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Dynamic Energy Budget theory

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 together 10 Evolution 11 Evaluation.

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Dynamic Energy Budget theory

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  1. 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 together 10 Evolution 11 Evaluation

  2. Diapauze 2.6.2c seeds of heather Calluna vulgaris can germinate after 100 year

  3. Embryonic development 2.6.2d Crocodylus johnstoni, Data from Whitehead 1987 embryo yolk O2 consumption, ml/h weight, g time, d time, d

  4. Embryonic development 2.6.2e Carettochelys insculpta Data from Web et al 1986 embryo yolk O2 consumption, ml/h weight, g time, d time, d

  5. High age at birth 2.6.2f Sphenodon punctatus (tuatara) Adult: 45-60 cm, Wm = 0.5 – 1 kg, ♂ larger than ♀ 10 eggs/litter, life span 60 - >100 a Body temp 20-25 °C, ap = 20 a, Wb = 4 g, ab = 450 d.

  6. Embryonic development 2.6.2g Salmo trutta Data from Gray 1926 yolk embryo weight, g time, d

  7. Respiration ontogeny in birds 2.6.2h ml O2 d-1 ml CO2 d-1 altricial Troglodytes aëdon precocial Gallus domesticus age, d age, d • Observations: just prior to hatching • respiration shows a plateau in precocial, not in altricial birds • pore size and frequency in egg shell is such that O2 flux has constant resistance • Conclusion: ontogeny is constrained by diffusion limitation in precocial birds (Rahn et al 1990) • DEB theory: reserve dynamics controls ontogeny (same pattern in species without shells) • Minimization of water loss causes observed constant flux resistance

  8. Effects of nutrition 2.6.2i scaled length at birth scaled age at birth scaled res density at birth scaled res density at birth scaled initial reserve scaled res density at birth

  9. Reduction of initial reserve 2.6.2j scaled maturity 1 scaled reserve 0.8 0.5 scaled age scaled age scaled struct volume scaled age

  10. Foetal development 2.6.2k Foetusses develop like eggs, but rate not restricted by reserve (because supply during development) Reserve of embryo “added” at birth Initiation of development can be delayed by implantation egg cell Nutritional condition of mother only affects foetus in extreme situations weight, g Mus musculus time, d Data: MacDowell et al 1927

  11. DEBtool/animal/initial_scaled_reserve 2.6.2l • The routine calculates the initial scaled reserve mass UE0 = ME0/ {JEAm}. • The constraint [UEb] = f [UEm] applies. • Inputs: • n-vector with scaled functional response • 5-vector with parameters • VHb, d.mm^2, scaled maturity at birth: M_H^b/ ((1 - kap) {J_EAm}) with kap is fraction allocated to soma • g, -, energy investment ratio • kJ, 1/d, maturity maintenance rate coefficient • kM, 1/d, somatic maintenance rate coefficient • v, mm/d, energy conductance • optional scalar or n-vector with initial estimates for Lb • Outputs: • n-vector with initial scaled reserve: M_E^0/ {J_EAm} • n-vector with length at birth Lb • n-vector with indicators for success (1) or failure (0) • Example of use (for Daphnia magna at 20 C): • p_Dm = [.8 .42 1.7 1.7 3.24 .012]; initial_scaled_reserve(1,p_Dm). Kooijman 2009 J Math Biol58: 377-394

  12. DEBtool/animal/get_lb 2.6.2m • Obtains scaled length at birth, given the scaled reserve density at birth. • A Newton Raphson scheme is used with Euler integration, starting from an optional initial value. • The default initial value is the exact one for maintenance ratio 1. • Consider the application of get_lb_foetus for an alternative initial value. • Comparable functions: • get_lb1 uses a Newton Raphson scheme with advanced integration (but is rather slow), • get_lb2 uses a shooting method (in one variable; and is faster than get_lb1). • Inputs • 3-vector with parameters • g: energy investment ratio • k: maintenance ratio kJ/ kM • vHb: scaled maturity at birth UHb g2 kM3/ ((1 - kap) v2) with kap: fraction of mobilised reserve allocated to soma • optional scalar with scaled reserve density at birth (default 1) • optional scalar with initial value for scaled length at birth • Outputs • scalar with scaled length at birth: lb = Lb/ Lm • indicator for success (1) or failure (0) • An example of use is given in mydata_ue0 Kooijman at al 2008 Biol Rev83: 533-525

  13. DEBtool/animal/get_tb 2.6.2n • Obtains scaled age at birth, given the scaled reserve density at birth. • Multiply the result with the somatic maintenance rate coefficient to arrive at age at birth. • Inputs • 1- (if third input is specified) or 3 -vector with parameters • g: energy investment ratio • k: maintenance ratio kJ/ kM • vHb: scaled maturity at birth UHb g2 kM3/ ((1 - kap) v2) with kap: fraction of mobilised reserve allocated to soma • optional scalar with scaled reserve density at birth (default 1) • optional scalar with scaled length at birth. • Default calls get_lb but then the first input should have 3 rather than 1 elements. • Output • scalar with scaled age at birth: taub = ab kM • An example of use is given in mydata_ue0 Kooijman at al 2008 Biol Rev83: 533-525

  14. DEBtool/animal/get_lb_foetus 2.6.2o Obtains the scaled length at birth of a foetus, which is not restricted by reserve availability. Inputs 1 or 3-vector with energy investment ratio g, see get_tb_foetus optional scalar with scaled age at birth. Default calls get_tb_foetus but then the input parameter should have 3 elements. Output scalar with scaled length at birth: lb = Lb/Lm An example of use is given in mydata_ue0_foetus Kooijman at al 2008 Biol Rev83: 533-525

  15. DEBtool/animal/get_tb_foetus 2.6.2p • Obtains scaled age at birth, given the scaled reserve density at birth. • Multiply the result with the somatic maintenance rate coefficient to arrive at age at birth. • Inputs • 3-vector with parameters • g: energy investment ratio • k: maintenance ratio kJ/ kM • vHb: scaled maturity at birth UHb g2 kM3/ ((1 - kap) v2) with kap: fraction of mobilised reserve allocated to soma • optional scalar with initial value for scaled age at birth. • Default exact value for maintenance ratio 1. • Output • scalar with scaled age at birth: taub = ab kM. • indicator for succes (1) of failure (0). • An example of use is given in mydata_ue0_foetus Kooijman at al 2008 Biol Rev83: 533-525

  16. Reproduction 2.7

  17. Vegetative propagation 2.7a Examples of vegetative propagation in mosses (Bryophytes) From: Probst, W. 1987 Biologie der Moos- und Farnpflanzen, UTB, Wiesbaden

  18. Vegetative propagation 2.7b Examples of vegetative propagation in ferns (Filicatae) From: Probst, W. 1987 Biologie der Moos- und Farnpflanzen, UTB, Wiesbaden

  19. Reproduction at constant food 2.7c 103 eggs 103 eggs Rana esculenta Data Günther, 1990 Gobius paganellus Data Miller, 1961 length, mm length, mm

  20. Gametes production 2.7d Male mammals produce sperm cells during their whole adult life, but Female mammals produce new egg cells during their late foetal period only. These egg cells still grow during a much longer period. From: Mader, S. S. 1993 Biology, WCB

  21. Appendicularia 2.7.1 Oikopleura dioica Oikopleura labradoriensis

  22. DEB parameters 2.8 • primary parameters determine • food uptake • changes of state variables (reserve, maturity, structure) • compound parameters: functions of primary parameters • composition parameters • food, reserve, structure, products (feaces, N-waste) • thermodynamic parameters • free energies (chemical potentials) • entropies • dissipating heat

  23. Primary DEB parameters 2.8a time-length-energy time-length-mass

  24. Reserve & maturity: hidden 2.8b Maturity: information, not mass or energy quantified as cumulated mass of reserve that is invested Scale reserve & maturity

  25. Primary  thermodynamic pars 2.8c • Given primary parameters: • get composition parameters • get mass fluxes (respiration) • get entropies, free energies

  26. One-sample case 2.8d

  27. Two-sample case: D. magna 20°C 2.8e Optimality of life history parameters?

  28. measured quantities  primary pars 2.8f Standard DEB model (isomorph, 1 reserve, 1 structure) reserve & maturity: hidden variables measured for 2 food levels primaryparameters

  29. DEBtool/animal/get_pars 2.8g Functions get_pars_* obtain compound DEB parameters from easy-to-observe quantities and the functions iget_pars_* do the reverse, which can be used for checking. The routines are organized as follows: get_pars iget_pars food level one several one several Constraint kJ = kM kJ != kM kJ = kM kJ = kM kJ != kM kJ = kM growth get_pars_gget_pars_hget_pars_iiget_pars_giget_pars_higet_pars_i growth & reprod get_pars_rget_pars_sget_pars_tiget_pars_riget_pars_siget_pars_t Functions for several food levels do not use age at birth data. If one food level is available, we have to make use of the assumption of stage transitions at fixed amounts of structure (k_M = k_J). If several food levels are available, we no longer need to make this assumption, but it does simplify matters considerably. Functions elas_pars_g and elas_pars_r give elasticity coefficients. Function get_pars_u converts compound parameters into unscaled primary parameters at abundant food. Kooijman at al 2008 Biol Rev83: 533-525

  30. DEBtool/animal/get_pars 2.8h g r h get_pars_ s u g r iget_pars_  h s red quantities depend on food level, green do not Kooijman at al 2008 Biol Rev83: 533-525

  31. Add_my_pet: Phyton_regius 2.8i weight, g time since birth, d Data by Bart Laarhoven

  32. General assumptions 2.9 • State variables: structural body mass & reserve & maturity • structure reserve do not change in composition; maturity is information • Food is converted into faeces • Assimilates derived from food are added to reserves, • which fuel all other metabolic processes • Three categories of processes: • Assimilation: synthesis of (embryonic) reserves • Dissipation: no synthesis of biomass • Growth: synthesis of structural body mass • Product formation: included in these processes (overheads) • Basic life stage patterns • dividers (correspond with juvenile stage) • reproducers • embryo (no feeding • initial structural body mass is negligibly small • initial amount of reserves is substantial) • juvenile (feeding, but no reproduction) • adult (feeding & male/female reproduction)

  33. Specific assumptions 2.9a • Reserve density hatchling = mother at egg formation • foetuses: embryos unrestricted by energy reserves • Stage transitions: cumulated investment in maturation > threshold • embryo  juvenile initiates feeding • juvenile  adult initiates reproduction & ceases maturation • Somatic maintenance  structure volume & maturity maintenance  maturity • (but some somatic maintenance costs  surface area) • maturity maintenance does not increase • after a given cumulated investment in maturation • Feeding rate  surface area; fixed food handling time • Body mass does not change at steady state • Fixed fraction of mobilised reserve is spent on • somatic maintenance + growth (-rule) • Starving individuals: priority to somatic maintenance • do not change reserve dynamics; continue maturation, reprod. • or change reserve dynamics; cease maturation, reprod.; do or do not shrink in structure

  34. 1E,1V isomorph 2.9b All powers are cubic polynomials in l

  35. 1E,1V isomorph 2.9c all quantities scaled dimensionless

  36. 1E,1V isomorph 2.9d length l, survival S reserve density, e maturity, vH time,  time,  time,  cum. feeding, reprod. acceleration, q hazards, h, hH time,  time,  time, 

  37. 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 together 10 Evolution 11 Evaluation

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