DEB-based body mass spectraBas Kooijman

Dept theoretical biologyVrije Universiteit Amsterdam

Bas@bio.vu.nlhttp://www.bio.vu.nl/thb/

Marseille, 2007/01/17

Body mass spectrum

M

MMMM

) ,( density mass

)( spectrum massbody

)() ,(density length

)( spectrumlength LnL

LLLL

),( length with per volume ind. # : )(),(

)()(:exist species When

2121

1

2

1

LLdLLnLLN

LnLnk

L

L

k

i i

Derive it from:

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

maximum length Lm = {JEAm} / [JEM] Kooijman 1986J. Theor. Biol. 121: 269-282

Metabolic rate 8.2.2

Log weight, g

Log metabolic rate,

w

endotherms

ectotherms

unicellulars

slope = 1

slope = 2/3

Length, cm

O2 consum

ption,

l/h

Inter-speciesIntra-species

0.0226 L2 + 0.0185 L3

0.0516 L2.44

2 curves fitted:

(Daphnia pulex)

Feeding rate 8.2.2

slope = 1

poikilothermic tetrapodsData: Farlow 1976

Inter-species: JXm VIntra-species: JXm V2/3

Mytilus edulisData: Winter 1973

Length, cm

Filt

ratio

n ra

te, l

/h

Intra - Inter-specific scaling

intra inter

feeding L2 L3

reproduction L2.5 L-1

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

Spectrum determination

b

rh

bb

B

L

L

iiLbi

iii

LLLL

LLLnLn

LLrLdt

dhLhk

dLLnLRLdt

dLn

Ldt

dLn

LLnLh

B

p

b

for )()(

)(;)(;1 :Example

)()()(

)()()(

/

1

Parameters of spectrum

P producer density

Lma mean maximum length

k number of species

hb background mortality

ll min relative prey length

lu max relative prey length

{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

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

111

;1

1 11

k

i

k

ikj

k

ikj jkj

Canonical community 9.4

Short 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)