Dynamic Energy Budget Theory - I

1. DynamicEnergy Budget Theory - I Tânia Sousa withcontributionsfrom : Bas Kooijman

2. Energyflows vs. Massflows • Fluxes • Parameters = • StateVariables

3. DEB Dynamics • Thedynamicsofthestate-variables are givenby:

4. DEB Dynamics • Thedynamicsofthestate-variables are givenby:

5. Exercises • Obtain an expression for the dynamics of the reserve density mEusingtheequations for thedynamicsof MEand MVandthefollowingequations:

6. Exercises • Obtain an expression for the dynamics of the reserve density mE • Set dmE/dt=0 (weakhomeostasis). • WhatisthemaximumvalueofmE?

7. Exercises • Obtain an expression for the dynamics of the reserve density mE • Set dmE/dt=0 (weakhomeostasis). • WhatisthemaximumvalueofmE? • Can youunderstandthemeaning? • Whatisthevalue for mEin weakhomeostasis? -maximumreserve density

8. Exercises • Obtain an expression for the dynamics of the reserve density mE • Set dmE/dt=0 (weakhomeostasis). • WhatisthemaximumvalueofmE? • Can youunderstandthemeaning? • Whatisthevalue for mEin weakhomeostasis? -maximumreserve density

9. Exercises • Obtain an expression for the dynamics of the reserve density mE • Set dmE/dt=0 (weakhomeostasis). • WhatisthemaximumvalueofmE? • Can youunderstandthemeaning? • Rewrite usingmEm. -maximumreserve density

10. Exercises • Obtain an expression for the dynamics of the reserve density mE • Set dmE/dt=0 (weakhomeostasis). • WhatisthemaximumvalueofmE? • Can youunderstandthemeaning? • RewriteusingmEm. Whatisthemeaningof? -maximumreserve density

11. Exercises • Obtain an expression for the dynamics of the reserve density mE • Set dmE/dt=0 (weakhomeostasis). • WhatisthemaximumvalueofmE? • Can youunderstandthemeaning? • Rewrite usingmEm. Whatisthemeaningof? -maximumreserve density - maximumlength -maximumreserve density

12. Exercises • What wouldbetheexpression for a parameterthatistheequivalentof for thesomaticmaintenanceassociatedwith volume? • Suggestions: • Write as a functionof - energyspent in themaintenanceofstructurebuiltwith 1 unitof reserve energy per unit time - energyspent in themaintenanceofmaturitybuiltwith 1 unitof reserve energy per unit time

13. Exercises • What wouldbetheexpression for a parameterthatistheequivalentof for thesomaticmaintenanceproportional to volume? === = - energyspentper unit time inthemaintenanceofstructurethatwasbuiltwith 1 unitof reserve energy - energyspent in themaintenanceofmaturitybuiltwith 1 unitof reserve energy per unit time

14. A DEB organismAssimilation, dissipationandgrowth • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of foodJXA, reserveJEA, JEC, JEM, JET, JEG, JER, JEJor structureJVG. • Circles are processes • The full square is a fixed allocation rule (the kappa rule) • The full circles are the priority maintenance rule. Feeding ME- Reserve Mobilisation Assimilation Offspring MER MaturityMaintenance Reproduction Growth SomaticMaintenance Maturation MH - Maturity MV - Structure

15. 3 types of aggregated chemical transformations • Assimilation: X(substrate)+M  E(reserve) + M + P • 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

16. Exercises • Identify in theseequationsyXE, yPEandyEV. • Constraintsonthe yield coeficients • Degreesoffreedom

17. Exercises • Identify in theseequationsyXE, yPEandyEV. • Constraintsonthe yield coeficients • Degreesoffreedom • Obtaintheaggregatedchemicalreactions for assimilation, dissipationandgrowthconsideringthatthechemicalcompositions are: food CH1.8O0.5N0.2, reserve CH2O0.5N0.15, faeces CH1.8O0.5N0.15,structure CH1.8O0.5N0.15and NH3.

18. Exercises • Identify in theseequationsyXE, yPEandyEV. • Constraintsonthe yield coeficients • Degreesoffreedom • Obtaintheaggregatedchemicalreactions for assimilation, dissipationandgrowthconsideringthatthechemicalcompositions are: food CH1.8O0.5N0.2, reserve CH2O0.5N0.15, faeces CH1.8O0.5N0.15,structure CH1.8O0.5N0.15and NH3. • Howwouldyouobtaintheaggregatechemicaltransformation?

19. Exercises • What istherelationshipbetweentheseequationsand, ,,, , and .

20. Exercises • What istherelationshipbetweentheseequationsand, ,,, , and . • Compute the total consumptionof O2. • Writeit as a functionof, and .

21. Exercises • What istherelationshipbetweentheseequationsand, , , , , and . • Compute the total consumptionof O2. • Writeit as a functionof, and . • Thestoichiometryoftheaggregatechemicaltransformationthatdescribestheorganismhas 3 degreesoffreedom: anyflowproducedorconsumed in theorganismis a weightedaverageofanythreeotherflows

22. Exercises • Write theenergy balance for eachchemical reactor (assimilation, dissipationandgrowth)

23. Exercises • Write theenergy balance for eachchemical reactor (assimilation, dissipationandgrowth) • Compute the total metabolicheatproductionas a function of , and .

24. Exercises • Write theenergy balance for eachchemical reactor (assimilation, dissipationandgrowth) • Compute the total metabolicheatproductionas a function of , and . • Iftheorganismtemperatureisconstantthenthemetabolicheat must beequal to theheatreleased • Indirectcalorimetry (estimatingheatproductionwithoutmeasuringit): Dissipatingheatisweighted sum ofthreemassflows: CO2, O2andnitrogeneouswaste (Lavoisier in the XVIII century).

25. Dissipating heat Steam from a heap of moist Prunus serotina litter illustrates metabolic heat production by fungi