Lecture 2 Standard DEB model

1-  maturity maintenance maturity offspring maturation reproduction Standard DEB model foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth  One type of food faeces reserve structure Isomorphy

Topological alternatives 11.1c From Lika & Kooijman 2011 J. Sea Res 66:

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

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

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) 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 residence time 2.3.1b

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: 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)

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

Growth

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

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

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

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

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

Embryonic development 2.6.2e time, d weight, g O 2 consumption, ml/h Carettochelys insculpta Data from Web et al 1986 yolk embryo

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

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

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

1E,1V isomorph 2.9C, continued

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.

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

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