1. DEB-based body mass spectra
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam
Marseille, 2007/01/17

2. Body mass spectrum
Derive it from:

3. 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]

4. Metabolic rate 8.2.2 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)

5. poikilothermic tetrapods
Feeding rate 8.2.2
slope = 1
Filtration rate, l/h
Mytilus edulis
Data: Winter 1973
poikilothermic tetrapods
Data: Farlow 1976
Length, cm
Inter-species: JXm  V
Intra-species: JXm  V2/3

6. Intra -  Inter-specific scaling
feeding L2 L3
reproduction
L2.5
L-1

7. Spectrum definition
individuals follow standard DEB model in homogeneous environment
kM = kJ; no reproduction buffer
max lengths represent random trials from exponential distribution
individuals eat other individuals in length-range linked to own length
background mortality has constant hazard rate
individuals with length below threshold feed on producers (constant)
individuals with length below threshold feed on producers+consumers
with a linear preference shift between the two thresholds

8. Spectrum determination

9. Parameters of spectrum
{bP}
spec searching for producers
{bX}
spec searching for consumers lb
relative length at birth lp
relative length at puberty
[MV]
mass-volume coupling MP
mass of producer
yEX
yield of reserve on consumer
yEP
yield of reserve on producer
yVE
yield of structure on reserve 
fraction to growth + som maint R
fraction to embryo v
energy conductance kM
som maintenance rate coefficient P
producer density
Lma
mean maximum length k
number of species hb
background mortality ll
min relative prey length lu
max relative prey length

10. Trials from exponential distribution
Suppose that mean = 1, else multiply result by mean
Expected value of the i-th ordered trial from a sample of size k

11. Canonical community 9.4 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)