1. 1-  maturity maintenance maturity offspring maturation reproduction Basic DEB scheme foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth 

2. Feeding 3.1 Feeding has two aspects disappearance of food (for food dynamics): J X,F appearance of substrate for metabolic processing: J X,A = J X,F Faeces cannot come out of an animal, because it was never in it is treated as a product that is linked to assimilation: J P,F = y PX J X,F

3. Feeding 3.1 time binding prob. fast SU slow SU arrival events of food items 0 0 Busy periods not only include handling but also digestion and other metabolic processing

4. Assimilation 3.3 Definition: Conversion of substrate(s) (food, nutrients, light) into reserve(s) Energy to fuel conversion is extracted from substrates Implies: products associated with assimilation (e.g. faeces, CO 2 ) Depends on: substrate availability structural (fixed part of) surface area (e.g. surface area of gut) Consequence of strong homeostasis: Fixed conversion efficiency for fixed composition of substrate However, biomass composition is not fixed many species feed on biomass

5. Assimilation 3.3 food density saturation constant structural volume reserve yield of E on X

6. Reserve dynamics 3.4 Increase: assimilation  surface area Decrease: catabolism  reserve density (= reserve/structure) First order process on the basis of densities follows from weak homeostasis of biomass = structure + reserve Mechanism: structural & local homeostasis  -rule for allocation to growth + somatic maintenance: constant fraction of catabolic rate

7. Reserve partitioning 3.4 structure, V If reserves are partitioned e.g. into lipids and non-lipids maintenance and growth are partitioned as well Partitioning requirement for catabolic power (  use of reserves, [p M ] = p M /V and [E G ] constant) for some function [p C ]= p C /V of state variables [E],V

8. Reserve dynamics 3.4 Relationship assimilation, growth and maintenance Weak homeostasis Partionability Conclusions Function H is first degree homogeneous: Function  is zero-th degree homogeneous in [E]: : So  may depend on V, but not on [E] Result reserve density max reserve density spec growth cost structural volume spec assim power assim power maint. power catabolic power fraction catabol. energy conductance scaled funct. resp. parameter vector

9. Reserve dynamics 3.4 Isomorphs V1-morphs food density reserve energy structural volume assimilation power catabolic power scaled functional response saturation constant max spec assimilation power max reserve capacity energy conductance reserve turnover rate

10. Reserve dynamics

11. reserve & structure: spatially segregated reserve mobilized at rate  surface area of reserve-structure interface rejected reserve flux returns to reserve SU-reserve complex dissociates to demand-driven maintenance supply-driven growth (synthesis of structure) abundance of SUs such that local homeostasis is achieved

12. Reserve dynamics SU abundance, relative to DEB value sd specific use of reserve for assimilation being an alternating Poisson process 10 h -1 50 h -1 2 h -1 assim = 0 assim = 1 0 1 time assimilation 10 h -1 hazard rates

13. Reserve dynamics time, h PHB density, mol/mol in starving active sludge Data from Beun, 2001

14. Yield of biomass on substrate 1/spec growth rate, h -1 Data from Russel & Cook, 1995 maintenance reserve

15.  -rule for allocation 3.5 Age, d Length, mm Cum # of young Length, mm Ingestion rate, 10 5 cells/h O 2 consumption,  g/h large part of adult budget to reproduction in daphnids puberty at 2.5 mm No change in ingest., resp., or growth Where do resources for reprod. come from? Or: What is fate of resources in juveniles? Respiration  Ingestion  Reproduction  Growth: Von Bertalanffy

16. Somatic maintenance 3.6 Definition of maintenance (somatic and maturity): Collection of processes not associated with net production Overall effect: reserve  excreted products (e.g. CO 2, NH 3 ) Somatic maintenance comprises: protein turnover (synthesis, but no net synthesis) maintaining conc gradients across membranes (proton leak) maintaining defence systems (immune system) (some) product formation (leaves, hairs, skin flakes, moults) movement (usually less than 10% of maintenance costs) Somatic maintenance costs paid from flux  J E,C :  structural volume (mosts costs), p M  surface area (specific costs: heating, osmo-regulation), p T

17. Maturity maintenance 3.6 Definition of maturity maintenance: Collection of processes required to maintain current state of maturity Main reason for consideration: making total investment into maturation independent of food intake Maturity maintenance costs paid from flux (1-  )J E,C :  maturity constant in adults (even if they grow) Else: size at transition depends on history of food intake

18. 0 number of daphnids Maintenance first 3.6 10 6 cells.day -1 300 200 100 0 1206030126 max number of daphnids 30 35 400 300 200 100 81115182124283237 time, d 30  10 6 cells.day -1 Chlorella-fed batch cultures of Daphnia magna, 20°C neonates at 0 d: 10 winter eggs at 37 d: 0, 0, 1, 3, 1, 38 Kooijman, 1985 Toxicity at population level. In: Cairns, J. (ed) Multispecies toxicity testing. Pergamon Press, New York, pp 143 - 164 Maitenance requirements: 6 cells.sec -1.daphnid -1

19. Growth 3.7 Definition: Conversion of reserve(s) into structure(s) Energy to fuel conversion is extracted from reserve(s) Implies: products associated with growth (e.g. CO 2, NH 3 ) Allocation to growth: Consequence of strong homeostasis: Fixed conversion efficiency

20. Mixtures of V0 & V1 morphs 3.7.2 volume,  m 3 hyphal length, mm time, h time, min Fusarium  = 0 Trinci 1990 Bacillus  = 0.2 Collins & Richmond 1962 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961

21. structural volume reserve density max res density spec assim power spec heating costs spec som maint costs spec growth costs fraction catabolic p Growth 3.7 heating length max length maint rate coeff en investment ratio energy conductance

22. Growth at constant food 3.7 time, dultimate length, mm length, mm time Length L. at birth ultimate L. von Bert growth rate energy conductance maint. rate coefficient shape coefficient Von Bert growth rate -1, d Von Bertalanffy growth curve:

23. Embryonic development 3.7.1 time, d weight, g O 2 consumption, ml/h ;  : scaled time l : scaled length e: scaled reserve density g: energy investment ratio Crocodylus johnstoni, Data from Whitehead 1987 yolk embryo

24. Foetal development 3.7.1 weight, g time, d Mus musculus Foetes 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 Data: MacDowell et al 1927

25. Maturation 3.8 Definition: Use of reserve(s) to increase the state of maturity This, however, does not increase structural mass Implies: products associated with maturation (e.g. CO 2, NH 3 ) Allocation to maturation in embryos and juveniles: This flux is allocated to reproduction in adults Dissipating power: with  R = 0 in embryos and juveniles Notice that power also dissipates in association with

26. Metamorphosis The larval malphigian tubes are clearly visible in this emerging cicada They resemble a fractally-branching space-filling tubing system, according to Jim Brown, but judge yourself …. Java, Nov 2007

27. Reproduction 3.9.1 Definition: Conversion of adult reserve(s) into embryonic reserve(s) Energy to fuel conversion is extracted from reserve(s) Implies: products associated with reproduction (e.g. CO 2, NH 3 ) Allocation to reproduction in adults: Allocation per time increment is infinitesimally small We therefore need a buffer with buffer-handling rules for egg prod (no buffer required in case of placental mode) Strong homeostasis: Fixed conversion efficiency Weak homeostasis: Reserve density at birth equals that of mother Reproduction rate: follows from maintenance + growth costs, given amounts of structure and reserve at birth

28. Reproduction at constant food 3.9.1 length, mm 10 3 eggs Gobius paganellus Data Miller, 1961 Rana esculenta Data Günther, 1990

29. DEBtool/animal/get_pars 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_g get_pars_h get_pars_i iget_pars_g iget_pars_h iget_pars_iget_pars_gget_pars_hget_pars_iiget_pars_giget_pars_higet_pars_i growth & reprod get_pars_r get_pars_s get_pars_t iget_pars_r iget_pars_s iget_pars_tget_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.elas_pars_gelas_pars_r Function get_pars_u converts compound parametersget_pars_u into unscaled primary parameters at abundant food. Theory in KooySous2008

30. DEBtool/animal/get_pars Theory in KooySous2008 g get_pars_  iget_pars_  r s h u s h r g red quantities depend on food level, green do not

31. General assumptions 3.10 State variables: structural body mass & reserves they do not change in composition 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)

32. Specific assumptions 3.10 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 (but some maintenance costs  surface area) Maturity maintenance  maturity Feeding rate  surface area; fixed food handling time Weak homeostasis: comp. body mass does not change at steady state Fixed fraction of catabolic energy 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