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

Feeding 3.1 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 3.1 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 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, 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 3.3 food density saturation constant structural volume reserve yield of E on X

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

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, [p M ] = p M /V and [E G ] constant) for some function [p C ]= p C /V of state variables [E],V

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

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

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

Reserve dynamics SU abundance, relative to DEB value sd specific use of reserve for assimilation being an alternating Poisson process 10 h h -1 2 h -1 assim = 0 assim = time assimilation 10 h -1 hazard rates

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 3.5 Age, d Length, mm Cum # of young Length, mm Ingestion rate, 10 5 cells/h O 2 consumption,  g/h 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? Respiration  Ingestion  Reproduction  Growth: Von Bertalanffy

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

0 number of daphnids Maintenance first 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 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. 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

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

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

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

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

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. CO 2, NH 3 ) 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

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 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)

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