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Spatial heterogeneity in marine ecology : two examples
Jean-Christophe POGGIALE
Centre d’Océanologie de Marseille (OSU)
Laboratory of Marine Microbiology, geochemistry and Ecology (UMR 6117)
Case 901 – Campus de Luminy – 13288 Marseille Cedex 09
[email protected]
NVTB Symposium 7 Nov 2006
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Dr. David NERINI
Marie EICHINGER (PhD)
Dr. Claude MANTE
Dr. Anne-Françoise YAO
Caroline TOLLA (PhD)
Mathematical Ecology
NVTB Symposium 7 Nov 2006
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NVTB Symposium 7 Nov 2006
EXAMPLE 1EXAMPLE 1
NITROGEN CYCLE IN MARINE SEDIMENTS:
Impact of heterogeneity on degradation processes intensity
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NVTB Symposium 7 Nov 2006
Nitrogen cycle in marine sediments
Oxic sediment
Anoxic sediment
Column water
NO3
NO3
NO3
Diffusion
Diffusion
NO2 N2O N2
N2
NH4
DenitrificationAmmonification
NO2 NH4 Norg
Assimilatrice reduction
AmmonificationNitrification
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iAnoxMinin
AnoxMinin
Minéri
is
Minéri
CKO
O
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NOR
CKO
OR
ONO
i
O
i
23
2
2
2
3
3
2
2
1Dénit
OxicMin
NVTB Symposium 7 Nov 2006
Usual formulations in biogeochemical models
Reactions2
2
z
Cv
z
CD
t
C
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NVTB Symposium 7 Nov 2006
Role of bioturbation
• Bioturbation : reworking activities and displacements induced by macro – organisms in sediments
• Transport of particles, solutes and microorganisms
• Presence of oxic zones in the anoxic layer and of anoxic zones in the oxic layer (spatial heterogeneity)
• Source of temporal and spatial heterogeneity
• Permanent modifications of the micro-organisms environment (temporal heterogeneity)
How does it affect the fate of organic matter?
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NVTB Symposium 7 Nov 2006
Example of experiments
Oxic layer
Anoxic layer
N2
45 days 45 days 45 days
oxic anoxic RedOx oscillations
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Conclusions of experiments
NVTB Symposium 7 Nov 2006
• Quantification of nitrogen mineralization (organic nitrogen transformed in NH4, NO3, N2O or N2)
• Nitrogen mineralization in oxic conditions>1.6 * nitrogen mineralization in anoxic conditions
• Nitrogen mineralization in oscillating conditions>4.8 * nitrogen mineralization in oxic conditions
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NVTB Symposium 7 Nov 2006
How to proceed to understand the previous result?
• define a model which describes the degradation processes;
• couple this model with a bioturbation model which reproduces the spatial and temporal heterogeneity.
• define a model which describes the degradation processes;
• reproduce temporal variations with a periodic forcing associated to RedOx oscillations.
INTERMEDIATE PROCEDURE
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Cochran model - 1985
2
2
z
CD
t
Cb
C C C
z z z
NVTB Symposium 7 Nov 2006
Modelling bioturbation
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²xt
z
Day 0:luminophores added
(4 g; 80-150 µm)
MUC Core(diam.: 10 cm)
Sediment andfluorescent particles
macrofauna
sieving1-cm thickslicing
Day 9:
[Luminophores] = f (z,t)
Biodiffusive profiles Cochran (1985)
2CC
bD
drying+
homogeneization
Luminophore countingunder UV light
NVTB Symposium 7 Nov 2006
Quantification by luminophores technique
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z
T0:luminophores added
(2 g; 80-150 µm)
Plexiglas squared corefrom Usnel Box corer
time seriepictures
May 2001 cruise
NVTB Symposium 7 Nov 2006
Quantification with 2D-optical system
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0 18Time (h)
NVTB Symposium 7 Nov 2006
Example of images
Same kind of images for oxygen, nitrate, pH, …
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x z z
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s M h bB i
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NVTB Symposium 7 Nov 2006
Biogeochemical models
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BAC (%) POC (mmol/l) O2 (µmol/l) NO3 (µmol/l)
0 12. 20. 40. 80. 100 . 150. 200. 300. 0 0.2 0.4 1.6 3.2 6.4 10. 15. 20. 0 0.2 1. 5. 20. 40. 80. 140 . 180. 0 1.5 3. 6. 10. 15. 20. 25.
0
1 2 3 4 5 6 7 8
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2
4
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2
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2
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2
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NVTB Symposium 7 Nov 2006
Example of numerical simulations
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NVTB Symposium 7 Nov 2006
Conclusions and perspectives
• Need a more biologically relevant formulation
• Micro-organisms respond to environmental perturbations at individuals levels
• DEB theory permits to:
• take individuals level into account in population dynamics models,
• describe the role of organisms on elements cycles by using mass balance arguments,
• maintain a trade off between biological realism and required simplicity of models at the ecosystem level
• Use a DEB approach to explain how a heterogeneous environment may support higher degradation rates than homogeneous environment
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NVTB Symposium 7 Nov 2006
EXAMPLE 2EXAMPLE 2
COMPETITION IN THE COLUMN WATER:
Impact of heterogeneity on biodiversity
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NVTB Symposium 7 Nov 2006
The problem position
• Exclusion principle : no more than one species on one limiting factor in homogeneous environment, the other species are outcompete
• Plankton paradox (Hutchinson, 1961)
• Lots of explanations, a few of them are really satisfying from a theoretical point of view
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Availability of nutrients at individuals scale
NVTB Symposium 7 Nov 2006
Temporal heterogeneity induced by physics
Time (sec.)
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NVTB Symposium 7 Nov 2006
A first approximation : Oscillating conditions
Sa
SmSG
NdSGdt
dN
NdSGdt
dN
NSGNSGtbeSSDdt
dS
ii
ii
with
22222
11111
22110
iii dSG / of solution theis and i
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NVTB Symposium 7 Nov 2006
A first approximation : Oscillating conditions
m2/d2
m1/d1
sp 1 excludes sp 2
sp 2 excludes sp 1
Region of coexistence
21
Extinction
(Hsu, 1980, Smith, 1980)
H. Smith, 1997 : monospecific Droop Model
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Q
QrN
dt
dN
QQrQmSGdt
dQ
QNSGtfdt
dS
m
m
1
NVTB Symposium 7 Nov 2006
Surge uptake
Some experiments suggest that absorption rate increases with reserve at a short time scale
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Sa
SmSG
Q
QNr
dt
dN
Q
QNr
dt
dN
QQrQmSGdt
dQ
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dQ
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dS
ii
ii
m
m
m
m
with
1
1
2
2,22
2
1
1,11
1
2,222222
1,111111
222111
NVTB Symposium 7 Nov 2006
Competition in heterogeneous conditions
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22
202
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ab
NVTB Symposium 7 Nov 2006
Time scales and mathematical simplifications
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NVTB Symposium 7 Nov 2006
Competition in fluctuating food conditions
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NVTB Symposium 7 Nov 2006
Competition in fluctuating food conditions
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NVTB Symposium 7 Nov 2006
Competition in fluctuating food conditions
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NVTB Symposium 7 Nov 2006
Competition in fluctuating food conditions
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NVTB Symposium 7 Nov 2006
Competition in fluctuating food conditions
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A
T
NVTB Symposium 7 Nov 2006
Competition in fluctuating food conditions
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NVTB Symposium 7 Nov 2006
Competition in fluctuating food conditions
1
2cos
ii
ii t
TAXtX
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NVTB Symposium 7 Nov 2006
• Intermittency of food supply simulation : long range memory processes (fractional brownian processes)
• Mechanistic basis of the population dynamics model : DEB theory
CONCLUSION
• Fast response of individuals to food supply fluctuations