Lecture 2 Outline of basic theory Standard

Lecture 2 Outline of basic theory

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

Topological alternatives 11. 1 c From Lika & Kooijman 2011 J. Sea Res 66: 381 -391

Test of properties 11. 1 d From Lika & Kooijman 2011 J. Sea Res, 66: 381 -391

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

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

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)

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

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

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

-rule for allocation Length, mm • 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 Age, d in juveniles? Length, mm Cum # of young Reproduction Ingestion rate, 105 cells/h O 2 consumption, g/h Respiration Ingestion Length, mm Growth: Von Bertalanffy Age, d

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)

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)

Maintenance first Chlorella-fed batch cultures of Daphnia magna, 20°C 300 200 neonates at 0 d: 10 Kooijman, 1985 Toxicity at population level. winter eggs at 37 d: In: Cairns, J. (ed) Multispecies toxicity testing. Pergamon Press, New York, pp 143 - 164 0, 0, 1, 38 number of daphnids 400 cells. day-1 300 200 Maitenance requirements: 6 cells. sec-1. daphnid-1 100 0 max number of daphnids 30 106 8 11 15 18 21 24 2830 32 3537 time, d 0 106 cells. day-1 6 12 30 60 120

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:

Growth

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

Mouse goes preying 2. 1 c 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

Weight 1/3, g 1/3 diameter, m Isomorphic growth 2. 6 c Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 time, h Weight 1/3, g 1/3 length, mm time, h Pleurobrachia pileus Greve 1971 Toxostoma recurvirostre Ricklefs 1968 time, d

volume, m 3 Bacillus = 0. 2 Collins & Richmond 1962 time, min Fusarium = 0 Trinci 1990 time, h volume, m 3 hyphal length, mm Mixtures of V 0 & V 1 morphs Escherichia = 0. 28 Kubitschek 1990 time, min Streptococcus = 0. 6 Mitchison 1961 time, min

Shape changes -- growth f=1 length f = 0. 7 V 0 -, V½-, V⅔-morph time

Maturation 2. 5. 2

Dissipating power 2. 5. 2

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

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

Extremes in relative maturity at birth in mammals 2. 5. 2 a 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

Extremes in relative maturity at birth in birds 2. 5. 2 b 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

Extremes in relative maturity at birth in fish 2. 5. 2 c 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 Latimeria chalumnae (coelacanth) ♂, ♀ 1. 9 m, 90 kg Egg: 325 g At birth: 30 cm; ab = 395 d Feeds on fish

Short juvenile period 2. 5. 2 d Lemmus lemmus (Norway lemming ) ap - ab = 12 d Hemicentetes semispinosus (streaked tenrec ) ap - ab = 35 d

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

Diapauze 2. 6. 2 c seeds of heather Calluna vulgaris can germinate after 100 year

weight, g 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 Mus musculus time, d Data: Mac. Dowell et al 1927

High age at birth 2. 6. 2 f 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.

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

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)

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

1 E, 1 V isomorph 2. 9 b All powers are cubic polynomials in l

1 E, 1 V isomorph 2. 9 c all quantities scaled dimensionless

1 E, 1 V isomorph 2. 9 C, continued

time, cum. feeding, 10 reprod. hazards, h, h. H acceleration, q maturity, v. H length l, survival S reserve density, e 1 E, 1 V isomorph 2. 9 d time,

scaled flux of NH 3 scaled flux of O 2 scaled flux of H 2 O scaled flux of CO 2 1 E, 1 V isomorph 2. 9 D, continued time,

Primary DEB parameters 2. 8 a time-length-energy time-length-mass