lecture 2 standard deb model. 1- maturity maintenance maturity offspring maturation reproduction...
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Lecture 2
Standard DEB model
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1- maturitymaintenance
maturityoffspring
maturationreproduction
Standard DEB model
food faecesassimilation
reserve
feeding defecation
structurestructure
somaticmaintenance
growth
One type of food faeces reserve structure
Isomorphy
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Topological alternatives 11.1c
From Lika & Kooijman 2011J. Sea Res 66: 381-391
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Test of properties 11.1d
From Lika & Kooijman 2011J. Sea Res, 66: 381-391
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Feeding
Definition:Disappearance of food from environmentEmbryo’s do not feedComprises:• searching of food (stochastic)• handling of food
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Feeding
time
time
bind
ing
prob
.bi
ndin
g pr
ob.
fast SU
slow SU
arrival events of food items
0
0
Busy periods not only include handling but also digestion and other metabolic processing
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AssimilationDefinition:Conversion of substrate(s) (food, nutrients, light) into reserve(s)Transformation: food + O2 reserve + excreted products (e.g. faeces, CO2, NH3)
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Reserve dynamics & allocation
Increase: assimilation structural surface areaDecrease: 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
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Reserve residence time 2.3.1b
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Reserve dynamics
time, h
PH
B d
ensi
ty,
mol
/mol
in starving active sludge
Data fromBeun, 2001
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Yield of biomass on substrate
1/spec growth rate, h-1
cusStreptococ mg
glucose mg
Data fromRussel & Cook, 1995
maintenance
reserve
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-rule for allocation
Age, d Age, d
Length, mm Length, mm
Cum
# of young
Length, m
mIngestion rate, 105
cells/h
O2 consum
ption,
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:
32 LkvL M2fL
332 )/1( pMM LkfgLkvL
)( LLrLdt
dB
Von Bertalanffy
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Somatic maintenanceDefinition:Collection of processes required to maintain current amount of structureTransformation : reserve + O2 excreted products (e.g. CO2, NH3)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)
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Maturity maintenanceDefinition:Collection of processes required to maintain current state of maturityTransformation : reserve + O2 excreted products (e.g. CO2, NH3)Comprises:• maintaining defence systems (immune system)
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0
num
ber
of d
aphn
ids
Maintenance first
106 cells.day-1
300
200
100
01206030126
max
num
ber
of d
aphn
ids
30 35
400
300
200
100
8 11 15 18 21 24 28 32 37time, d
30106 cells.day-1
Chlorella-fed batch cultures of Daphnia magna, 20°Cneonates at 0 d: 10winter 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
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GrowthDefinition:Conversion of reserve(s) to structure(s)Transformation : reserve + O2 structure + excreted products (e.g. CO2, NH3)
Allocation to growth:
Consequence of strong homeostasis:
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Growth
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Growth at constant food
time, dultimate length, mm
leng
th, m
m
Von
Ber
t gro
wth
rat
e -1, d
Von Bertalanffy growth curve:
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Isomorphic growth 2.6c
diam
eter
, m
Wei
ght1/
3 , g
1/3
leng
th, m
m
time, h time, h
time, dtime, d
Amoeba proteusPrescott 1957
Saccharomyces carlsbergensisBerg & Ljunggren 1922
Pleurobrachia pileusGreve 1971
Toxostoma recurvirostreRicklefs 1968
Wei
ght1/
3 , g
1/3
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Mixtures of V0 & V1 morphs
volu
me,
m
3vo
lum
e,
m3
volu
me,
m
3
hyph
al le
ngth
, mm
time, h time, min
time, mintime, min
Fusarium = 0Trinci 1990
Bacillus = 0.2Collins & Richmond 1962
Escherichia = 0.28Kubitschek 1990
Streptococcus = 0.6Mitchison 1961
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Maturation 2.5.2
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Dissipating power 2.5.2
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ReproductionDefinition:Conversion of adult reserve(s) into excreted embryonic reserve(s)Transformation : reserve + O2 reserve + excreted products (e.g. CO2, NH3)Involves: reproduction buffer + handling rules
Allocation to reproduction in adults:
Strong homeostasis: Fixed conversion efficiencyWeak homeostasis: Reserve density at birth equals that of motherReproduction rate: follows from maintenance + growth costs, given amounts of structure, reserve and maturity at birth
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Reproduction at constant food
length, mm length, mm
103
eggs
103
eggs
Gobius paganellusData Miller, 1961
Rana esculentaData Günther, 1990
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Embryonic development 2.6.2e
time, d time, dwei
ght,
g
O2 c
onsu
mpt
ion,
ml/h
Carettochelys insculptaData from Web et al 1986
yolk
embryo
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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)
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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
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1E,1V isomorph 2.9b
All powers are cubic polynomials in l
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1E,1V isomorph 2.9c
all quantities scaled dimensionless
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1E,1V isomorph 2.9C, continued
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1E,1V isomorph 2.9d
time, time, time,
time, time, time,
rese
rve
dens
ity,
e
leng
th l,
sur
viva
l S
mat
urit
y, v
H
acce
lera
tion
, q
haza
rds,
h, h
H
cum
. fee
ding
,10
r
epro
d.
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1E,1V isomorph 2.9D, continued
time, time,
time, time,
sca
led
flux
of C
O2
scal
ed fl
ux o
f H2O
scal
ed fl
ux o
f O2
scal
ed fl
ux o
f NH
3
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Primary DEB parameters 2.8a
time-length-energy time-length-mass