spatial heterogeneity in marine ecology : two examples

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

Dr. David NERINI

Marie EICHINGER (PhD)

Dr. Claude MANTE

Dr. Anne-Françoise YAO

Caroline TOLLA (PhD)

Mathematical Ecology



EXAMPLE 1EXAMPLE 1

NITROGEN CYCLE IN MARINE SEDIMENTS:

Impact of heterogeneity on degradation processes intensity


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

iAnoxMinin

AnoxMinin

Minéri

is

Minéri

CKO

O

KNO

NOR

CKO

OR

ONO

i

O

i

23

2

2

2

3

3

2

2

1Dénit

OxicMin


Usual formulations in biogeochemical models

Reactions2

2

z

Cv

z

CD

t

C


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?


Example of experiments

Oxic layer

Anoxic layer

N2

45 days 45 days 45 days

oxic anoxic RedOx oscillations

Conclusions of experiments


• 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


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

Cochran model - 1985

2

2

z

CD

t

Cb

C C C

z z z


Modelling bioturbation

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


Quantification by luminophores technique

z

T0:luminophores added

(2 g; 80-150 µm)

Plexiglas squared corefrom Usnel Box corer

time seriepictures

May 2001 cruise


Quantification with 2D-optical system

0 18Time (h)


Example of images

Same kind of images for oxygen, nitrate, pH, …

2 2

2 2

3 2

, 3

2

2

2

,

2

2 22 2 2

2

3

1

1

C CxC zC

O O

DenMin

s

M

it

s D Inhib

inMi

xO zO

ns M

R O R NO OC

K NO K

U C W C

CK O

R OC

K O

C C CD D

t x z x x z z

U O W OO O OD D

t x z x x z

NO

O

z

3 3

3 3

3 2

,

3 3

3 2

2

2

3

,

3

111 Denit

Ds D In

MinNit

s

NO NOxNO z

b Mh

O

i

N

R NO OC

K NO

U NO W NO NO NOD D

t x z x x

K

R OC

K OO

z z

2 2

2 2

2

2

3 2

, 3 2

2 22 2 2

2

, 2

1

1

Min

s

M

Deni

inMin

s

C CxC zC

O OxO zO

M

t

s D Inhib

R OC

K

U C W CC C CD D

t x z

R NO OC

K NO K OO

R OC

K O

x x z z

U O W OO O OD D

t x z x

B B

B

x z z

N

3 3

3 3

3 2

,

2

, 2

3

2

3 3 3 3

3

1 11

NO NOx

D Mi

NO zNO

B B

enitD

s D Inh

nNit

s Mib

xB zB

B B

U NO W NOO NO NOD

R NO OC

K N

Dt x z x x z

O K

z

B U B W B B BD D

t x z x x

R OC

O K

z z

O

2

,

3 2

, 22 3

11 Dénit

s D InBac

Min

s M h bB i

R NO O

K NO K

BB

O O

O

KC

R

K


Biogeochemical models

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

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

2 j

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

4 j

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

8 j

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

0

1 2 3 4 5 6 7 8

0

2

4

6

8

10

16 j


Example of numerical simulations


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


EXAMPLE 2EXAMPLE 2

COMPETITION IN THE COLUMN WATER:

Impact of heterogeneity on biodiversity


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

Availability of nutrients at individuals scale


Temporal heterogeneity induced by physics

Time (sec.)


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


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

Q

QrN

dt

dN

QQrQmSGdt

dQ

QNSGtfdt

dS

m

m

1


Surge uptake

Some experiments suggest that absorption rate increases with reserve at a short time scale

Sa

SmSG

Q

QNr

dt

dN

Q

QNr

dt

dN

QQrQmSGdt

dQ

QQrQmSGdt

dQ

NQSGNQSGtfdt

dS

ii

ii

m

m

m

m

with

1

1

2

2,22

2

1

1,11

1

2,222222

1,111111

222111


Competition in heterogeneous conditions

22

202

2

11

101

1

20222222

10111111

2211

1

1

NQ

Q

d

dN

NQ

Q

d

dN

QQQmSad

dQ

QQQmSad

dQ

SNaSNaId

dS

2

121

2

222

2

1

212

1

111

1

1

1

K

Nb

K

NN

dt

dN

K

Nb

K

NN

dt

dN

iii mQ

IK

0

i

jij a

ab


Time scales and mathematical simplifications


Competition in fluctuating food conditions

A

T





1

2cos

ii

ii t

TAXtX


• 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

spatial heterogeneity in marine ecology : two examples

Documents

impact of heterogeneity

n2 nitrogen mineralization

bioturbation model

marine ecology

anoxic zones

heterogeneous environment

oxic conditions1

oxic conditionshow