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Lecture 2 Outline of basic theory

Lecture 2 Outline of basic theory. defecation. feeding. food. faeces. assimilation. reserve. somatic maintenance. maturity maintenance. . 1- . maturation reproduction. growth. maturity offspring. structure. Standard DEB model. Topological alternatives 11.1c.

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Lecture 2 Outline of basic theory

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  1. Lecture 2 Outline of basic theory

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

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

  7. Assimilation Definition: Conversion of substrate(s) (food, nutrients, light) into reserve(s) Transformation: food + O2 reserve + excreted products (e.g. faeces, CO2, NH3)

  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 in starving active sludge PHB density, mol/mol Data from Beun, 2001 time, h

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

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

  12. Somatic maintenance • Definition: • Collection of processes required to • maintain current amount of structure • Transformation: • reserve + O2 excreted products (e.g. CO2, NH3) • 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 + O2  excreted products (e.g. CO2, NH3) • Comprises: • maintaining defence systems (immune system)

  14. Maintenance first 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

  15. Growth Definition: Conversion of reserve(s) to structure(s) Transformation: reserve + O2 structure + excreted products (e.g. CO2, NH3) Allocation to growth: Consequence of strong homeostasis:

  16. Growth

  17. Growth at constant food length, mm Von Bert growth rate -1, d time, d ultimate length, mm 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 Weight1/3, g1/3 Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 time, h time, h Weight1/3, g1/3 Toxostoma recurvirostre Ricklefs 1968 length, mm Pleurobrachia pileus Greve 1971 time, d time, d

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

  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 + O2 reserve + excreted products (e.g. CO2, NH3) 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 103 eggs 103 eggs Rana esculenta Data Günther, 1990 Gobius paganellus Data Miller, 1961 length, mm length, mm

  26. Extremes in relative maturity at birth in mammals 2.5.2a Didelphus marsupiales (Am opossum) ♂, ♀ 0.5 + 0.5 m, 6.5 kg At birth: <2 g; ab = 8-13 d 10-12 (upto 25) young/litter, 2 litters/a 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; ab = 270 d

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

  28. Extremes in relative maturity at birth in fish 2.5.2c Mola mola (ocean sunfish) ♂,♀ 4 m, 1500 (till 2300) kg Egg: 3 1010 eggs in buffer At birth: 1.84 mm g; ab = ? d Feeds on jellfish & combjellies Latimeriachalumnae (coelacanth) ♂, ♀ 1.9 m, 90 kg Egg: 325 g At birth: 30 cm; ab = 395 d Feeds on fish

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

  30. Embryonic development 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

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

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

  33. 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.

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

  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 length l, survival S reserve density, e maturity, vH time,  time,  time,  cum. feeding,10  reprod. acceleration, q hazards, h, hH time,  time,  time, 

  41. 1E,1V isomorph 2.9D, continued scaled flux of CO2 scaled flux of H2O time,  time,  scaled flux of NH3 scaled flux of O2 time,  time, 

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

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