Dynamic Energy Budget Theory - I
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Transcript of Dynamic Energy Budget Theory - I
Dynamic Energy Budget Theory - I
Tânia Sousa with contributions from : Bas Kooijman
Energy flows vs. Mass flows
Fluxes Parameters�̇�𝑋= �̇� 𝑋 𝐴𝑋= 𝑓 (𝑋 ) {�̇�𝑋𝑚 }𝑉 2/3
�̇�𝐴= �̇� 𝐸𝐴𝐸= 𝑓 (𝑋 ) {�̇�𝐴𝑚}𝑉 2 /3
�̇�𝑆= �̇� 𝐸𝑆𝐸= [�̇�𝑀 ]𝑉 + {�̇�𝑇 }𝑉 2/3
=�̇�𝑅= �̇� 𝐸𝑅𝐸
{�̇�𝑋𝑚 }=𝑋 { �̇� 𝑋𝑚 }{�̇�𝐴𝑚 }=𝐸 { �̇� 𝐴𝑚}
State Variables
[�̇�𝑀 ]=𝐸 [ �̇� 𝐸𝑀 ]�̇�𝐶= �̇�𝐸𝐶 𝐸=𝐸( �̇�𝐿 − �̇� ) {�̇�𝑇 }=𝐸 { �̇�𝐸𝑇 }
�̇�𝐺= �̇� 𝐸𝐺𝐸=[𝐸𝐺 ] 𝑑𝑉𝑑𝑡
[𝐸𝐺 ]=𝑦𝐸𝑉 𝐸 [𝑀𝑉 ]
What would be the expression for a parameter
that is the equivalent of for the somatic maintenance associated with volume?
Suggestions: Write as a function of
Exercises
- energy spent in the maintenance of structure built with 1 unit of reserve energy per unit time - energy spent in the maintenance of maturity built with 1 unit of reserve energy per unit time
Metabolism in a DEB
individual. Rectangles are state
variables Arrows are flows of food
JXA, reserve JEA, JEC, JEM, JET , JEG, JER, JEJ or structure JVG.
Circles are processes The full square is a fixed
allocation rule (the kappa rule)
The full circles are the priority maintenance rule.
A DEB organism Assimilation, dissipation and growth
MV - Structure
Feeding
MH - Maturity
XAJ EAJ
Assimilation
ME - ReserveMobilisation
ECJ
Offspring MER
Somatic Maintenance
Growth
Maturity Maintenance
Reproduction
Maturation
ESJ
EGJEJJ
ERJ
VGJ
Assimilation: X(substrate)+M E(reserve) +
M linked to surface area
Dissipation: E(reserve) +M M
somatic maintenance: linked to surface area & structural volume
maturity maintenance: linked to maturity maturation or reproduction overheads
Growth: E(reserve)+M V(structure) + M Compounds:
Organic compounds: V, E, X and P Mineral compounds: CO2, H2O, O2 and Nwaste
3 types of aggregated chemical transformations
�̇�𝐷=�̇�𝑆+�̇� 𝐽+(1−κ𝑅 ) �̇�𝑅
Obtain the aggregated chemical reactions for
assimilation, dissipation and growth considering that the chemical compositions are: food CH1.8O0.5N0.2, reserve CH2O0.5N0.15, faeces CH1.8O0.5N0.15, structure CH1.8O0.5N0.15 and NH3.
Identify in these equations yXE, yPE and yEV. Constraints on the yield coeficients Degrees of freedom
Exercises
What is the relationship between these
equations and , , , , , and . Compute the total consumption of O2.
Write it as a function of , and . Compute the aggregate chemical
transformation
Exercises
The stoichiometry of the aggregate chemical transformation that describes the organism has 3 degrees of freedom: any flow produced or consumed in the organism is a weighted average of any three other flows
Write the energy balance for each chemical
reactor (assimilation, dissipation and growth) Compute the total metabolic heat production
as a function of , and .
If the organism temperature is constant then the metabolic heat must be equal to the heat released
Exercises
Indirect calorimetry (estimating heat production without mesuring it) : Dissipating heat is weighted sum of three mass flows: CO2, O2 and nitrogeneous waste (Lavoisier in the XVIII century).
T EA T A EG T G ED T Dp J p J p J p
Dissipating heat
Steam from a heap of moist Prunus serotina litter illustrates metabolic heat production by fungi
Definition:
O2 consumption that is associated with assimilation per unit of ingested food
Strange name relates to common practice to take pT+ JO which generally does not hold true
Exercise: What is the relationship between O2 consumption and heat production
Heat increment of feeding
Metabolic rates: the effect of temperature
The Arrhenius relationship has good empirical support The Arrhenius temperature is given by minus the slope: the higher the Arrhenius
temperature the more sensitive organisms are to changes in temperature
ln ra
te
104 T-1, K-1
reproductionyoung/d
ingestion106 cells/h
growth, d-1
aging, d-1K 293K; 6400
}exp{)(
1
11
TTTT
TTkTk
A
AA
Daphnia magna
All metabolic rates depend on temperature and all depend on the same way (evolutionary principle)