces
assimilation
reserve
feeding
defecation
structure
somatic
maintenance
growth 
1-
maturity
maintenance
offspring
maturation
reproduction
Assumptions of standard DEB model as member of DEB models
One food type of constant composition and particle size that can be used to complete life cycle
One reserve type
One structure type
Isomorphy
only food is limiting, not e.g. dioxygen
Extensions that are sometimes included in the standard DEB model
foetal development (as alternative to egg development)
ageing
metabolic acceleration between birth and metamorphosis
reproduction
via reproduction buffer
buffer handling rules

4. Add_my_pet www.bio.vu.nl/thb/deb/deblab/
started in Feb 2009 as exercise in DEB course (DEBtool application)
referenced data, par-estimates, implied properties, Matlab code
now 400 animal species most phyla, all chordate orders
very good fits (typically: mean relative error < 0.2)
Jan 2015 new set-up. Conversion completed by Dec 2015

5. Concepts

6. Inter-species body size scaling
parameter values tend to co-vary across species
parameters are either intensive or extensive
appropriate ratios of extensive parameters are intensive
maximum structural 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:

7. Scaling of respiration
Respiration: contributions from growth and maintenance
Weight: contributions from structure and reserve
Kooijman 1986
J Theor Biol
121:

8. Metabolic rate 2 curves fitted: slope = 1 0.0226 L2 + 0.0185 L3
Log metabolic rate, w
O2 consumption, l/h
endotherms
L L3
L2.44
slope = 2/3
ectotherms
20°C
unicellulars
Length, cm
Log weight, g
Intra-species
Inter-species
(Daphnia pulex)
Data: Richman 1958; curve fitted from DEB theory
Data: Hemmingson 1969; curve fitted from DEB theory

9. poikilothermic tetrapods
Feeding rate
slope = 1
Filtration rate, l/h
Length, cm
Intra-species: JXm  V2/3
Inter-species: JXm  V
Mytilus edulis
Data: Winter 1973
poikilothermic tetrapods
Data: Farlow 1976

10. Specific O2 consumption
slope = -1/4
20°C
predicted max dry weight predicted specific O2 consumption

11. Thank you, organisors, for inviting me Thank you, audience, for your attention Any questions?
DEB course 2015 had 124 participants →
DEB course 2017 will be organized by
DEB newsletter:

12. Waste to hurry Exploiting blooming resources
Kooijman 2013
Oikos 122:
Waste to hurry
Exploiting blooming resources
requires blooming yourself
high numerical response
short life cycle
small body size
fast reproduction
fast growth
high feeding rate
resting stages between blooms
-rule explains why
[pM] needs to be high
Ecosystem significance:
flux through basis food pyramid
Waste-to-hurry is the hypothesis that species increase somatic maintenance for the purpose of boosting growth and reproduction, such that max body size remains small. This strategy is possible because of the kappa-rule.
Fast growth and reproduction is only possible if specific assimilation is large.
If that would be the only difference a very large body size results, which comes with a long life cycle.
Not fit for profiting from temporary resources.

13. No Effect Conc ↔ spec som maint
Data sources
NEC:
EPA-data base
survival data
[pM]:
add_my_pet
energetics data
Pesticides:
NEC  [pM]-2
Baas & Kooijman 2015
Ecotoxicology, 24:
Metals:
NEC  [pM]0
to be published

14. Supply-demand spectrum
Lika et al 2014
J. Theor. Biol.
354:35-47
Supply-demand spectrum
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.
metabolic control external metabolic control internal

15. Supply-demand spectrum 10.5.5
Lika et al 2014
J. Theor. Biol.
354:35-47
Supply-demand spectrum
The constraint R_m > 0 can be translated into the constraint kap^2 (1 – kap) < s_s, from which follows that s_s < 4/27.
Moreover kap must be between the two positive roots of kap^2 (1 – kap) – s_s = 0.
The metric s_d = 4/27 – s_s can be called “distance to puberty edge”, and has the interpretation of the distance to the demand-end of the supply-demand spectrum.
Most species are supply species, only vertebrates classify as demand species.
A more detailed study on the 5 fish classes shows that bony fish are supply species.
The open symbols indicate acceleration.

16. Supply-demand spectrum
Lika et al 2014
J. Theor. Biol.
354:35-47
Supply-demand spectrum
The distance to the supply end of the supply-demand spectrum, s_s, is plotted against the minimum scaled functional response that is required to reach puberty, f_min. Contrary to s_s, f_min does depend on kappa.
Only vertebrates populate the area under the curve s_s = f_min^3 4/27.
Open symbols indicate acceleration.
The value of kappa is indicated for birds (blue) and mammals (red) in the right picture.
High kappa-values for birds are close the both axes (s_s = 0 and f_min – 1).
High kappa-values for mammals are at low s_s and f_min.
All evertebrates are in the lower-left corner of the picture.