Basic DEB scheme

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

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

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

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, CO2) • 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 • partitionability of reserve dynamics (essential for symbioses) • 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, [pM] = pM/V and [EG] constant) for some function [pC]= pC/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 dynamics • 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 for assimilation being an alternating Poisson process hazard rates assimilation assim = 1 assim = 0 1 0 time 50 h-1 10 h-1 sd specific use of reserve 10 h-1 10 h-1 10 h-1 2 h-1 SU abundance, relative to DEB value

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

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

15. -rule for allocation 3.5 Ingestion  Respiration  Ingestion rate, 105 cells/h O2 consumption, g/h Length, mm Length, mm Length, mm Reproduction  Cum # of young • 80% 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? Growth: Von Bertalanffy Age, d Age, d

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. CO2, NH3) • 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 JE,C: •  structural volume (mosts costs), pM •  surface area (specific costs: heating, osmo-regulation), pT

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-)JE,C: •  structural volume in embryos and juveniles, pJ • constant in adults (even if they grow) • Else: size at transition depends on history of food intake

18. Maintenance first 3.6 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 30106 cells.day-1 400 Maitenance requirements: 6 cells.sec-1.daphnid-1 300 300 number of daphnids max number of daphnids 200 200 100 100 106 cells.day-1 0 0 6 12 30 60 120 8 11 15 18 21 24 28 32 35 37 30 time, d

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. CO2, NH3) Allocation to growth: Consequence of strong homeostasis: Fixed conversion efficiency

20. Mixtures of V0 & V1 morphs 3.7.2 volume, m3 hyphal length, mm Bacillus  = 0.2 Collins & Richmond 1962 Fusarium  = 0 Trinci 1990 time, min time, h volume, m3 volume, m3 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961 time, min time, min

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

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

23. Embryonic development 3.7.1 Crocodylus johnstoni, Data from Whitehead 1987 embryo yolk O2 consumption, ml/h weight, g time, d time, d : scaled time l : scaled length e: scaled reserve density g: energy investment ratio ;

24. Foetal development 3.7.1 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 weight, g Mus musculus time, d 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. CO2, NH3) 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. 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. CO2, NH3) 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

27. Reproduction at constant food 3.9.1 103 eggs 103 eggs Rana esculenta Data Günther, 1990 Gobius paganellus Data Miller, 1961 length, mm length, mm

28. 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)

29. 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 & maturity maintenance  structure volume • (but some maintenance costs  surface area) • maturity maintenance does not increase • after a given cumulated investment in maturation • Feeding rate  surface area; fixed food handling time • Partitioning of reserves should not affect dynamics • 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