Basic deb scheme
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defecation. feeding. food. faeces. assimilation. reserve. somatic maintenance. maturity maintenance. . 1- . maturation reproduction. growth. maturity offspring. structure. Basic DEB scheme. Feeding 3.1. Feeding has two aspects

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Basic DEB scheme

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Basic DEB scheme

Feeding 3.1

  • Feeding has two aspects

  • disappearance of food (for food dynamics): JX,F

  • appearance of substrate for metabolic processing: JX,A= JX,F

  • Faeces

  • cannot come out of an animal, because it was never in it

  • is treated as a product that is linked to assimilation: JP,F= yPX JX,F

Busy periods

not only include handling

but also digestion and

other metabolic processing

Feeding 3.1

arrival events of food items

fast SU

binding prob.



slow SU

binding prob.



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, CO2)

  • 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


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, [pM] = pM/V and [EG] constant)

for some function [pC]= pC/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



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 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

for assimilation being an alternating Poisson process

hazard rates


assim = 1

assim = 0




50 h-1

10 h-1

sd specific use of reserve

10 h-1

10 h-1

10 h-1

2 h-1

SU abundance, relative to DEB value

Reserve dynamics

in starving active sludge

PHB density, mol/mol

Data from

Beun, 2001

time, h

Yield of biomass on substrate



Data from

Russel & Cook, 1995

1/spec growth rate, h-1

-rule for allocation 3.5

Ingestion 

Respiration 

Ingestion rate, 105 cells/h

O2 consumption, g/h

Length, mm

Length, mm

Length, mm

Reproduction 

Cum # of young

  • 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?


Von Bertalanffy

Age, d

Age, d

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. CO2, NH3)

  • 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 JE,C:

  •  structural volume (mosts costs), pM

  •  surface area (specific costs: heating, osmo-regulation), pT

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-)JE,C:

  •  structural volume in embryos and juveniles, pJ

  • constant in adults (even if they grow)

  • Else: size at transition depends on history of food intake

Maintenance first 3.6

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



Maitenance requirements:

6 cells.sec-1.daphnid-1



number of daphnids

max number of daphnids
























time, d

Growth 3.7


Conversion of reserve(s) into structure(s)

Energy to fuel conversion is extracted from reserve(s)

Implies: products associated with growth (e.g. CO2, NH3)

Allocation to growth:

Consequence of strong homeostasis:

Fixed conversion efficiency

Mixtures of V0 & V1 morphs 3.7.2

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

Growth 3.7

heating length

max length

maint rate coeff

en investment ratio

energy conductance

structural volume

reserve density

max res density

spec assim power

spec heating costs

spec som maint costs

spec growth costs

fraction catabolic p

Growth at constant food 3.7

length, mm

Von Bert growth rate -1, d

time, d

ultimate length, mm

Von Bertalanffy growth curve:



L. at birth

ultimate L.

von Bert growth rate

energy conductance

maint. rate coefficient

shape coefficient

Embryonic development 3.7.1

Crocodylus johnstoni,

Data from Whitehead 1987



O2 consumption, ml/h

weight, g

time, d

time, d

: scaled time

l : scaled length

e: scaled reserve density

g: energy investment ratio


Foetal development 3.7.1

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

weight, g



time, d

Data: MacDowell et al 1927

Maturation 3.8


Use of reserve(s) to increase the state of maturity

This, however, does not increase structural mass

Implies: products associated with maturation (e.g. CO2, NH3)

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 3.9.1


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. CO2, NH3)

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 3.9.1

103 eggs

103 eggs

Rana esculenta

Data Günther, 1990

Gobius paganellus

Data Miller, 1961

length, mm

length, mm

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

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