Dynamic Energy Budget theory

1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par values 9 Living together10 Evolution11 Evaluation

Scales of life 8a

Life span

10log aVolume

10log m3earth

whale

bacterium

water molecule

life on earth

whale

bacteriumATP molecule

30

20

10

0

-10

-20

-30

• parameter values tend to co-vary across species• parameters are either intensive or extensive• ratios of extensive parameters are intensive• maximum body 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

Inter-species body size scaling 8.2

][/}{ MAmm pκpL

}{ Amp][ Mp

mAm Lp }{

Kooijman 1986Energy budgets can explain body size scaling relationsJ. Theor. Biol. 121: 269-282

Intra - Inter-specific scaling 8.2a

intra inter

feeding L2 L3

reproduction

L2.5 L-1

Primary scaling relationships 8.2.1

assimilation {JEAm} max surface-specific assim rate Lm

feeding {Fm} surface- specific searching rate

digestion yEX yield of reserve on food

growth yVE yield of structure on reserve

mobilisation 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 maturity at birth

life cycle MHp maturity at puberty

aging ha aging acceleration

aging sG Gompertz stress coefficientmaximum length Lm = {JEAm} / [JEM]

Kooijman 1986J. Theor. Biol. 121: 269-282

Inter-species zoom factor 8.2.1a

Body weight 8.2.2

Body weight has contribution from structure and reserveif reproduction buffer is excluded

West-Brown: scaling of respiration 8.2.2b

Explanation: Minimizing of transportation costs in space-filling

fractally branching tube systems results in ¾ - “law” West et al 1997 Science 276: 122-126

Problems:• Protostomes have open circulation system, no tube system

scaling of respiration also applies to protostomes• Flux in capillaries is much less than in big tubes, not equal• Transport rate must match peak metabolic requirements

rather than standard• No differentiation between inter- and intra-specific scaling• Transport costs are tiny fraction of maintenance costs

minimum argument is not convincing (nor demonstrated) • Scaling of respiration does not explain all other scaling “laws”

nor “the growth curve” of demand systems

Banavar: scaling of respiration 8.2.2c

Explanation: Dilution of biomass with transport material between maintenance-requiring nodes in efficient networks results in ¾ -”law”; Banavar et al 1999 Nature 399: 130-132

Problems:• Transport rate must match peak metabolic requirements

rather than standard• No differentiation between inter- and intra-specific scaling• criterion• Assumption about the scaling of mass involved in transport

is not tested; tubing material does not dominate in whales• Efficiency criterion is anthropomorphic

Scaling of respiration 8.2.2d

Respiration: contributions from growth and maintenanceWeight: contributions from structure and reserve

Kooijman 1986J Theor Biol

121: 269-282

Metabolic rate 8.2.2e

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)

Data: Hemmingson 1969; curve fitted from DEB theoryData: Richman 1958; curve fitted from DEB theory

Feeding rate 8.2.2f

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

log zoom factor, z

log zoom factor, z

log zoom factor, z

log

scal

ed in

itial

res

erve

log

scal

ed a

ge a

t birt

h

log

scal

ed le

ngth

at b

irth

approximate slope at large zoom factor

Scaling relationships 8.2.2g

Length at puberty 8.2.2h

Clupea• Brevoortia° Sprattus Sardinops Sardina

Sardinella+ Engraulis* Centengraulis Stolephorus

Data from Blaxter & Hunter 1982

Clupoid fishes

Length at first reproduction Lp ultimate length L

25 °CTA = 7 kK

10log ultimate length, mm 10log ultimate length, mm

10lo

g vo

n B

ert

grow

th r

ate

, a-1

)exp()()( 3/13/13/13/1 arVVVaV Bb

3/1V

a

3/1V

3/1bV

1Br

↑

↑0

Von Bertalanffy growth rate 8.2.2i

Body temperature of Maiasaurs 8.2.2j

• determine v Bert growth rate & max length• convert length to weight (shape)• obtain v Bert growth rate for that weight at 25 °C (inter-spec)• calculate ratio with observed v Bert growth rate• convert ratio to body temperature (inverse Arrhenius)• result: 37 °C

age, a

length, cm

Incubation time 8.2.2k

10log egg weight, g 10log egg weight, g

10lo

g in

cuba

tion

time,

d

10lo

g in

cuba

tion

time,

d

lb equal° tube noses

slope = 0.25

Data from Harrison 1975

European birds

4/104

0

EaLE

Lab

m

mb

Incubation timeEgg weight

tube noses

Gestation time 8.2.2l

10log adult weight, g

10lo

g ge

stat

ion

time,

d

Data from Millar 1981

Mammals* Insectivora+ Primates Edentata Lagomorpha Rodentia Carnivora Proboscidea Hyracoidea Perissodactyla Artiodactyla

slope = 0.33

mL

396.0

weightbirth

weightadulttimegestationactualtimegestation

3/1

Kooijman 1986J Theor Biol 121: 269-282

Costs for movement 8.2.2m

slope = -1/3slope = -1/3

Walking costs:5.39 ml O2 cm-2 km-1

Swimming costs:0.65 ml O2 cm-2 km-1

Movement costs per distance V2/3

Investment in movement V included in somatic maintenanceHome range V1/3

Data: Fedak & Seeherman , 1979

Data: Beamish, 1978

Aging among species 8.2.2n

Conclusion for life span • hardly depends on max body size of ectotherms• increases with length in endotherms

slope 1/3, 1/5

Right whale

Ricklefs & Finch 1995

Abundance 8.2.3

feeding rate Vfood production constant

Abundance V-1

Data: Peters, 1983

Kooijman 1986J Theor Biol

121: 269-282

1,1 compartment model 8.3.1

Suppose andwhile

Kooijman et al 2004Chemosphere 57: 745-753

Elimination rate & partition coeff 8.3.2

log P01 log P01

log

10%

sat

urat

ion

time

1 film 2 filmdiffusivities

low

high

Transition: film 1,1-compartment model

Kooijman et al 2004Chemosphere 57: 745-753

QSARs for tox parameters 8.3.4

10lo

g N

EC

, m

M

10lo

g el

im r

ate,

d-1

10lo

g ki

ll ra

te,

mM

-1 d

-1

10log Pow 10log Pow10log Pow

Slope = -1 Slope = 1Slope = -0.5

Hazard model for survival:• one compartment kinetics• hazard rate linear in internal concentration

Alkyl benzenes in PimephalesData from Geiger et al 1990

Assumption:Each molecule has same effect

Kooijman et al 2004Chemosphere 57: 745-753

QSARs for tox parameters 8.3.4a

10lo

g N

EC

, m

M

10lo

g el

im r

ate,

d-1

10lo

g ki

ll ra

te,

mM

-1 d

-1

10log Pow 10log Pow10log Pow

Slope = -1 Slope = 1Slope = -0.5

Benzenes, alifates, phenols in PimephalesData from Mackay et al 1992,

Hawker & Connell 1985

Assumption:Each molecule has same effect

Hazard model for survival:• one compartment kinetics• hazard rate linear in internal concentration Kooijman et al 2004

Chemosphere 57: 745-753

Covariation of tox parameters 8.3.4b1

0log

NE

C, m

M

10log killing rate, mM-1 d-1

Slope = -1

PimephalesData from Gerritsen 1997 Kooijman et al 2004

Chemosphere 57: 745-753

10log Pow10log Pow

10lo

g LC

50.1

4d, M

LC50.14d of chlorinated hydrocarbons for Poecilia. Data: Könemann, 1980

QSARs for LC50’s 8.3.4c

SimilaritiesQSAR body size scaling 8.4

1-compartment model: partition coefficient (= state) is ratio between uptake and elimination rate

DEB-model: maximum length (= state) is ratio between assimilation and maintenance rate

Parameters are constant for a system, but vary between systems in a way that follows from the model structure

InteractionsQSAR body size scaling 8.4a

• uptake, elimination fluxes, food uptake surface area (intra-specifically) elimination rate length-1 (exposure time should depend on size) food uptake structural volume (inter-specifically)

• dilution by growth affects toxicokinetics max growth length2 (inter-specifically)

• elimination via reproduction: max reprod mass flux length2 (inter-specifically)

• chemical composition: reserve capacity length4 (inter-specifically) in some taxa reserve are enriched in lipids

• chemical transformation, excretion is coupled to metabolic rate metabolic rate scales between length2 and length3

• juvenile period length, abundance length-3 , pop growth rate length-1

links with risk assessment strategies

Dynamic Energy Budget theory

1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par values 9 Living together10 Evolution11 Evaluation