Download - Standard DEB model
1- maturitymaintenance
maturityoffspring
maturationreproduction
Standard DEB model
food faecesassimilation
reserve
feeding defecation
structurestructure
somaticmaintenance
growth
Feeding
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
Feeding
time
time
bind
ing
prob
.bi
ndin
g pr
ob.
fast SU
slow SU
arrival events of food items
raten associatio:rate;on dissociati:density; food:
:response functionalwith ;/
:ratefeeding
:fraction mequilibriu;)1(:SUoffractionunbounded
,*
,
*
bkXXK
XfJf
Xbk
kXbXθJ
bXk
kθbXθθkθ
dt
d
FmXFX
0
0
Busy periods not only include handling but also digestion and other metabolic processing
AssimilationDefinition:Conversion of substrate(s) (food, nutrients, light) into reserve(s)Energy to fuel conversion is extracted from substratesImplies: 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
EXAXEXAE yJyJ fixedfor,,
Assimilation
KX
Xf
JyJJfJ
VJJ
AmXEXAmEAmEAE
AEAE
responsefunctionalscaledand
}{}{fixedfor}{}{with
}{onassimilatitolinkedfluxreserve
,,,,
3/2,,
EXyEVKX food density
saturation constantstructural volumereserveyield of E on X
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 to soma: constant fraction of mobilisation rate
Reserve dynamics
time, h
PH
B d
ensi
ty,
mol
/mol
in starving active sludge
Data fromBeun, 2001
Yield of biomass on substrate
1/spec growth rate, h-1
cusStreptococ mg
glucose mg
Data fromRussel & Cook, 1995
maintenance
reserve
-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
Somatic maintenanceDefinition of maintenance (somatic and maturity):Collection of processes not associated with net productionOverall 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 maintenanceDefinition of maturity maintenance:Collection of processes required to maintain current state of maturity
Maturity maintenance costs paid from flux (1-)JE,C: • maturity• constant in adults (even if they grow)
Else: size at transition depends on history of food intake
p
MEpJE
Vκ
κjVVj
sizefixedatoccurstransitionstage
1)/,1min(If ,,
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
GrowthDefinition: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
][fixedfor][
fixedfor,,,
VVV
EVGEEVVVGVVGV
MVMM
yJyMrMjMdt
dJ
constantandwith ,,,,,, MEVMEMEMECEGE jMjJJJκJ
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
Growth
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:
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 speciesbreed on Gough and are
now threatened with extinction
Metamorphosis
The larval malphigian tubes are clearly visible in this emerging cicadaThey resemble a fractally-branching space-filling tubing system, according to Jim Brown, but judge yourself …. Java, Nov 2007
ReproductionDefinition: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 smallWe therefore need a buffer with buffer-handling rules for egg prod (no buffer required in case of placental mode)
Strong homeostasis: Fixed conversion efficiencyWeak homeostasis: Reserve density at birth equals that of motherReproduction rate: follows from maintenance + growth costs, given amounts of structure and reserve at birth
constantwith)1( ,,,, JEJECERE JJJκJ
eggpercostswith/ 00, EEJκR RER0E
Reproduction at constant food
length, mm length, mm
103
eggs
103
eggs
Gobius paganellusData Miller, 1961
Rana esculentaData Günther, 1990
Maturity & its maintenanceDEB 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) ♂ 1.7-2.1 m, 129-216 kg♀ 1.3-2.2 m, 159-204 kgAt birth: 1 m, 16.5 kg; ab = 270 d
Didelphus marsupiales (Am opossum) ♂, ♀ 0.5 + 0.5 m, 6.5 kgAt birth: <2 g; ab = 8-13 d10-12 (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 kgEgg: 12×8 cm, 550 g; ab = 63-92 d
Cuculus canorus (cuckoo) ♂,♀ 115 gEgg: 3.3 g; ab = 12 d
Extremes in relative maturity at birth in fish 2.5.2c
Latimeria chalumnae (coelacanth) ♂, ♀ 1.9 m, 90 kgEgg: 325 gAt birth: 30 cm; ab = 395 dFeeds on fish
Mola mola (ocean sunfish) ♂,♀ 4 m, 1500 (till 2300) kgEgg: 3 1010 eggs in bufferAt birth: 1.84 mm g; ab = ? dFeeds on jellfish & combjellies
Short juvenile period 2.5.2d
Hemicentetes semispinosus (streaked tenrec )
ap - ab = 35 d
Lemmus lemmus (Norway lemming ) ap - ab = 12 d
Embryonic development
time, d time, d
wei
ght,
g
O2 c
onsu
mpt
ion,
ml/h
l
ege
dτ
d
ge
legl
dτ
d
3
3,
3, l
dτ
dJlJJ GOMOO
; : scaled timel : scaled lengthe: scaled reserve densityg: 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 developmentw
eigh
t, 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 cellNutritional condition of mother only affects foetus in extreme situations
33/20 )3/()(;0)0(;:For vttVVvVV
dt
dE
Data: MacDowell et al 1927
High age at birth 2.6.2f
Sphenodon punctatus (tuatara)Adult: 45-60 cm, Wm = 0.5 – 1 kg, ♂ larger than ♀10 eggs/litter, life span 60 - >100 aBody temp 20-25 °C, ap = 20 a, Wb = 4 g, ab = 450 d.
ReproductionDefinition: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 smallWe therefore need a buffer with buffer-handling rules for egg prod (no buffer required in case of placental mode)
Strong homeostasis: Fixed conversion efficiencyWeak homeostasis: Reserve density at birth equals that of motherReproduction rate: follows from maintenance + growth costs, given amounts of structure and reserve at birth
constantwith)1( ,,,, JEJECERE JJJκJ
eggpercostswith/ 00, EEJκR RER0E
Reproduction at constant food
length, mm length, mm
103
eggs
103
eggs
Gobius paganellusData Miller, 1961
Rana esculentaData 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