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

Feeding 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

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

Assimilation 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

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

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 to soma: constant fraction of mobilisation rate

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

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

 -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

Somatic maintenance 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

Maturity maintenance Definition of maturity maintenance: Collection of processes required to maintain current state of maturity 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

0 number of daphnids Maintenance first 10 6 cells.day max number of daphnids 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 Maitenance requirements: 6 cells.sec -1.daphnid -1

Growth 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

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

Growth

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

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

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

Reproduction 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

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

Maturity & its maintenance DEB implementation is motivated by 4 observations 1 Contrary to age, volume at birth or puberty hardly depends on food density. So stage transitions cannot be linked to age. 2 Some species continue growing after puberty. Other species, such as birds, only reproduce well after the growth period. So stage transitions cannot be linked to size. 3 Total cumulative energy investment in development at any given size of the individual depends on food density; this can be removed by allowing for maturity maintenance. 4 Ultimate reproduction rate is a continuous function of food density This demonstrates the existence of maturity maintenance.

Maintenance ratio 2.5.3b

Extremes in relative maturity at birth in mammals 2.5.2a Ommatophoca rossii (Ross Seal) ♂ m, kg ♀ m, kg At birth: 1 m, 16.5 kg; a b = 270 d Didelphus marsupiales (Am opossum) ♂, ♀ m, 6.5 kg At birth: <2 g; a b = 8-13 d (upto 25) young/litter, 2 litters/a

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 = d Cuculus canorus (cuckoo) ♂,♀ 115 g Egg: 3.3 g; a b = 12 d

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: eggs in buffer At birth: 1.84 mm g; a b = ? d Feeds on jellfish & combjellies

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

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

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

Foetal development 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

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

Reproduction 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

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

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 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)

Specific assumptions 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 & 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 Fixed fraction of mobilised reserve 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

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