1. Biodiversity in the context of DEB theory
This lectures assumed that chapters 1-4 of Kooy2010 are known
Tromsø, 2017/05/11-06/02
deb.akvaplan.com/symposiuml.html

2. Contents Intro Add_my_Pet Co-variation of parameter values - Bergmann
- r-K spectra, body size-scaling, Kleiber,
- supply-demand spectra
- waste-to-hurry
- acceleration
- altricial-precocial spectra
Patterns to be understood
Outlook
3 items to discuss

3. Why AmP? Theory ↔ Applications (Jolyn’s talk)
theory is tool in natural sciences in societal context
impove tool by use
AmP
ease applications DEB by examples
database ready for applications
checking consistency of data
finding weird species
identify patterns
= ecology/evolution
= use in parameter estimation
(estimation in context)

4. Add_my_Pet Comparison on the basis of parameter values
2017/06/01

5. Scales of life Life span Volume 10log a 10log m3 earth life on earth30
Life span
10log a
Volume
10log m3
earth 20
life on earth 10
whale
whale
bacterium
ATP molecule
-10
bacterium
-20
water molecule
-30
volume-range in AmP
16 orders of magnitude

6. Bergmann 1847
Bergmann observed in 1847 that intra-taxon body weight increases towards to poles.
DEB theory explains this by the increase in differences between the seasons, where growth is synchronised with the good season, so better food conditions during growth.
Parameter values are individual-specific, with variation between individuals within a species.
Body genotypic and phenotypic factors contribute to the setting of the parameters values as is recognised by quantitative genetics.
Races can differ in parameter values and these differences are partly genetically fixed.

7. Dwarfing in Platyrrhini
Cebidae
130 g
Saimiri g
Saguinus g g g g g
3500 g
Callimico
Callitrix
Evolutionary dwarfing occurred within the Cebidae where new groups splitted off of smaller body size and larger distance to center-Amazonia.
Cebus, Saimiri and Aotus are relatively big and occur in center-Amazonia
Saguinus, Leontopithecus and Callimico split off, are smaller and occur at the border of center Amazonia
Callithrix, Mico and Cebuella followed, are even smaller and outside center Amazonia on the slopes of the Andes
This dwarfing is supposed to be related to food availability.
DEB theory suggests the same explanation for Bergmann’s rule that max body size in a taxon increases from the equator to the poles.
Bergmann’s rule does not apply here, but DEB’s explanation does.
Cebuella
Leontopithecus
MYA
Mico
Aotus
24.8
20.2
Perelman et al 2011
Plos Genetics 7, 3, e
Cebus

8. r-K spectra
MacArthur & Wilson 1967
d/dt N = r N (K – N)

9. Body size scaling Kooijman, J Theor Biol (1986) 121: 269-282 Quantity
Within
Between
Max ingestion rate
2/3 1
Max filtering rate
Saturation constant
1/3
Max assim rate
Min food density
> 1/3
Min ingestion rate
Max size
Max storage
Min storage
4/3
Starvation time
-1/3 to 1/3
Quantity
Within
Between
Abundance
-1 to -2/3 -1
Max growth rate
2/3
Respiration rate
2/3 to 1
Birth, adult size 1
Juvenile period
1/3
Egg storage
4/3
Egg water loss
Incubation time
Reprod rate
-2/3 to -1/3
Pop growth rate -
Species can be ranked in the gradient r to K strategies.
Kooijman, J Theor Biol (1986) 121:

10. Scaling of O2 consumption

11. Behind O2 scaling

12. Waste to hurry: increase [pM]
slope 1
max spec growth
ulitmate length
slope -1
slope 2
spec reprod investment

13. Acceleration sM

14. 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.

15. Supply-demand spectrum
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 “demand stress”, 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
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.

17. Supply-demand spectrum
The small deviations from the surface ss (κ,epmin) = ep3 κ2 (1−κ)
are caused by acceleration sM dependeng on food level

18. Altricial - Precocial spectra

19. Altriciality index
animals
birds
mammals
Birds stand out since they grow during a short period only,
and get offspring long after reaching ultimate weight

20. Altriciality index
The 2 altricity coefficients show little correlation,
except for the tetrapods

21. that of the density altriciality index much less so
The scatter of the absolute altriciality index increases with max struc length,
that of the density altriciality index much less so

22. Altriciality index, Actinopterygii
slope 4
slope 0 b
slope -1 b
slope 4 p p
slope 0
slope 0

23. Maturity vs κ b p

24. Energy investment vs κ
energy investment
energy outvestment

25. Ultimate length vs κ
Actinopterygii
Mammalia

26. Ultimate length vs κ κ with random permutations of Actinopterygii
Mammalia κ
with random permutations of , ,

27. Ultimate length vs [pM]