1. Lecture 2 Outline of basic theory

2. 1-  maturity maintenance maturity offspring maturation reproduction Standard DEB model foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth 

3. Topological alternatives 11.1c From Lika & Kooijman 2011 J. Sea Res 66: 381-391

4. Test of properties 11.1d From Lika & Kooijman 2011 J. Sea Res, 66: 381-391

5. Feeding Definition: Disappearance of food from environment Embryo’s do not feed Comprises: searching of food (stochastic) handling of food

6. Feeding 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

7. Assimilation Definition: Conversion of substrate(s) (food, nutrients, light) into reserve(s) Transformation: food + O 2  reserve + excreted products (e.g. faeces, CO 2, NH 3 )

8. Reserve dynamics & allocation Increase: assimilation  structural surface area Decrease: mobilisation  reserve-structure interface Change in reserve density  structural length -1 Reserve dynamics follows from weak homeostasis of biomass = structure + reserve  -rule for allocation of mobilised reserve to soma: constant fraction of mobilisation rate

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

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

11.  -rule for allocation 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

12. Somatic maintenance Definition: Collection of processes required to maintain current amount of structure Transformation : reserve + O 2  excreted products (e.g. CO 2, NH 3 ) Comprises: protein turnover (synthesis, but no net synthesis) maintaining conc gradients across membranes (proton leak) (some) product formation (leaves, hairs, skin flakes, moults) movement (usually less than 10% of maintenance costs)

13. Maturity maintenance Definition: Collection of processes required to maintain current state of maturity Transformation : reserve + O 2  excreted products (e.g. CO 2, NH 3 ) Comprises: maintaining defence systems (immune system)

14. 0 number of daphnids Maintenance first 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

15. Growth Definition: Conversion of reserve(s) to structure(s) Transformation : reserve + O 2  structure + excreted products (e.g. CO 2, NH 3 ) Allocation to growth: Consequence of strong homeostasis:

16. Growth

17. Growth at constant food time, d ultimate length, mm length, mm Von Bert growth rate -1, d Von Bertalanffy growth curve:

18. Mouse goes preying 2.1c On the island Gough, the house mouse Mus musculus preys on chicks of seabirds, Tristan albatross Diomedea dabbenena Atlantic petrel Pterodroma incerta The bird weights are 250  the mouse weight of 40 g, Mice typically weigh 15 g 99% of these bird species breed on Gough and are now threatened with extinction

19. Isomorphic growth 2.6c diameter,  m Weight 1/3, g 1/3 length, mm time, h time, d Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 Pleurobrachia pileus Greve 1971 Toxostoma recurvirostre Ricklefs 1968 Weight 1/3, g 1/3

20. Mixtures of V0 & V1 morphs 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. Shape changes -- growth length time V0-, V½-, V⅔-morph f = 1 f = 0.7

22. Maturation 2.5.2

23. Dissipating power 2.5.2

24. Reproduction Definition: Conversion of adult reserve(s) into excreted embryonic reserve(s) Transformation : reserve + O 2  reserve + excreted products (e.g. CO 2, NH 3 ) Involves: reproduction buffer + handling rules Allocation to reproduction in adults: 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, reserve and maturity at birth

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

26. Extremes in relative maturity at birth in mammals 2.5.2a Ommatophoca rossii (Ross Seal) ♂ 1.7-2.1 m, 129-216 kg ♀ 1.3-2.2 m, 159-204 kg At birth: 1 m, 16.5 kg; a b = 270 d Didelphus marsupiales (Am opossum) ♂, ♀ 0.5 + 0.5 m, 6.5 kg At birth: <2 g; a b = 8-13 d 10-12 (upto 25) young/litter, 2 litters/a

27. Extremes in relative maturity at birth in birds 2.5.2b Apteryx australis (kiwi) ♂ 2.2 kg; ♀ 2.8 kg Egg: 12×8 cm, 550 g; a b = 63-92 d Cuculus canorus (cuckoo) ♂,♀ 115 g Egg: 3.3 g; a b = 12 d

28. Extremes in relative maturity at birth in fish 2.5.2c Latimeria chalumnae (coelacanth) ♂, ♀ 1.9 m, 90 kg Egg: 325 g At birth: 30 cm; a b = 395 d Feeds on fish Mola mola (ocean sunfish) ♂,♀ 4 m, 1500 (till 2300) kg Egg: 3 10 10 eggs in buffer At birth: 1.84 mm g; a b = ? d Feeds on jellfish & combjellies

29. Short juvenile period 2.5.2d Hemicentetes semispinosus (streaked tenrec ) a p - a b = 35 d Lemmus lemmus (Norway lemming ) a p - a b = 12 d

30. Embryonic development 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

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

32. Foetal development weight, g time, d Mus musculus Foetus develops like egg but rate not restricted by reserve (because supply during development) 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

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

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

35. General assumptions 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 reserve Mobilised reserve fuels all other metabolic processes: somatic & maturity maintenance, growth, maturation or reproduction 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)

36. Specific assumptions Reserve density hatchling = mother at egg formation (maternal effect) 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 (weak homeostasis) Fixed fraction of mobilised reserve is spent on soma: somatic maintenance + growth (  -rule) Starving individuals: can shrink to pay somatic maintenance till some threshold can rejuvenate to pay maturity maintenance, but this increases the hazard

37. 1E,1V isomorph 2.9b All powers are cubic polynomials in l

38. 1E,1V isomorph 2.9c all quantities scaled dimensionless

39. 1E,1V isomorph 2.9C, continued

40. 1E,1V isomorph 2.9d time,  reserve density, e length l, survival S maturity, v H acceleration, q hazards, h, h H cum. feeding,10  reprod.

41. 1E,1V isomorph 2.9D, continued time,  scaled flux of CO 2 scaled flux of H 2 O scaled flux of O 2 scaled flux of NH 3

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